Lab Packet for Chem 457 Experimental Physical Chemistry (2017)

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Lab Packet 
FOR 
CHEM 457 
Experimental 
Physical 
Chemistry 
Spring, 2017 
Instructor : Dr. Bratoljub H. Milosavljevic 
Revised: January, 2017 
Foreword 
Experimental Physical Chemistry, CHEM 457 course is designed to reinforce the 
theoretical Physical Chemistry courses with the introduction of physical chemistry 
applications in a laboratory environment. Placing abstract concepts in an experimental 
framework, physical chemistry may become more self-explanatory and more enjoyable. 
This laboratory course mainly utilizes fast kinetics, thermodynamics, electrochemistry, 
surface chemistry, and spectroscopy experiments. The topics for this course are chosen 
to improve the science and engineering students theoretical and experimental physical 
chemistry backgrounds and skills. In addition, each student will work on a special 
project to demonstrate her/his independent ability in performing literature searches, 
planning and designing the experiment, interpreting the data, communicating in written 
scientific language, by writing a paper in the format of a Physical Chemistry Journal, and 
in verbal scientific language, by presenting a poster. The synopsis of the eleven 
experiments performed in this course is given below. 
1) Dissociation of a Propionic Acid Vapor 
The equilibrium constant for the dissociation of propionic acid dimer in the vapor 
phase will be determined as a function of temperature. From this data, thermodynamic 
constants and enthalpy and entropy changes will be calculated. The change in enthalpy is 
a measure of the strength of the hydrogen bonds in the dimer. 
2) Adsorption from Solution 
An adsorption isotherm will be constructed for the adsorption of acetic acid onto 
charcoal. Using this isotherm, the surface area of the charcoal will be determined. The 
relation between adsorption and surface chemistry will be introduced. 
11 
3) The determination of thermodynamic functions of the reactions in commercial 
alkaline-manganese dioxide galvanic cell (Duracell®) 
Temperature resolved measurement of the electromotive force of AA Duracell® 
galvanic cell will be performed in order to determine the thermodynamic parameters such 
as ~rG0, ~rS0 and ~rH0 • 
4) Real Gas Behavior: Determination of the Second Virial Coefficient of C02 
The pressure vs. amount of COi relation under isochoric condition will be studied 
in order to determine departure from ideal behavior in the pressure range 0 to 10 bar. The 
data obtained will also be used to determine the second virial coefficient of C02. 
5) Nanosecond Laser Photolysis Study of Pyrene Fluorescence Quenching by r 
Anion 
Pyrene in its singlet excited state oxidizes iodide anion. The pyrene fluorescence 
decays in the presence of various iodide concentrations will be measured using pulse 
laser photolysis technique in order to determine the second order reaction constant. 
6) Modeling Stretching Modes of Common Organic Molecules with the Quantum 
Mechanical Harmonic Oscillator 
The use of the harmonic oscillator model to interpret a vibrational spectroscopy 
will be introduced. Using a refined value for the effective single-bond force constant, 
stretching mode frequencies will be estimated to within about ±10% with a simple 
calculation. 
7) Resonance Energy of Naphthalene by Oxygen Bomb Calorimetry 
The resonance energy of naphthalene will be determined by calculating its 
standard enthalpy of combustion both experimentally using bomb calorimeter and by 
using bond energies. 
lll 
8) Pyrene Excimer Formation Kinetics 
Combined steady state fluorimetry and time resolved laser photolysis 
measurements will be performed in order to explore a complex kinetic system comprising 
two parallel and two consecutive reactions, that is, to determine the kinetic rate constants 
associated with pyrene excimer formation and decay using laser photolysis. 
9) Polypropylene Phase Transitions Studied by Differential Scanning Calorimetry 
The enthalpy of melting and T g of two different polypropylene samples will be 
measured using a first class research grade instrument as an illustration of a typical 
industrial problem solved in material chemistry labs. 
10) Fluorometric Determination of the Rate Constant and Reaction Mechanism for 
Ru(bpy)32+ Phosphorescence Quenching by 02 
A Stem-Volmer plot will be constructed to find an experimental kq for the 
quenching of Ru(bpy)32+ by oxygen The fundamental principles of fluorescence 
measurements as well as quenching mechanisms will be covered. 
11) Determining the Spin-Lattice Relaxation (Tt) of 1-Hexanol using 13C-NMR 
The spin-lattice times (T1) of each C atom of n-hexanol will be determined by using 
NMR spectroscopy. The inversion recovery method will be utilized to obtain T1 times of 
C atoms of n-hexanol. The observed times will be related to atomic motion of C 
J 
lV 
Table of Contents 
I. Preliminaries 
1. Forward . .. ..... ................ ............. ........... ....... ..... .. ............. . .... . 
2. Table of Contents............................ .. . ...... ..... ............. . .. ...... .. ... 1v 
3. General Information.. .... .. ....... ............. .... .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v111 
II. The Experiments 
1. Dissociation of a Propionic Acid Vapor 
Objectives................ ..................... ... .... ....... .. . ........................ 1-1 
Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1 
Laboratory Procedure.. . .. .. ............... .......................................... 1-5 
In Lab Questions.. .. ............. ...... ... ... .... .. .... . .. ..... . ..... .... .. . ......... 1-12 
Data Analysis.......... ..... .... . ....... ..... .. .. .. .. ..... .. ......... . . .. ... .......... 1-13 
Report Questions............. .. ..... ................. ... .. .. .... .... ... ..... ...... ... 1-15 
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15 
2. Adsorption from Solution 
Objectives... . .................... ... .. .. .... . ....... .. ........ ...... . ........ ..... ..... 2-1 
Introduction..... .. . .................. .. ..... ... ............ ......... .. .... ... .... . .. ... 2-1 
Laboratory Procedure... . ........ .......... .... ... .... .................. .............. 2-4 
In Lab Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6 
Data Analysis........ .. .... . ........... . ........... ..... ... . .. ............. .... .. ..... . 2-6 
Report Questions............................. . .. .. ........... ....... ...... .. ....... ... 2-9 
References.. ........... ..... ... ...... ..... . ....... . ... ... ... .. .. ..... .. .. . .. .... . ....... 2-9 
3. The determination of thermodynamic functions of the reactions in 
commercial alkaline-manganese dioxide galvanic cell (Duracell®) 
Objectives........................ ......... ............ ................... . .. ........... 3-1 
Introduction.... .............. .. ..... .... .................. ... ....... .... .... . .... .. .. .. 3-1 
Laboratory Procedure.. ........ .. ... .............. ... ................ .... ... .. ........ 3-2 
Data Analysis..... . .............. . ........ ....... ..................................... 3-4 
References.. .... ................... ... ................................................. 3-5 
4. Real Gas Behavior: Determination of the Second Virial Coefficient of 
C02 
Objectives..... ... ...... ................. ..... ........ .. .. ... ..... .. ..... ............... 4-1 
Introduction .... ................................. .. .. ...... :.................... ........ 4-1 
Laboratory Procedure...................................... . .. .... ... .... . ............ 4-4 
Data Analysis........ .. .. ..................... .......... . .............. .... .. . ......... 4-6 
Report Questions................... .. ... .. ................................. . .......... 4-7 
References........... . .............. ... . ..................................... . .......... 4-7 
5. Nanosecond Laser Photolysis Study of Pyrene Fluorescence Quenching 
by 1- Anion 
Objectives....... .......... ... ....................... .. ........ ... ......... ............ . 5-1 
Introduction.... .... .. .. ............... ..... . ....... ...... .......... ...... ........ ...... 5-1 
Laboratory Procedure.... . ................... ............. ... ... .. ... .. ..... .... ...... 5-5 
Data Analysis... ............. .. ......................................... .. .......... ... 5-7 
v 
6. Modeling Stretching Modes of Common Organic Molecules with the 
Quantum Mechanical Harmonic Oscillator (QMHO) 
Objectives..... ........... ..... ... ........ ....... ... .. ............. ... . ...... ..... .. . 6-1 
Introduction................ ............. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6-1 
Vl 
Laboratory Procedure.. . ....... ... .. .... ..... .. .. .... .. ... . ............ . ..... .. ..... 6-10 
In Lab Questions... ... .... .... . ........ . ........... . .................... ........ .. .. 6-13 
Data Analysis.................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-14 
Report Questions.............. .. ...................... . ....... . ................ ..... 6-15 
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-16 
7. Resonance Energy of Naphthalene by Bomb Calorimetry 
Objectives...... . .. .. .................... .... . .................................. ... . .... 7-1 
Introduction...... . ... .. . .... . ........... .. .... . ............ ... ................ ..... ... 7-1 
Laboratory Procedure......... .. ...... . ....... . .. ... ... ... ..... . ... ........ .... ... . .. 7-11 
In Lab Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 -1 7 
Data Analysis......... ................ . ..... .. .... ... .. . .. .... . ... .................... 7-18 
Report Questions......................... ...... .. .. ........ ... ...... .. ..... .......... 7-22 
References .. ... ................... ... ... ........ . .. .. .. ........ ... ......... . ...... .. .. 7-22 
8. Pyrene Excimer Formation Kinetics 
Objectives. .... . ....... ...... .... ... ..... ....... .. . ..... ... .. ..... .... ................ .. 8-1 
Introduction............. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-1 
Laboratory Procedure............. . ............... . ........ ........................... 8-3 
Data Analysis........ .......... . .......................... . .......... . .... ... .... ... ... 8-5 
References.............................. ...... .... . .. ........ ... .... .. . .... . ............ 8-8 
9. Polypropylene Phase Transitions Studied by Differential Scanning 
Calorimetry 
vu 
Objectives..... ..... .. ...... ...... ... ...... .. ...... .. .. .... ... .......... .. .............. 9-1 
Introduction........... .. ...... ........... .... .... . .......... ... ... .................... 9-2 
Laboratory Procedure....... .... .... ... . ... ... . ........................... ... ..... ... 9-3 
Data Analysis... . ........ ......................... .. ... ... ............. .. ..... ...... .. 9-5 
References.............................. .... ..... ........................ .. ........ . ... 9-5 
10. Fluorimetric Determination of the Rate Constant and Reaction 
Mechanism for Ru(bpy)32+ Phosphorescence Quenching by 02 
Objectives........... . .... ... ..... . .. ... .......... .. .... ................... . .... .. ...... 10-1 
Introduction........ .. .... . .................... . ....................... .......... ... .. .. 10-1 
Laboratory Procedure. .. .... .............. .. . .. ............ . ............. .. ........... 10-8 
In Lab Questions... ... .. . ... ............. .. .... ...... ...... ...... ..... .. ... .... .. .. ... 10-9 
Data Analysis............... .. ... ......... ... ............. .. .. .............. .... ....... 10-10 
Report Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1 0 
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-10 
11. Determining the Spin-Lattice Relaxation (Ti) of 1-Hexanol using 
13C-NMR 
Objectives.. ........ . ... .... ... ... ... . .... ..... ... .. .... ..... .. .... .. .. ... ...... ........ 11-1 
Introduction................... .......... ..... ............ .... .... . ..... ....... . . ... .... 11-1 
Laboratory Procedure.......... ... . . .. .... .. ................. .................. ....... 11-8 
In Lab Questions... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-18 
Data Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-19 
Report Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-19 
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-19 
Vlll 
3. General Information 
Instructor: Dr. Bratoljub H. Milosavljevic 
331C Whitmore, 865-7481, bhml l@Qsu.edu 
Office Hours: As announced in class and by appointment 
Prerequisite: CHEM450 
Materials Needed 
1) CHEM 457 Lab Packet. 
2) Lab notebook with alternate tear-out carbonless copy pages. 
3) A flash drive. 
4) Approved safety gogg]es. 
Eye Protection 
There are three types of eye protection acceptable for use in the Penn State 
Undergraduate Chemistry Labs. You MUST wear one of these models in the laboratory 
AT ALL TIMES! 
1) Safety Glasses: Comfortable and offer better peripheral vision compared to gogg]es. 
However, they offer less protection than goggles. The bookstore has Panaspec Plus 
(Bouton). 
2) Visor goggles: Reasonably comfortable, good splash protection, better peripheral 
vision than goggles. The Penn State Bookstore carries, Visorgogs (Jones and 
Company). 
3) Goggles: The highest level of splash protection. However, fog may build up and 
limit peripheral vision. There are four different kinds of goggles available at the Penn 
State Bookstore. 
Course Requirements 
You need to complete eight experiments, and a special project to fulfill the 
requirements of this laboratory course. A student should submit the following for each 
lX 
experiment: a pre-lab quiz (before the start of the lab), and in lab questions (when 
applicable) and the data collected (after the completion of the lab). Eight experiments are 
required to be written in full lab report format (in the format of a Journal of Physical 
Chemistry paper). Special projects are to be reported by a full lab report, a PowerPoint 
presentation, and a poster presentation. Only the special project report, PowerPoint 
presentation, and poster presentation will be submitted per group and all the remaining 
will be submitted individually. 
During the experiments students will be working collaboratively in the groups of 
2 or 4. In the data analysis and lab report preparation,students may study with their 
group members; however, when submitting the lab reports and uncertainty assignments, 
each student must present his/her own original individual work. 
What is Needed for Each Experiment? 
Pre-Lab Quiz (10 points): 
Each Pre-Lab Quiz will be posted on the ANGEL Course Management system and must 
be completed and turned in before the start of the lab session. 
In-Lab and Report Questions (when applicable): 
Number the answers including subdivision that may exist. If the question has parts (a) 
and (b ), the answers should not be together but labeled and answered separately. In lab 
questions must be handed to your TA or the instructor at the end of the experiment, 
before leaving the lab, otherwise they will not be accepted. 
Data Collected: 
Hand in a copy of the primary data collected during the experiment to the TA BEFORE 
leaving the lab on the day the experiment is performed. These data will consist of entries 
you made in your lab notebook and any printouts of data you have. 
Data Analysis: 
Special instructions of the data analysis should be followed as given in the manual. 
x 
Full or Short Lab Reports: 
Full formal laboratory reports will be submitted to your TA or instructor the week 
following the completion of the laboratory experiment. Your lab report will be in the 
format of a journal paper. Although students work in groups, in this laboratory work, the 
reports must be prepared individually. Reports must demonstrate your own 
understanding of the scientific work. You may not paraphrase or use other students' 
reports in the preparation of your own reports. Otherwise actions will be taken due to 
academic dishonesty. Furthermore, data analysis will be used in the preparation of the 
lab report. An electronic copy of each laboratory report will be submitted in the 
appropriate drop-box on the ANGEL Course Management system to check reports for 
possible plagiarism. 
Supplementary Information to Lab Reports: 
Lab reports must be accompanied by the supplementary documents of the related 
experiment: sample calculations and uncertainty analysis. 
1-1 
Dissociation of a Propionic Acid Vapor 
Objectives 
• To determine the equilibrium constant for the dissociation of propionic acid dimer 
as a f'Unction of temperature. 
• To calculate the enthalpy of dissociation by collecting pressure - temperature 
data. 
• To calculate the entropy and the free energy changes for the dissociation process. 
• To relate the experimental enthalpy of dissociation to the strength of hydrogen 
bonds. 
1. Introduction 
When low molecular weight carboxylic acids vaporize, they go into the gas phase 
as a mixture of dimers and monomers. The dimers form as a consequence of hydrogen 
bonding and have a structure roughly similar to that shown in Figure 1. 
H H H H H H H I I o----H-o I I I I o--
~ "\. ---2 / H-c-c-c c-c-c-H --- x H-c-c- c 
I I "o-H----cf I I I I ~ 
H H H H H H 
Figure 1. The dissociation of dimers of propionic acid vapor 
In this experiment the gas pressure of a fixed amount of vaporized_propionic acid 
is measured as its temperature is raised. From these data, the equilibrium constant for the 
dissociation of acid vapor dimers into monomers is calculated. The enthalpy change 
(Aff0) fo r the dissociation process is determined from the slope of the best-fit line in a 
plot of the natural log of the equilibrium constant against the reciprocal temperature. The 
magnitude of Aff0 can be considered a measure of the strength of the hydrogen bonds in 
1-2 
the dimer since hydrogen bonds hold the acid vapor monomers in the dimer form, as 
suggested in Figure 1. The entropy (~S0) and free energy (~G0) of the acid dissociation 
can be calculated from the calculated Aff0 . 
Theoretical Background 
By measuring the total pressure (at a known temperature and volume) of a known 
mass of a volatile carboxylic acid, the equilibrium constant for the gas phase dissociation 
of the acid dimers into monomers can be obtained. If the entire vapor were in its 
monomer form, the total pressure would be rnice of what it would be if the entire vapor 
were in its dimer form. If some of the vapor were monomer, and some dimer, the total 
pressure would be somewhere in between. A measurement of the pressure can be 
converted to relative amounts of dimer and monomer. From this the equilibrium constant 
can be determined. Any homogeneous gas phase dissociation equilibrium can be written 
as in Eq. (1). 
D !+ 2M (1) 
Under low pressure conditions where all species behave ideally, the equilibrium constant, 
Kp, can be expressed in terms of pressures by: 
( (~ )' 
K, ~ ( ; ) 
(2) 
where PM and Pn are the partial pressures of the monomer and dimer and P0 is the 
pressure of the standard state. P0 = 1.0 atm (see physical chemistry textbook for a 
discussion of the choice of units and standard states). 
Allowing a (a number between 0 and 1) to represent the degree of dissociation 
of the dimer, PM can be expressed as: 
p =(~)p 
M I+a (3) 
1-3 
where (~) represents the mole fraction of monomers, since two monomers (2a.) are 
l+a 
produced from each dimer dissociation. As each dimer dissociates, there is a net increase 
of one particle which results in the total number of particles present in the system being 
(1 +a). Pis the total pressure of the gas mixture. Similarly, Po can be expressed as: 
p = (~)p 
D l+a (4) 
where, --(1-a) l + a represents the mole fraction of dimers, since (1-a.) indicates that one 
dimer is lost for each dissociation and there is a net increase of one particle (1 +a.) for the 
total number of particles in the system, as each dissociation occurs. By substituting Eqs. 
(3) and (4) into Eq. (2) the following for Kp expression is obtained: 
K = (~JP 
P l-a2 f 5) 
At equilibrium, because number of moles of dimer (no}, bulb volume (V), temperature 
(T), and pressure (P) are known, the total number of moles of gas molecules, no(l +a.) is 
given by 
PV 
n0 (l+a)= -
RT 
Stated in slightly different terms, this relationship is: 
p 
l+a = -
Pi 
{6) 
(7) 
where, ,Pi is the pressure that would be observed if there were no dissociation.• Pi can be 
calculated using the following equation: 
P = n0 RT =( gR Jr 
I v (A1W)V) 
(8) 
where, g is the mass of the carboxylic acid vaporized and MW is the molecular mass of 
the carboxylic acid dimer. By substituting Eq. (7) into Eq. (5) and Eq. (9), Kp for the 
dissociation of carboxylic acid dimers is obtained from the experimental pressures at the 
measured temperatures, volume and mass of vapor. 
1-4 
K = 4(P-P;'j 
P 2P-P 
I 
(9) 
All quantities on the right-hand side of the equation are determined from the 
experimental data. The value of Kp depends on the pressure units. (Express the pressure 
units in atm.) 
Based on Kp and its temperature dependence, standard thermodynamic quantities 
can be readily obtained using the following thermodynamic relationships. 
Mi° -d(lnKP) 
--= 
R d(I I T) 
thlo = '3Ho -11G o) 
T 
(10) 
(11) 
(12) 
where, .AG0 , .AH0 and .AS0 are the standard free energy, enthalpy and entropy for the 
dissociation of the carboxylic acid dimers. Temperature (K) corresponds to Kp. Note 
that the right-hand side of Eq. (11) is the negative slope of a plot ofln Kp versus lff. 
The experimental value of entropy, L).S0 , can be compared with the theoretical 
prediction using Sackur-Tetrode equation for entropy. In this approach only 
translational part of entropy is calculated. 
!hl0sackur- Tetrode = 2S,w - SD 
!13) 
where, Srvds the entropy of the monomer and SD is the entropy of the dimer. 
S = 2.303{- log P + ~log T + ~ log(M)-0.5053} 
R 2 2 
(14) 
In Eq. (14), Pis in atm, Tis in K, and Mis the molecular mass of the species (monomer 
- ' 
or dimer) in g mo1-1• When calculating S0 , pressure is in 1 atm and temperature is 25.0°C 
1-5 
(see your physical chemistry textbook for a discussion ofthe Sackur-Tetrode equation 
and for further explanation of its derivation and usage). 
2. Laboratory Procedure 
In this experiment, a known amount of propionic acid will be expanded into a 
known volume of an evacuated glass bulb. The bulb is attached to a capacitance 
manometer and enclosed in an oven to measure the pressure change while raising the 
temperature in. increments of 3-5°C from approximately 20°C to 70°C. rThe temperature 
will be measured using a thermocouple in conjunction with a digital multimeter. 
Capacitance manometer, measures the pressure, has a transducer and a digital readout 
outside the ovefil Figures 2 and 3 show the experimental setup. 
Before filling the bulb with the propionic acid vapor, all the gaseous molecules 
,-
from the system must be removed under vacuum. Figure 2 shows a series of valves and 
glass lines that are used to carry out the evacuation of the system and for theiintro-~uction 
of the acid vapor into the bulb. 
To the oven -7 
~To vacuum le 
Figure 2. Vacuum line of the acid dissociation apparatus. 
1-6 
CAUTION: The vacuum system is made of glass and is fragile. If not properly 
handled, it could implode or explode and send glass flying throughout the laboratory. 
GOGGLES MUST BE WORN AT ALL TIMES DURING THE EXPERIMENT!! 
Please become familiar with the valves and the fragile components of the vacuum line in 
order to work efficiently and safely. When turning valves and stopcocks, use two bands 
to avoid applying torsion on the glass tubing. Do not overly tighten the stopcocks 
that are hard to close or unscrew them very far to open. Ask a TA or instructor to show 
you how the o-ring seals operate. The o-rings have to be replaced quite often due to the 
corrosive nature of the acid vapor in the system. 
Gas line 
Gross adjust oven 
temperature knob 
Fine adjust oven 
temperature knob 
Figure 3. Oven part of the acid dissociation apparatus. 
1. Fill large Dewar flask with liquid nitrogen. This flask will be fit around the vacuum 
trap at step #7. 
CAUTION: Do NOT put your hands into the liquid nitrogen. Liquid nitrogen boils 
at 77K; and can freeze tissue quickly and painfully. Ask for help from your TA or 
instructor to get this for you. 
1-7 
2. Check the acid sample container; it should be at least half full and all o-rings 
should be in good condition. Have a TA or instructor demonstrate the proper 
method for the turning off the valves. 
3. Close valve A that vents to the room. If valve A is left open for approximately 20 
minutes after liquid nitrogen is placed around the trap, air will begin to liquefy in 
the trap which could lead to a potentially dangerous situation when the vacuum 
pump is turned on and the liquefied air is vaporized. Another reason for having 
valve A closed is to prevent sample distribution into the air in the room. Also close 
valve D. 
4. Carefully place the large Dewar of liquid nitrogen around the vacuum trap and 
firmly clamp the Dewar into position. Wear the blue cryo gloves when doing this 
or have the TA do it for you. 
5. Start the vacuum pump by pushing on the toggle switch on the cord. 
6. Open valves B, C, and E, if they are not already open. Notice an almost immediate 
drop of pressure. If there is no sudden drop in the pressure, check if valve A is 
completely closed. Allow the system to fully evacuate for 5-10 min. While waiting 
for the full evacuation move to step #10. Later on, this step will be called the 
residual pressure step and the pressure value will be recorded. 
7. WhHe waiting for the evacuation to take place, cool the sample by carefully placing 
the small Dewar containing the ice-water bath prepared in step #4 around the 
sample container. Clamp the Dewar securely into place. This step is to cool down 
the sample to avoid pumping away too much vapor during outgassing. 
8. When the pressure reading is between 0.60 and 0.40 torr, close valve E (***do 
not over tighten metal valve E doing so will damage the valve and cause a leak in 
the vacuum system). This pressure reading will be recorded and called the initial 
residual pressure. 
1-8 
9. When the sample is cold, open valve D and pump on the sample for approximately 
1 to 1.5 min to completely outgas the sample. Outgassing purifies the sample from 
any air dissolved in the acid or in the sample container environment. 
10. Close valve D and remove the ice-water bath. Place the ice water Dewar on the lab 
bench and place the thermocouple reference wire into it, as you will soon be 
recording temperatures. 
11. Close valve C and with a kimwipe, remove the acid container from the vacuum 
line. Kimwipes prevent fingerprints on the sample container, as fingerprints will 
affect the mass. Set the container on the lab bench in a manner so that the acid 
inside does not touch the valve. Refer to Figure 4 and let sample container warm 
to room temperature. Once room temperature is reached, place a small square 
piece of plywood on the balance and weigh it, then place the acid container on the 
plywood and record the weight. Since accurate mass determinations are crucial to 
the success of this experiment, be consistent in weighing measurements. 
Figure 4. Proper placement of an acid container on a plastic weight tray as it warms up 
to room temperature to be weighed. 
15. The thermocouple reference wires are already in the small Dewar containing ice-
water mixture and connected the leads to the voltmeter. Compare the reading on the 
voltmeter and the thermometer, which is on the top of the oven. Voltmeter and 
thermometer readings should be in close agreement, if not seek the assistance of a 
TA or the instructor. 
1-9 
16. Reattach the sample container to the vacuum line. The volume between valves C 
and D must be evacuated before the sample can be admitted into the system. 
Therefore, open valve C and pump for 1-2 min. Do not open valve D at this time. 
17. Check the pressure reading, it may have slightly increased. Record this pressure as 
the current residual pressure. If the pressure is above 0.40 torr, open valve E 
and allow the bulb to pump down to a pressure between 0.40 and 0.20 torr. 
Record this as the final residual pressure. 
18. Open valve E (if it hasn't been opened in step # 17). 
19. You are now ready to expand the sample into the bulb in the oven (volume of the 
bulb is 3.4 L ± 0.1 L). Close valve B and open valve D and allow the pressure to 
reach 2.85 to 3.35 torr, such that the subtraction of the residual pressure gives a net 
pressure of at least 2.25 to 2.75 torr. Do not fill the bulb to greater than 3.35 torr. 
Pressure change should start almost immediately. If not inform a TA. It will take 
approximately 10 minutes to fill the bulb to the prescribed pressure. Do not fill the bulb 
for any longer than 15-20 min even if you have not reached a net pressure of2.25 torr. If 
time needed to reach pressure is too short inform TA, you may have leak in the system. 
20. Once the desired pressure is achieved, isolate the sample (which is propionic acid 
vapor) in the bulb by closing valve E. 
21. Since only the mass of the gas in the sample bulb is of interest, the remaining 
vapor must be condensed back into the sample container. Therefore, place a 
small Dewar containing liquid nitrogen (filled by the TA) around the acid sample 
container and allow the vapor in the line to condense back into the sample container 
for 2 to Smin. 
22. Close valves C and D. Remove the liquid nitrogen, and allow the acid container to 
return to room temperature (since this procedure takes several minutes, continue 
onto the next step and come back to this step when room temperature is reached). 
Once room temperature is attained, re-weigh the sample container and record the 
weight. The difference between this and the initial weight gives the mass of the 
propionic acid in the sample bulb. 
1-10 
NOTE: An accurate measurement ofthe weight difference is crucial to the success of 
this experiment. A weight difference in the range of 0.070 - 0.091 g must be otherwise 
consult with your TA BEFORE continuing. 
23. Begin taking readings while waiting for the acid sample to warm up. Record the 
temperature and corresponding pressure readings at this time. This will be the 
initial set of data points. 
24. Now, close the oven door. Set the left-hand dial (gross adjust oven temperature 
knob) to low by turning it counter-clockwise. This will turn on a red light. Tum the 
right-hand dial (fine adjust oven temperature knob) clockwise, until the lower 
orange light just comes on. This should cause the temperature to rise at a slow 
enough rate that accurate readings can be taken. When the orange lights goes off, 
the right-hand dial should be turned just far enough to bring the orange light back on 
again. Using this method of heating, temperature readings should be taken at 
approximately every 3°C with the corresponding pressure readings. It is 
suggested that one person read the pressure and temperature readings while the 
other records them. In this way, the most accurate data sets will be obtained. 
The uncertainty of the pressure reading is AP = ±o.20%. 
A sample data/results table may look like this: 
T, 'C I P, mm Hg I P, atm I P;, atm I 
Determine 1) Pin atm., 2) Pi, and 3) Kp to answer one of the in-lab questions. 
BEFORE leaving lab: 
The conversion between the P in mm Hg or torr to P in atm. is: 
p 
P(atm) = mmHg 
760 {15) 
1-11 
Refer to the introduction to obtain the equations needed to calculate Pi and Kp. Use an 
Excel spreadsheet to do these calculations; though you should do one set by hand so that 
you are sure you have the formulas put into the spreadsheet correctly. 
25. Continue taking readings at 3°C increments up to approximately 70°C. This 
process will take approximately one hour. 
26. Whlle waiting for the temperature to change during the experiment, calculate the Kp 
values for the previous set of readings. (You may do this on a spare computer using 
an Excel spreadsheet.) The Kp values should be 0 ~ Kp ~ 1 and should increase or 
decrease in a regular pattern. 
NOTE: Have the second mass of your sample before calculating Kp. 
You may find that some values ofKp are negative (due to the denominator in Eq. (9) 
being negative). If this happens with only one or two of the high temperature points and 
the others seem reasonable you may ignore this. If it happens with any of your first few 
points, stop and get help. 
27. Once you have collected 7-10 good data points (the more, the better), shut off the 
. oven at the dials and open the oven door. In order to get a good idea of the quality 
of the data points, plot a graph of In Kp versus lff, K-1. Generally the slope of the 
best-fit line should be - 7000 to - 15000 with a fairly high R2 value. 
28. Pump the propionic acid from the bulb by opening valves B and E. (Be careful! 
Valve E may be HOT! ) 
29. Leave the liquid nitrogen in the Dewars for the next lab group, unless you are the 
last lab group for the day. Pour the ice water down the drain and dry out this Dewar 
for the next lab group that will use it. 
30. Tum in your in lab questions BEFORE leaving the lab. Also be sure your lab area 
is neat and clean before leaving the lab. 
1-12 
3. In Lab Questions 
1. Explain why the total pressure of a given sample of propionic acid completely in its 
dimer form would be half the total pressure if the same sample were completely in its 
monomer form. 
2. Explain why it is important to let the propionic acid sample warm up to room 
temperature before weighing it. You should be as thorough as possible in answering 
this question. 
3. Think about what is going on at the molecular level as the prop ionic acid dimers 
dissociate. What sign do you expect LiH0 to have? Do you expect the magnitude of 
ll.H0 to be relatively large or small compared to ll.H0 for the combustion of propionic 
acid? What sign do you expect ll.S0 to have? Give reasons for all your answers. 
4. Prepare a table for collecting the data and tabulating your results similar to that shown 
in Step 24 of the procedure. Be prepared to hand in a table of your calculated 
values of Kp BEFORE leaving the lab. 
4. Data Analysis 
1. Carry out the calculations needed to complete the table shown in Step 24 of the 
procedure. Calculate the corresponding uncertainties for each result as you proceed 
through the calculations and report these uncertainties along with the tabulated 
calculated results. It is best to put the uncertainties in their own columns in a 
spreadsheet for ease of calculations. You may find it easiest to break down the error 
propagation of Kp into parts and put these intermediate values and their uncertainties 
into their own columns on the Excel spreadsheet. 
2. Plot ln Kp versus lff, where the temperature is in reciprocal of Kelvin. 
3. Determine the best-fit line for this data and display the equation of the line and its R2 
value on the graph. Also carry out the least squares fit for this line using the 
regression analysis program on Excel used for your error analysis problem set. 
1-13 
Determine the standard error of the slope, Sm, and the standard error of the y-
intercept, Sb, from the regression analysis printout. Report the uncertainty in the 
slope as the Sm value and the uncertainty in they-intercept as the Sb value. 
4. Calculate the Kp and its uncertainty at 25.0°C. In the uncertainty calculation, use the 
Sm and Sb values, respectively, from the linear regression analysis. Simplification 
rules #1 and #4 given in this manual can be found helpful in the uncertainty analysis. 
5. Calculate the value of Af1° using the slope (-£\H0/R) of lnK.p vs 1/T graph. Use the 
uncertainty in the slope to determine the uncertainty in Af1°. 
6. Calculate AG0 • (Keep in mind that 0 means at 298.15 Kand l atm.) Then calculate 
AS0 from the calculated value of £\G0 and the value of Af1° determined in step #5. 
Once again remember to calculate the corresponding uncertainties in each. 
7. Use Reference 2 to find the literature values for £\H0 , £\G0 and £\S0 at the conditions 
closest to your experimental conditions (MacDougall's values) in Table 1 and Table 2 
(a copy of this reference exists in the lab on the bulletin board and also in the Chem 
457 binder on reserve). Find the literature values for only £\H0 and £\S0 . From these 
values, calculate 6G0 and use its value as the literature value for 6G0 • 
8. Calculate the AS0 sackur-Tetrode value corresponding to the changes in translational 
entropy as the dimers are dissociated into their monomer form. Use standard 
thermodynamic values for the temperature (298.15 K) and pressure (1 atm) in the 
Sackur-Tetrode equation. 
9. Compare the values of the experimental 6S0 and the 6S0saclrur-Tetrode. Calculate the 
difference for these two values and comment on their differences. This means you 
should suggest possible reasons for these differences. The comments should appear 
m your summary. 
10. Finally compare the value of the experimental MI0 to the MI0 of a hydrogen 
bond3. Discuss this comparison in the report questions. 
Reminders: 
Carry out the error analysis on each of the values calculated and report them as the 
calculated value± propagated error reported to a value between 3 and 30, such as 25.02 
1-14 
± 0.30 g, but not 25.02 ± 0.50 g. The latter should be reported as 25.0 ± 0.5 g. Present 
your data in a table. 
Show detailed sample calculations for each different kind of calculation and a detailed 
error analysis for each sample calculation shown. If unsure of what is expected here, 
refer to your introductory course material or ask one of the TAs or the instructor. 
5. Report Questions 
1. B~ed on your results, what happens to the dimer-monomer equilibrium as the 
temperature increases? Does the reactionshift to more dimer or more monomer at 
higher temperatures? Does this agree with what you would predict from Le 
Chatelier's principle? Give reasons for each of your answers to the above questions. 
2. Do both .6.H0 and .6.S0 contribute to .6.G0 in the same way? Explain. 
3. Discuss how the experimental .6.H0 compares with typical hydrogen bond energies. 
References: 
1. Barton, D.; Ralph, R.; Kane, K. J Chem. Educ. 1968, 45, 440. 
2. Allen, G.~ Caldin, E. F. Quarterly Reviews 1953, 7, 255. 
3. Pauling, L. The Chemical Bond; Cornell University Press, 221 (1967). 
Additional references used but not cited in the experiment: 
Clagnue, A. D. H.; Bernstein, H.J. Spectrochimica Acta 1969, 25A, 593. 
Joesten, M. D.; Schaad, L. J. Hydrogen Bonding, 2 (1974). 
Adsorption from Solution 
Objectives 
• To understand and apply the general adsorption phenomenon and its kinetics in 
surface chemistry. 
2-1 
• To utilize the Langmuir model isotherm for determining the surface area of charcoal. 
1. Introduction 
Adsorption plays a major role in industries, from petrochemical to food processing, due 
to its involvement in chemical, biochemical reactions, and purification, filtration 
processes, and catalysis. In general, adsorption describes the greater concentration of 
adsorbed molecules at the surface of the solid than in the gas phase or in the bulk 
solution. Solid adsorbents consisting of small particle sizes having surface defects such 
as cracks and holes increase the surface area per unit mass over the apparent geometrical 
area. These adsorbent particles may have specific surface areas from 10 to 2000 m2g·1• 
Some common adsorbents are charcoal, silica gel (Si02), alumina (Ah03), zeolites, and 
molecular sieves. In this experiment the adsorption of acetic acid on an activated 
charcoal surface is investigated. 
Adsorption 
Adsorption onto a surface (for example charcoal) is a separation process in which certain 
components (adsorbates) of gaseous or liquid phase are selectively transferred to the 
surface of a solid adsorbent. 1 In general, there are two adsorption mechanisms: 
chemisorption and physisorption. In both mechanisms, the adsorbate becomes attached 
to the surface of the solid as a result of the attractive forces at the solid surface 
(adsorbent). 
The main differences between chemisorption and physisorption are 2: 
2-2 
1) Physisorption occurs when the adsorbate becomes physically fastened to the 
adsorbent by electrical attractive forces (weak van der Waals forces). 
Chemisorption involves the formation of chemical bonds between adsorbate and 
adsorbent. 
2) In physisorption, depending on the strength of the attractive forces, desorption can 
easily be accomplished by reducing the pressure or increasing the temperature 
(low energies on the order of 40 kJ mol-1). Therefore, the process is fully 
reversible. In chemisorption, higher temperatures are required to break the 
chemical bonds (requires high heats of adsorption: 40 to 400 kJ mol-1) . 
3) Physisorption layers can be many molecules thick depending on adsorption 
conditions and adsorbate concentrations. In chemisorption, only monolayer 
adsorption occurs . . 
Isotherms 
An adsorption isotherm describes the equilibrium adsorption of a material at constant 
temperature. The amount adsorbed per gram of solid is related to the specific area of the 
solid, the equilibrium solute concentration in solution, temperature, and the specific 
molecules involved. By analyzing isotherms the relations between the amount adsorbed, 
the nature of the molecules, and even the surface area can be determined at a specific 
temperature. 
" . 
:o 
Figure 1. Freundlich isotherm Figure 2. Langmuir isotherm 
2-3 
An adsorption isotherm can be plotted by drawing N, the number of moles adsorbed per 
gram of solid vs c, the equilibrium solute concentration at constant temperature. 
One of the first efforts involves the Freundlich isotherm utilizing Eq. (1):3 
N=K·ca (1) 
where Kand a are constants that can be obtained from a plot of log N vs log c. The 
Freundlich isotherm fails to predict the behavior at low and high concentrations (at low 
concentrations, N is often directly proportional to c; at high concentrations N usually 
approaches a constant limiting value, which is independent of c). 
Another isotherm theory suggested by Langmuir can be applied to simple systems. Here 
simple systems refer to cases where only one layer of molecules can be adsorbed at the 
surface. One layer of molecule adsorption, namely "mono layer adsorption" describes the 
complete coverage of the surface of the adsorbent by a layer of one molecule thickness. 
In monolayer adsorption the amount adsorbed reaches a maximum value at moderate 
concentrations and remains constant with increase in concentration thereafter. The 
Langmuir isotherm can be derived from kinetic or equilibrium arguments.3.4 Eq. (2) 
shows the surface coverage fraction based on the Langmuir theory for adsorption from 
solution: 
B =--5_ 
l+kc C2) 
where e is the fraction of the solid surface covered by adsorbed molecules and k is a 
constant at constant temperature. B can be replaced by N!Nm, where N is the number of 
moles adsorbed per gram of solid at equilibrium solute concentration c, and Nm is the 
number of moles per gram required to form a monolayefJand Eq. (3) can be obtained as 
follows: 
c c 1 
- = -+ --
N Nm kNm 
(3) 
Based on the assumption of the Langmuir isotherm as the adequate description of the 
adsorption process, a plot of c/N versus c yields to a straight line with slope I/Nm. Once 
2-4 
the slope is found from this graph with the knowledge of, a , area occupied by an 
adsorbed molecule on the surface, the specific area, A (in square meters per gram), can be 
calculated: 
A = N · N ·a .10-20 m 0 
where No is Avogadro's number and a is area in square angstroms. Plotting the 
adsorption isotherms at several temperatures, the slopes of the c/N vs c graphs can be 
predicted to be the same if the number of adsorption sites, Nm, is independent of 
temperature. Although slopes are expected to be the same with changing temperature, 
the intercepts are expected to be different, due to the fact that k ~s a function of 
temperature. Eqs. (5) and (6) can be used to relate the thermodynamic theory of 
adsorption from solution with Nm, solution ·concentration, and the k values. 
(8lnc) = ar p,8 RT2 
where, D. His a differential heat for adsorption at constant pressure p and coverage e. 
The interpretation of D.H is complicated, since adsorption process involves the 
adsorption of solute and the displacement of solvent molecules. Eq. (5) can be 
rearranged, since l lkNm is equal to co.s!Nm (from Eq. (3)), and co.sis the equilibrium 
concentration at 8 = 0.5 (where N = Y:z Nm). At 1 atm: 
dln(l / kNm) = (8lnc) 
dT 8T 8= 05 
D.H 
RT 2 
• The W in Eq. (6) is usually found to be positive, indicating greater extent of 
adsorption at lower temperatures. 
Materials 
7 x 250 ml Erlenmeyer flasks, their glass-stoppers or rubber stoppers; 
3 x funnels; funnel holders (or three rings, with clamps and stands); 
(4) 
(5) 
(6) 
3 x 250 ml beakers; stirring rod; one 10 and one 50 ml burette; burette stand and holder; 
several 100 ml titration flasks; a 5, 10, 25, 50, and 100 ml pipette; spatula. 
Activated charcoal (acid-free, 10 g); fine porosity filter paper; 
2-5 
Various molarity acetic acid solutions; 0.1 M sodium hydroxide (150 ml); and 
phenolphthalein indicator. 
2. Laboratory Procedure 
1. Organize and label clean and dry seven 250 ml Erlenmeyer flasks and their stoppers. 
2. Weigh approximately 1 g of activated charcoal accurately to the nearest milligram. 
Record the weight (and the corresponding label number) and place the charcoal into 
the flask. Repeat this procedure for six flasks. 
3. Using a 100 ml volumetric flask accurately measure 100 ml of acetic acid solution 
andadd this to each flask. Use the previously prepared acetic acid solutions with 
concentrations of 0.15, 0.12, 0.09, 0.06, 0.03, and 0.015 M (check with your 
instructor or TA proper handling of the pipettes). 
4. One of the flasks will contain no charcoal. Add 100 ml of 0.03 M acid to this flask; 
and use this solution as a control solution. 
5. Once charcoal is placed and all seven flasks with the solutions are prepared have 
them tightly stoppered, and allow them to stand in the drawer to equilibriate until next 
week. 
6. The following week, sample solution will be filtered through a filter paper. Discard 
the first 10 ml of the filtrate to prevent adsorption of the acid by the filter paper. Ask 
your TA to show you how to fold the filter paper. 
2-6 
7. Titrate two 25 ml aliquots with 0.1 N standardized sodium hydroxide solution using 
phenolphthalein as an indicator. To titrate 0.03 and 0.015 M solutions, use a 10 ml 
burette. Ask your TA to demonstrate a titration. 
Cleaning and Order 
l. Wash the flasks and the burettes with soap solution and rinse multiple of times with 
distilled water and let them dry on the rack. 
2. Wash the funnels and let them dry on a paper towel. 
3. Make sure the balances are left clean. 
4. Put the used filter papers into trash bin. 
5. Get approval of your TA that everything is nicely ordered and cleaned to not to get 
any deductions from your lab grade. 
3. In lab Questions 
1. Describe physisorption and chemisorption. Based on this description; 
a. Compare their relative heats of adsorption. 
b. Explain why the heat of adsorption of the physisorption and chemisorption 
are so different. 
2. What is a Langmuir isotherm? How is it derived? Describe how surface area of a 
solid can be calculated employing the Langmuir isotherm. 
3. Calculate the final concentration of acetic acid for each sample. The value for the 
control solution should agree with its initial value. 
2-7 
4. Data Analysis 
1. Using the initial and final concentrations of acetic acid in 100 ml of solution calculate 
the number of moles present before and after adsorption and obtain the number of 
moles adsorbed by difference. Prepare a table as shown in Table 1 which can be 
filled as you continue on working out the data and complete the units. 
' 
2-8 
Table I. Initial acetic acid concentrations ([HAc];), charcoal mass (fficharcoaJ), titration data (VNaOH.; and VNaOH. r) 
and their uncertainties (D.). 
Flask Run [HAc]; [HAc]r fficharcoal tilllcharcoal VNaOH,i a VNaOH. i VNaOH. f /':i.VNaOH, f 
1 1 
2 
2 1 
2 
3 1 
2 
4 1 
2 
5 1 
2 
6 1 
2 
2. a) Calculate N, the number of moles of acid adsorbed per gram of charcoal. Prepare a 
table as sho\Vn in Table 2 which can be filled as you continue on working out the 
data. 
b) Plot an isotherm of N versus the equilibrium (final) concentration c in moles per 
liter. 
2-9 
Table 2. Summary of all ca lculated values and their uncertainties. The amount of NaOH used in each titration is 
VNaOH. 
Flask Run V NaOH D. VNaOH c tic N D.N cfN D.c!N 
(ml) (±ml) (M) (±M) (mol/g) 
( ± ~olJ (~) (± ~) 
1 1 
2 
2 1 
2 
3 1 
2 
4 1 
2 
5 l 
2 
6 1 
2 
3. a) Plot c/N vs c, using Eq. (3). 
b) Calculate Nm from the slope of this plot. 
c) Assume that the adsorption area of acetic acid is 21A2, and calculate the area per 
gram of charcoal using Eq. (4). 
4. Compare the surface area obtained from this experiment to its literature value5 ( 400 
m2/g). 
5. By linear regression analysis, calculate the uncertainties in the intercept and the slope. 
1 
- ------------ - - --
2-10 
6. Calculate the uncertainty in final acetic acid molarity. 
7. Calculate the uncertainty of the surface area. 
5. Report Questions 
1. What are the three asswnptions the Langmuir isotherm based on? 
2. Check whether the adsorption in your experiment exceeded mono layer coverage. 
3. How does room temperature and pressure can change the result of this experiment? 
References 
1. Stenzel, M. H.; Chem. Engr. Prog. 1993, 89, 36. 
2. Byrne, J. F.; Marsh, H. Porosity in Carbons, Halsted Press: New York, 1995. 
3. Moore, W. J. Physical Chemistry; 4th Ed.; Prentice-Hall: Englewood Cliffs 1972, 
pp. 484-487. 
4. Rushbrooke, G. S. Introduction to Statistical lvfechanics; Oxford Univ. Press: 
New York, 1949, pp. 211-214; Hill, T. L. Introduction to Stalistical 
Thermodynamics; Addison-Wesley, Reading: Massachusetts, 1960, pp. 124. 
5. Sigma-Aldrich Catalog, 2004. 
The determination of thermodynamic functions of the reactions in 
commercial alkaline-manganese dioxide galvanic cell (Duracell®) 
Objectives 
• To determine the thermodynamic parameters for reactions in a commercial alkaline-
manganese dioxide galvanic cell including .6.rG, .6.rS and .6.rH 
• To compare .6.rH to the calculated enthalpy of formation (.6.rH0 ) of ZnO and Mni03. 
• To determine the equilibrium constant (K) for the reaction in a commercial alkaline-
manganese dioxide galvanic cell 
Introduction 
3-1 
Galvanic cells, devices in which the transfer of electrons occurs through an external 
pathway rather than directly between reactants, are useful portable electronic power sources. 
Alkaline cells are the most common (Duracell® is an example) and are commercially important 
(this is a billion dollar industry, with 1010 
alkaline batteries produced annually). In the 
1960s and 1970s, the alkaline cell gained 
popularity because of the vvidening field of 
consumer electronics. 
Make-up and Chemistry 
In the alkaline battery (Figure 1 ), the anode 
(negative terminal) is composed of zinc 
powder (Zn) (which allows more surface area 
for increased rate of reaction, and therefore 
increased electron flow) and the cathode 
(positive terminal) is composed of manganese 
dioxide (Mn02). (/\Ikaline batteries use 
potassium hydroxide (KOH) as an electrolyte. 
The concentrated KOH solution provides high 
ionic mobility with a low freezing point.' 
As the alkaline-manganese dioxide cell 
Zn(s) 
discharges, oxygen-rich manganese dioxide is Figure 1. DURACELL® cylindrical alkaline cen.131 
reduced and the zinc becomes oxidized, while ions are transported through the conductive 
alkaline electrolyte. The half-reactions are: 
Cathode: 
Anode: 
Overall: 
2 Mn02 (s) + H20 (l) + 2e- -tMil203 (s) + 2 OH- (aq) 
Zn Cs)+ 20H- (aq) -t ZnO Cs) + H20 CD + 2e-
Zn (s) + 2 Mn02 (s) -t ZnO (s) + Mn203 (s) 
+ 0.80 v 
- 0.76 v 
+1.56 v 
3-2 
The anode and cathode are separated by a porous, highly absorbent and ion-permeable 
fabric. The porous nature of the anode, cathode, and separator materials allows them to be 
thoroughly saturated with the alkaline electrolyte solution. The high conductivity of the 
electrolyte enables the cell to perform well at high discharge rates and continuous service. It is 
also responsible for the low internal resistance and good low temperature performance. 
Electrochemistry and Thermodynamics 
Spontaneous chemical reactions inside the galvanic cell result in current. The 
relationship between the reaction Gibbs energy (LirG) and the electromotive force (emf), E, of 
the cell is given by 
(1) 
Where Fis the Faraday constant (9.6 x 104 C mot1) and Eis the voltage. In the experiment, 
v = 2 because this reaction involves two electrons for the zinc to be oxidized and Mn02 to be 
reduced. · The maximum amount of electric energy that can be obtained from a commercial 
galvanic cell is equal: 
(2) 
where mis the mass of reactants in the battery, MMzn is the molar mass of Zn, MMMn02 is the 
molar mass of Mn02, and LirG is the reaction Gibbs energy. If the reaction has reached 
equilibrium, the equilibrium constant K can be calculated from the Nernst equation. 
lnK= vFEo 
RT 
(3) 
Although in this experiment you are not measuring the standard electromotive force, the 
equilibrium constant can be estimated from the battery potential. 
The temperature coefficient of the standard cell emf dE0 /dT, gives the standardentropy 
of the cell reaction. In this experiment, you will determine the entropy of the electrochemical 
reaction in the Duracell battery. From the thermodynamic relationship (8G/8T)p = -S and 
equation 1: 
dE LirS 
-=--
dT vF 
(4) 
From the results of equations 1 and 3, the reaction enthalpy corresponding to the Duracell battery 
can be calculated 
(5) 
Equation 4 provides a noncalometric method for determining the LirH. 
3-3 
Laboratory Procedure 
In this experiment, the voltage of a commercial alkaline-manganese dioxide galvanic cell, 
namely an AA Duracell® battery, will be recorded at various temperatures in the range of - 25 
°C to +40°C. The galvanic cell will be placed into a dewar filled with ethanol. The temperatures 
will be measured using digital thermometers. The voltage will be measured with a digital 
multimeter. In order to increase the precision of the voltage versus temperature measurements, a 
circuit consisting of the measured and the reference battery will be assembled. The complete 
experimental setup is shown in Figure 3. The galvanic cell holder has wires soldered to both the 
negative (black) and positive (red) poles; the same colors are used for corresponding voltmeter 
leads (Figure 3). 
Assemble Single Battery Circuit 
1. Connect the positive lead from the voltmeter to the positive end of the battery holder (red to 
red). 
2. Connect the negative lead from the voltmeter to the negative end of the battery holder (black 
to black). 
3. Record the temperature and voltage. This information is the voltage (not the voltage 
difference) and will be used in Equation 1 to calculate l:irG. 
Important notes: 
Do not allow the leads of the cell to make contact, even for a fraction of second. This action 
will short the battery, and cause the system to disequilibriate, resulting in a battery that 
can't be used for this lab anymore (keep in mind you are working with 1 µV precision). 
Important: 
These leads must not 
contact each other. 
Thermocouple head 
should touc.~~pattery. 
Figure 2. Battery Holder 
Assembling Measured and Reference Cell Circuit: 
1. Assemble the circuit according to the figures below. Simplified diagrams and a 
photograph of the experimental setup are shoVvn. 
Dewar Dewar 
Stir plate 
Figure 3. (Left) Circuit diagram of experiment. (Right) Simplified diagram of experimental setup. 
Dewars are insulating storage vessels typically used for handling liquids at temperatures other than 
ambient room temperature. Double-walled vacuum-sealed construction minimizes heat transfer 
through the vessel wall. For this reason, it is not possible to heat liquids in a dewar using a hot plate. 
An internal heat source, such as a heating coil, must be used instead. 
Figure 4. Photo of experimental setup. 
3-4 
2. Place the battery into the battery holder. Use a rubber band to secure the head of the 
thermocouple to the body of the battery (Figure 2). Red is positive, and black is negative 
for our battery holder. 
Ensure that the alligator clips remain clamped on their wire insulation sleeves to prevent 
shorting the circuit. Pay attention throughout the experiment to avoid shorting and have a 
lab member help you during assembly. 
3. Starting at the voltmeter: 
3-5 
Connect the positive end from the voltmeter (red, top connection) the positive end of the 
measured cell (Figure 3). The measured battery is the one you intend to vary the 
temperature for, so place it into the dewar resting on the stir plate. 
Find a wire with red insulation that has alligator clips at both ends. Use this to connect 
the negative leads of the measured and reference cells (Figure 3). 
Place the reference cell into the reference dewar (kept at 0 °c using ice+ water). Now 
connect the positive end of the reference battery to the negative end of the voltmeter 
(black). 
Add the ice bath to the reference dewar. Your circuit is now complete. 
Taking Voltage Measurements: 
Note: All temperature variation is performed on the measured battery only. The reference battery 
should be maintained at 0 °C throughout the experiment. 
1. Begin the experiment by measuring the circuit voltage at room temperature. Record both 
the temperature and voltage. 
T {°C) AE (µV) 
-9---~-
- 5 
-1 
-(-3) 
2. Heating instructions: Place the heating coil inside the measuring dewar with ethanol, and 
set the Varistat to 10 if you need to heat the battery and stir using a stir bar. Allow the 
galvanic cell to equilibrate for 10 minutes. To maintain temperatures, add small pieces of 
dry ice once the desired temperature is reached. Once thermally equilibriated, record 
both the temperature and voltage. 
NOTE: DO NOT TURN THE HEAT ON THE HEATING PLATE (the left knob)! For 
stirring purposes, make sure to use the right knob ONLY. 
3. Cooling instructions: Begin adding dry ice to the ethanol while stirring. Allow battery to 
thermally equilibriate at each of your cooling data points (25°C, 21°C, l 7°C, l 3°C, 9°C, 
5°C, 1°C, -3°C) for 10 minutes before you record both the temperature and voltage 
for those points. 
Also, wear protective cryogenic gloves (blue) when handling dry ice. SEVERE frostbite 
can result in a very short period of time. 
3-6 
4. Clean-up. Be sure to turn the power off for stir plates and the digital thermometers. 
Leave the voltmeter powered on. Dr. M will do the rest. 
Data Analysis 
1. Tabulate your temperature and voltage data. A sample data/results table might look like 
this: 
T (°C) AE (µV) 
25 
21 
2. Calculate the llrG from equation 1. 
3. Calculate the equilibrium constant, K, from equation 3. 
4. Plot E versus T. Determine the best-fit line for this data and display the equation of the 
line and its R2 value on the graph. Also carry out the least squares fit for this line using 
the regression analysis program on Excel (or whichever analysis program used). 
5. From the slope, determine the llrS for the galvanic cell. Use the uncertainty in the slope 
to determine the uncertainty in llrS. 
6. From the llrS, determine the llrH. Once again, remember to calculate the corresponding 
uncertainty. 
7. Use the enthalpies of formation, llrH0 , to calculate llrH and compare to the value 
determined in step 6. Explain the difference. 
8. Calculate the maximum amount of electric energy that can be obtained from the battery 
used in this experiment. 
References 
(1) Brown, T.L., LeMay, H.E. , Bursten, B.E. and Murphy, C.J., Chemistry: The Central 
Science, Eleventh Edition. (2009) Pearson-Prentice Hall: Upper Saddle River, New 
Jersey. 
(2) Atkins, P. and de Paula, J., Physical Chemistry, Seventh Edition. (2002) W.H Freeman 
and Company: New York City, New York. 
(3) Duracell® Alkaline Manganese Technical Bulletin (2005) 
Real Gas Behavior: Gravimetric Determination of the Second Virial 
Coefficient of C02 
Objectives 
• To observe deviations from ideal gas behavior in the pressure range up to 10 bar 
• To understand the reasons for a gas to behave in a non-ideal manner 
• To determine the second virial coefficient for C02 using the relationship between 
compressibility and the inverse of V m 
Introduction 
An equation of state is a mathematical operation that links the state properties of gas. 
The ideal gas equation stems from three individual gas laws: Boyle' s law, Charles' law, and 
Avogadro's principle and is shown in Eq. (1).1 
PV_=_nRT (I) 
4-1 
r i > 
I ar c: 
CD 
:§ 
E 
t5 .. 
E 
8 
~ J 
l r-------:::=-
§ 
·;;; 
A gas which abides by Eq. 1 under all conditions is defined as 
ideal. 1 A real gas closely resembles an ideal gas if it is monatomic, at low 
pressures, high temperatures, or large molar volumes. 1 The compression 
factor, Z, is used to assess deviations from gas ideality. 1 This can be done 
through Eq. (2), where the actual molar volume, V m, is measured in 
relation to the ideal molar volume, V m 0 . 1 
~ 
.!! 
dominant 
Z= Vm/ Vm0 (2) 
Figure I. Potential energy 
of intermolecular 
interactions.1When V mis less than V m 0 , the gas is moderately compressed, and 
attractive forces dominate (Z<l). 1 On the other hand, under very high 
pressure conditions, V m is greater than V m 0 because repulsive forces are dominant, causing the 
gas to expand beyond its ideal volume (Z> 1). 1 Figure 1 is a potential energy curve that 
illustrates how the attracting and repulsive forces that affect Z depend on intermolecular 
distance. 
4-2 
Since the V m 0 of an ideal gas is equal to RTIP, an equivalent expression for the compression 
factor can be derived as Eq. (3). 1 
PVm=RTZ (3) 
A variety of expressions have been adapted to account for deviations from ideality. One 
of these is the viral equation of state as shown in Eq. ( 4 ), where the first term illustrates the ideal 
gas law. 1 This equation of state can be derived from statistical mechanics and is used to explain 
thermodynamic quantities and their departure from ideality.2 
PVm=RT[l+(BNm)+(CN2m)+ ... ] (4) 
The series in brackets is analogous to the compression factor Z (refer to Eq. (3)). 1 The constant 
Bis the second virial coefficient and correlates to interaction between two molecules (C is 
consistent with three, etc.). Bis a function of temperature and is large and negative at low 
temperatures and small and positive at high temperatures. 2 The purpose of this lab is to derive 
the value for the second virial coefficient of carbon dioxide. The first virial coefficient is equal 
to l and B/ V m >> CN m2, with respect to molar volumes, making B most significant in 
deviations from ideality. 1 The Boyle temperature, Ta, corresponds to the temperature at which 
the second virial coefficient is zero, allowing real gases to sustain quasi ideal behavior over a 
Figure 2. Compression Factor, Z, 
versus Pressure for three 
different temperatures in 
relation to an ideal gas.' 
larger range of pressures. 1 Here Z approaches 1 with slope equal to 
zero, Eq. (5). 1 Under ideal gas conditions, the slope for Z is always 
zero. 
dZ/d(l/ Vm) -7 Bas Vm -7 oo and p -7 0 (5) 
Figure 2 shows the relationship between the Boyle temperature and 
an ideal gas. 
The Boyle temperature can be derived if B is set equal to a portion of 
the Van der Waals equation, Eq. (6), where a depends on attractive 
forces and b defines repulsive interactions. 
2 
B= b - (a/RT) (6) 
Table 1 lists second virial coefficient values of four different gases with their corresponding 
Boyle temperatures. 
Table 1. Second Virial Coefficients, ( cm3/mol) for four gases and Boyle temperatures.1 
Virial Coefficient, B 
at 273K at 600K Ts(K) 
Ar -21.7 11.9 411.5 
C02 -149.7 -12.4 714.8 
N1 -10.5 21.7 327.2 
Xe -153.7 -19.6 768.0 
4-3 
Other equations which aim to estimate deviations from ideal gas behavior are the van der 
Waals, Berthelot, and Dieterici equations (refer to Atkins page 19 for more detail). 
Modern day methods for predicting the second virial coefficient include those used by 
Iglasias-Silva and coworkers.3 The third virial coefficient for carbon dioxide has also been 
predicted at high temperatures. 4 Modern research involves determining third and fourth virial 
coefficients for hard prolate spherocylinders. 5 
Experimental Procedure 
Part 1: Balance Calibration 
1. Tare the balance. While wearing the provided gloves, place the vessel on the balance and 
record its mass. 
2. Using tweezers, add a one gram weight standard to the balance, and record the 
combined mass of the weight and vessel. 
3. Repeat step 2, each time adding the next combination of weights (two grams, three 
grams, four grams, etc.) and recording the new mass, until you reach 10 grams. 
4. Repeat steps 2 and 3 three times to ensure good statistics. 
5. Be sure to record the predicted masses of the weights. You will need these for your 
calculations. 
3 
Part 2: Evacuation of Vessel 
6. Using the provided gloves, attach the vessel to vacuum line C. Clamp it so it does not 
fall. 
4-4 
7. Fill a large dewar with liquid nitrogen, and place it around the vacuum trap. Make sure 
the vacuum pump is turned on. 
8. Open valve C (while the vessel is still screwed shut) in order to evacuate the vacuum line. 
Continue to evacuate until the pressure is 0.02 Torr (verify with manometer). This 
.should take approximately 10 minutes. 
9. While the line is being evacuated, measure atmospheric pressure using the Ashcroft 
pressure gauge. 
10. Once the line is evacuated, open the valve on the vessel. Evacuate the vessel to a 
pressure of 0.02 Torr for approximately 10 minutes. 
11 . Close the valve on the vessel, close valve C, and detach the vessel from the line. 
12. Record the mass of the evacuated vessel 
Part 3: Data Collection 
Therrn-ocoupJe. 
Stainless 
Steel 
Sleeve 
Pressure 
.Adj ustment 
Constant Temperature 
Water Bath 
Figure 3. Experimental apparatus schematic. 
4 
Ultra Pure 
Carbon Oicxid.e 
4-5 
13. Study figure 3 and identify the corresponding parts in the lab setup. Identify the gas 
regulator (annotated by the arrow), which will be used to control C02 loading into in the 
vessel. The inlet gauge (right) shows tank pressure; the outlet gauge (left) shows the 
pressure at which the regulator will cease delivering gas from the tank. 
14. Ensure the small round black valve (labeled C) is shut for this step: Open the tank valve 
(D), and set the regulator to load the correct pressure for C02 by turning the regulator 
knob. Verify that the loading pressure has been set to 9 bar by reading the outlet gauge on 
the.pressure regulator. 
15. Attach the vessel to the yellow C02 line, and place it in the stainless steel sleeve. Do not 
allow the vessel to touch water! 
16. While the vessel is still closed, fill the line with C02 until it reaches approximately 9 bar 
(valves C and D). Next, purge the line until the pressure is just above 0 bar (valve B). Do 
not purge the line completely or air will enter the line. Repeat. 
I 7. Open valve A on the vessel 
18. Allow the pressure to equilibrate for 5 minutes. 
19. Next, record the pressure and the thermocouple temperature. 
* All pressure readings are NIST calibrated within 0.05%. Thermocouple 
temperature readings have uncertainties of± 0.1 °C. 
20. Close valve A on the vessel. 
21. Open valve B below the pressure gauge to release remaining C02 from the line. 
22. Unhook the tank from the C02 line, and record the mass of the vessel. 
23. Readjust the regulator valve for the next data point by turning the knob counter-
clockwise. (Note that a positive pressure must be maintained within the regulator for the 
outlet gauge to correctly display the pressure at which it is set to stop delivering gas.) 
24. Reattach the vessel to the C02 line and place it in the stainless steel sleeve. 
25. Open valve A on the vessel. The pressure should drop to approximately 8 bar (i'.lP =I 
bar). If i'.lP < l bar, open valve B below the pressure gauge to release extra C02 from the 
line until the desired pressure is reached. 
5 
4-6 
26. Using the same procedure, obtain temperature and mass readings for six additional C02 
pressures (7, 6, 5, 4 and 3). Remember, these are only approximate pressure values and 
they indicate gauge pressures. 
27. Remember to obtain the atmospheric pressure. (Go to the organic labs on the second floor 
of Whitmore.) 
4. Data Analysis 
1. To assure balance accuracy with the added mass of the vessel, plot predicted mass values 
against obtained mass values (from Part 1 ). An R2 value close to one indicates acceptable 
measurements were obtained. Include this plot, regression line, and R2 value in your 
report. 
2. Convert the pressure data obtained in lab (Part 3) to absolute pressure in units of Torr. 
Keep in mind that gauge pressures were recorded (in bar). 
3. Determine the amount of carbon dioxide in the vessel in each trial by subtracting the 
evacuated cylinder's mass from the trial' s mass (cylinder plus gas)and converting to 
moles. 
4. Calculate the molar volume of each trial. (Vessel Volume = 0.5612 L) 
V m = V vesse1/moles of C02 
5. Create a table including pressure (in Torr) (step 1), temperature (in K), moles of C02 
(step 2) and molar volume (step 3). 
6. Make a plot of Pressure versus moles. Indicate a line which represents ideal behavior. 
Include this graph in your report. 
7. Calculate the compression factor Z for each trial. 
Z = PV.'11 
KT 
8. Plot Z - 1 versus lNm. Find the linear relationship ben.veen points of this data. Include 
the R2 value in your report. 
9. Report the experimental second virial coefficient of carbon dioxide, B. Calculate the 
error associated with this measurement using linear regression output data. 
I 0. Report the uncertainty associated with the calculation of Z. 
6 
11. Report they-intercept calculated in step 6 and its associated uncertainty. Indicate its 
ideal value. Explain any deviation from this ideal value. 
Report Questions 
4-7 
1. Why is it important to account for the atmospheric pressure when completing your data 
analysis? 
2. Compare your value for the second virial coefficient to the literature value. Don't forget 
to take temperature dependence into account. Consider possible sources of error for this 
experiment and the influence they could have on your results. 
3. What is happening at the molecular level that is causing the C02 to deviate from ideal 
behavior? 
References 
1. Atkins, P.; De Paula, J. Atkins' Physical Chemistry 8'11 ed. W.H. Freeman and Company: 
New York. 2006, 14-16, 19. 
2. Diamond, J.H.; Smith E.B. The Virial Coefficients of Gases: A Critical Compilation 
Oxford University Press. 1969. vii-xii. 
3. Iglesias-Si lva, G.A.; Hall, K. R. Ing. Eng. Chem. Res. 2001, 40 (8), 1968. 
4. Colina, C.M.; Olivera-Fuentes, C. Ind. Eng. Chem. Res. 2002, 41(5), 1064. 
5. Boublik, T. J Phys. Chem. B. 2004, 108 (22), 7424. 
7 
Objectives 
Time Resolved Pulsed Laser Photolysis Study 
of Pyrene Fluorescence Quenching by r Anion 
5-1 
• Understand how fluorescence decay can be used to measure rate constants of photochemical 
reactions utilizing a nanosecond laser photolysis technique. 
• Measure the rate constant for the inherent unimolecular decay of the pyrene first singlet state 
(spontaneous fluorescence decay) 
• Measure quenching rate constant for the reaction of r with excited pyrene 
Introduction 
Fluorescence spectroscopy is a powerful tool used tor gain information regarding the 
electronically excited states of various molecule.s. Molecules in an excited. state can have very 
different physical and chemical properties from those in the ground state. For example, the 
reduction potential of pyrene (Py) in the ground state differs from that of the excited state. 
Excited pyrene will undergo redox chemistry in the presence of another chemical species with a 
sufficiently low (or high) reduction potential. Such an excited-state reduction reaction will be 
measured in this experiment. 
This lab will explore the lifetime of the excited state of the pyrene (*Py) to determine its 
relaxation rate through various modes focusing primarily on fluorescence. This lab will also 
determine how r- quenches the fluorescence of pyrene and calculate the quenching rate constant 
through lifetime kinetics. 
5-2 
Photophysics 
A photon of sufficient energy, in this case 337. l nm, is absorbed by pyrene to yield an 
excited state pyrene molecule (*Py). An electron is promoted from the ground state energy level 
into an excited state. This excited state can then relax back to the ground state either by 
fluorescence of a photon or by radiationless decay as the molecule loses energy in the form of 
heat. The ratio of fluorescing molecules to total excited molecules is a value known as the 
quantum yield. During the lifetime of the excited state, there are some small vibrations which 
occur that lowers the energy of the fluorescent photon. This difference between the energies of 
the excitation and emission photons is called the Stokes shift. 
*Py 
Py 
Py+ hv1 - *Py 
*Py - Py+hv2 
*Py - Py + heat 
Figure 1 
*Py 
Py 
The time delay mentioned above between the excitation pulse and photon emission lasts on the 
order of hundreds of nanoseconds. This excited state lifetime as well as the decay rate will be 
measured in this experiment and will be discussed further in the kinetics section. 
Photochemistry 
Excited state pyrene, as has been mentioned, is a good electron acceptor. In the 
presence of r excited pyrene undergoes a reductive transition back to a lower energy state 
through the formation of the Py- anion and the r- radical. 
5-3 
*Py+ r· 
B 
3L - 1 · bPy + 
Py ~ I" 
Figure 2 
Transition A in figure 2 is not energetically favorable, and pyrene in the presence of 1- is quite 
stable and will undergo no reaction. However, if transition B is induced by excitation from a 
photon source, *Py will readily accept an electron from r through process C to form Py- and I. 
This process is referred to as a photo-induced electron transfer reaction. 
Kinetics 
The lifetime of the excited state can be treated in the same manner as one would treat 
reactants in basic reaction kinetics. The number of molecules relaxing from the excited state to 
the ground state is proportional to the number of molecules currently in the excited state 
multiplied by some constant ko (equation 1). Solving the simple differential equation and 
treating intensity I as being proportional to excited pyrene concentration yields equation 2. 
-d[*Py]/dt = ko[*Py] (1) 
(2) 
Plotting the natural logarithm of intensity versus time yields a plot in which the slope of the 
line is equal to -ko. An example of such a plot is shown in figure 3. This plot is for a simple, 
one component system as discussed in the photophysics section. 
>-
1-
Cf) 
z 
w 
1-z 
z 
.....! 
-2.5 
-3.0 
-3 .5 
-4.0 
-4 .5 
-5 .0 
-5 .5 
0 
Linear Regres sion: 
Y = A + B • X 
Parameter 
A - 2.4381 
B - 0.00335 
R SD 
- 0.99686 
200 
Value Error 
N 
0.00297 
S.668SE-6 
p 
0.0681 2212 <0 .0001 
400 600 
T I M E (n s ) 
Figure 3 
5-4 
800 1000 
To determine the quenching rate constant, kq, of the reaction of *Py with iodide anion, 
the equation used to determine the rate must include the concentrations of both parts of the 
system. The general equation for this reaction is given as equation 3. However, in special cases 
when one concentration (A) is much larger than the other (B), the reaction can be treated as a 
pseudo-first order reaction only dependent upon the concentration of the lower concentration 
component (B). For this approximation, formation of product molecules does not significantly 
change the concentration of larger component as shown in eqliation 4. In this experiment, the 
concentration of 1- is much greater than the concentration of excited pyrene formed. 
-d(B)/dt = k[A][B] (3) 
-d(B]/dt = k'[B] (4) 
k ' = k[A] (5) 
When determining the rate constant for the decay of the excited state in the presence of 
r-, the rate constant is comprised of two primary means of relaxation, fluorescence and 
5-5 
quenching. The fluorescence rate constant is already known from working with the single 
component system, but the quenching rate constant still has yet to be determined. If the rate 
constant for pyrene in the presence of r is measured, then the observed rate constant, kobs, is 
equal to ko plus the constant of the 1- quenching k'. The rate constant for the r quenching can 
be determined using equation 4 . From the pseudo first order reaction approximation, the r 
quenching rate is proportional to the r concentration (equation 5). Making this substitution 
yields an equation for the rate in terms of both the fluorescence and quenching decay pathways 
(equation 6) where k' is kq [r]. 
-d[*Py]/dt = (ko + kq [r]) [*Py] 
In I = ln Io - (ko + kq [r])t 
(6) 
(7) 
Solvingthe differential equation for 6 and treating [*Py] as being proportional to the 
fluorescent intensity, the relationship between the observed relaxation rate kobs, the 
fluorescence rate ko and the quenching rate kq becomes evident. Once kobs is determined for 
each r concentration, a plot of kobs versus concentration [r] will yield a line with a slope of kq 
and with a y-intercept of ko. 
Experimental Procedure 
This experiment is done using a laser photolysis setup. A diagram of the setup is given in figure 
4. The excitation source is a pulsed nitrogen laser emitting a lN light the wavelength of which 
is 337.1 nm. The optical filter absorbs light below 350 nm; any scattered laser light will not 
reach the photodiode, whereas emitted light (370 nm < A < 480 nm) is unaffected. Emitted 
photons are collected using a photodiode. Photodiodes use semiconductors (photovoltaic) that, 
when impacted by a photon, produce a charge/potential difference. The current of charge is 
then converted into the signal on the oscilloscope, hence, the charge read on the oscilloscope is 
proportional to the number of photons fluoresced and allows for a photon count to be obtained. 
Sample Preparation 
sample 
cell 
laser 
optical filter 
1---~ I-
Figure 4 
5-6 
oscilloscope 
photo 
diode 
Samples for analysis should be prepared in l 0 mL volumetric flasks having 10 µM pyrene 
concentrations and KI concentrations of 0, 10, 20, 30 and 40 mM. KI solutions will be prepared by 
serial dilution. Calculate the amount of KI needed to prepare 10 mL of a 0.1 M solution and weigh the 
corresponding amount on a balance. Carefully transfer the solid into the volumetric flask labeled "40 
mM". Next, transfer approximately 50 mL of the provided 50% ethanol-water solution from the 
volumetric flask to a graduated cylinder. Using a Pasteur pipet, fill the "40 mM" flask approximately 
halfuray -with the 50% ethanol-water solution in the graduated cylinder and mix until all of the KI is 
dissolved. Fill to the line with 50% ethanol-water solution and mix again. From this solution, 
CAREFULLYpipet 1.00 mL into the flask labeled "10 m1v1". Then pipet 2.00 mL from the "40 mM" 
flask into the flask labeled "20 mM". Finally, pipet 3.00 mL from the "40 mM'' flask into the flask 
labeled "30 mM" . If any of the pipet transfers are done incorrectly, the serial dilution must be 
completely repeated. There will be a 100 µM pyrene in ethanol solution provided. From this solution, 
pipet 1 mL in each flask (including the "O mM" flask). This will produce the required 10 µM pyrene 
solution. Carefully mix each solution. Finally, fill each volumetric flask up to the line with the 
provided 50% water-ethanol solution and mix. 
Oxygen must be purged from the cell because it quenches pyrene fluorescence. To do this, 
place the desired sample in the cell and put the long needle to the bottom of the cell to make sure all of 
5-7 
the oxygen is purged from the sample. Cap the cell with the needle in it. After the needle and cap are 
in place, connect the purge needle to a nitrogen line with a slow flow and purge for 5 minutes. After 5 
minutes, while keeping the cap in place, increase the nitrogen flow (be very careful not to increase the 
flow too much while the needle is still under the solvent level) and slowly remove the needle. Make 
sure to keep the cap on and minimize any exposure to ambient oxygen. 
Data Collection 
Before operating the photolysis apparatus, make sure that everyone in the vicinity (including 
others working nearby) is wearing eye protection that blocks 337 nm light. UV light can cause 
damage to the eye; plastic and amorphous glass will not transmit UV light at 337.1 nm. Normal 
lab goggles will sufficiently protect your eyes for this experiment. To operate the photolysis 
apparatus, turn the key to turn on the laser. The small black knob on the laser controls the laser 
pulse rate. Turn on the oscilloscope, press ACQUIRE then SAMPLE then RUN. At this point 
you may want to adjust the pulse rate. Then press STOP. The signal on the oscilloscope is the 
fluorescent lifetime of the pyrene sample. Press SA VE/RECALL then SA VE TO FILE. This 
will save the file to a USB drive located on the front of the oscilloscope. Note the file name 
given on the oscilloscope screen. 
Data analysis 
1. Plot the fluorescence intensity vs. time data from the .CSV file (originally saved from the 
oscilloscope) in an appropriate software program (i.e., Excel, Origin, Mathematic, etc.). 
2. Fit the plot with an exponential trend line and determine the best-fit equation and R2 value. 
Note: An exponential fit will require that you delete the raw data associated with the initial 
baseline and increase in your fluorescence lifetime curve. 
3. Determine the k obs for each [i-] from the best-fit equation (y = ae·"'). 
4. Determine the k9 by plotting kobs vs. [I-] and find the best-fit equation and R
2
• (Note: 
What is the value ofko and what does the value mean?) 
5. Estimate uncertainty of kq from linear regression analysis. Report in appropriate format the 
quenching rate constant with uncertainty. 
·6. Determine and report the uncertainty for [KI] for each serial dilution. 
Modeling Stretching Modes of Common Organic Molecules with the 
Quantum Mechanical Harmonic Oscillator (QMHO) 
Objectives 
• To understand the influence of reduced mass and bond order on the observed 
wavenumber for various bond stretching modes. 
• To develop a simple model to predict the frequencies of the infrared absorptions 
associated with the vibrational stretching modes of single, double, and triple bonds in 
covalently bound (CHON) molecules. 
• To calculate the force constant predicted by the model. 
6-1 
• To visualize the vibrations of atoms in a molecule using its optimized geometry by the 
Gaussian 09 software and to understand the limitations of modeling. 
1. Introduction 
Infrared Absorption and Vibrational Motion 
A molecule absorbs infrared radiation by undergoing a net change in its dipole moment 
as a result of its vibrational motion. Consequently stretching and bending may be observed as 
the two major classes of the vibrational motions. Stretching vibrational motion appears as a 
change in the interatomic distance between two bonded atoms. A bending vibration is 
characterized by a change in the angle between two bonds. There are four types of bending 
vibration, which are scissoring, rocking, wagging, and twisting. These vibrational motions are 
shown in Figure 1. Absorption bands in the 4000 to 1450 cm·1 infrared region are usually due 
to stretching vibrations of diatomic units. In stretching bands, the functional groups are found 
in a higher frequency region than the corresponding bending frequencies. More energy is 
required to stretch (or compress) a bond, than to bend it. The region below 1500 cm·1 is often 
referred as the fingerprint region which may be quite complex but is a unique pattern for the 
molecule.1 
a) Stretching vibrations: symmetric and asymmetric (from left to right). 
b) Bending vibrations: In-plane rocking, in-plane scissoring, out of plane wagging, out-of-
plane twisting (from left to right). 
Figure 1. Molecular vibration types: (+)refers to motion from page towards the reader · 
and(-) motion away the reader. 1 
6-2 
To calculate the total number of possible vibrations in a polyatomic molecule, the 
molecular degrees of freedom must to be found. A molecule's degrees of freedom refer to the 
minimum set of coordinates that completely describe its mechanical motion. This system is 
based on the number of atoms in the molecule (N) to be fixed in space and the total number of 
molecular motions resulting in 3N degrees of freedom. Considering that a molecule has three 
different motions; translational, rotational, and vibrational, by subtracting the sum of the 
translational and the rotational motions from the total number ofdegrees of freedom, the 
degrees of vibrational freedom are found. A linear polyatomic molecule containing N atoms 
has 3N-5 and a nonlinear molecule has 3N-6 normal modes of vibration (fundamental 
vibrations). Normal mode is an independent, synchronous motion of atoms or groups of atoms 
that may be excited without leading to the excitation of any other normal mode and without 
involving translation or rotation of the molecule as whole.5 Not all normal modes might be 
seen in IR spectrum. The selection rule for normal mode active in infrared is that the motion 
corresponding to a normal mode should be accompanied by a change of dipole moment. 5 
Simple Harmonic Motion and Quantum Harmonic Motion 
The stretching vibration can be analyzed using a simple harmonic motion and Hooke' s 
Law.1'2 In simple systems, atoms are considered to be point masses and linked to a spring 
with a force constant of k. The spring is assumed to be hanging from a fixed location, such as 
a wall. Figure 2 and Eq. (1) illustrates Hooke's law. 
6-3 
mass 
---[:~ -: quilibrium 
--- +x 
Figure 2. Vibration of a mass on a spring 
F=-k·x (1) 
where, F is the restoring force, k is the force constant, and x is the displacement from the 
equilibrium point due the force applied along the spring axis. Once the mass is moved from 
the equilibrium point, the force along the axis becomes negative and acts as a restoring force. 
The force is proportional to the displacement with proportionality being the force constant, 
which reflects the rigidity of spring. When the mass reaches the equilibrium point, the force is 
equal to zero, but the velocity is not zero and the mass will continue to move. Displacement of 
the mass results in a simple harmonic motion. The amplitude of vibration depends on the 
initial position and the initial velocity of the mass. In classical mechanics any value of the total 
energy (sum of the potential and kinetic energies) of the oscillator is possible. When the same 
potential energy function (force is the first derivative of potential energy) is used in quantum 
mechanics the total energy of the oscillator can only be equal to specific values, see Figure 3. 
The energy levels of a quantum mechanical harmonic oscillator (QMHO) are given by: 
(2) 
where, n is the quantum number of the energy level, n =}!__, and m is angular frequency, 
2n 
The state of minimum energy of a quantum mechanical harmonic oscillator is named 
the ground vibrational state. It occurs when n=O and its energy is not zero but rather 
E - nm 0 - . 
2 
This energy is termed the zero-point energy of the oscillator. 
In the case of a diatomic molecule the same equation for frequency can be used by 
replacing mass by the effective or reduced mass: 
mm 
µ = 1 2 , where m1 and m2 are the masses of the two atoms. 
mi +m2 
> 
~ ----+-------- ---! v = 6 
Qi 
Jj .... v = 5 
(ij ...... v = 4 
""E 
2 ······ · v = 3 
g_ fiw 
v =O 
0 Displacement, x 
Figure 3. Potential energy diagram of quantum mechanical harmonic motion. 
Infrared spectroscopy commonly utilizes wavenumber, v (cm-1), the reciprocal of 
wavelength to determine the frequency or the energy, since, vis directly proportional to the 
energy (E = hvc). 
Modeling 
6-4 
In this experiment, the vibrational frequencies ( v cm-1) for the stretching modes of 
various covalent bonds will be predicted using the QMHO model.3 The development of this 
model is based on two major assumptions: In the first assumption, a stretching mode of 
vibration effectively involves two atoms. Although this assumption is not completely accurate, 
for example, C-H stretching motions of a methyl group, involves more than two nuclei in the 
vibrational motion, it is safe to assume that atoms further away from the bond being 
considered do not contribute significantly to the vibration. In the second assumption, the force 
constant for a given bond is directly proportional to the bond order. 
In this study a common organic "CHON" family \.\ill be used, which consists of 
covalently bonded molecules containing only C, H, 0, and N elements. The reason for 
choosing C, H, 0, and N elements in the construction of the CHON family is due to the 
6-5 
similar magnitude diatomic bond strengths. Typical covalent bonds in common organic 
molecules, have bond dissociation energies in the range of 300-400 kl/mole and the effective 
force constants are found to be in between 500-700 Nm-1• 
The following steps will be followed in the modeling of stretching modes of common 
organic molecules.3 
A. Force constant determination: Specific bonds will be modeled as pseudo diatomic 
molecules. Using the assumption mentioned above, the wavenumber of the stretching 
vibrational mode of the pseudo-molecule can be defined as a function of the reduced mass and 
the force constant of the bond 
- 1 [k 
v = 2;rrc 1{;; 
(3) 
where, c is the speed of the light (in cm·s-1) , k is the force constant of the bond in question (in 
N·m-1), and µis the reduced mass of the system (in kg). Using Eqs. (1) and (2) and the 
observed wavenumbers, V:,bs , force constants for each of the bond types studied can be 
calculated. 
B. Effective force constant determination: In the development of the model it is assumed 
that the force constant for a given bond is directly proportional to the bond order. See Table 1 
for illustration. Based on this assumption each force constant is divided by the number of 
bonds and effective single-bond force constants, k eff , are calculated. 
k = k 
eff bond order 
(4) 
Averaging the k.ff values of all the bond types studied, an effective averaged force 
constant, k:J/ , is approximated. 
T bl 1 B d 0 d a e : on r ers an dF req uenc1es o fC b ar on an dN' 1tro2en Md 34 0 es · 
Mode Bond Order Frequency ( cm-1) 
C-N 1 1180-1360 
C=N 2 ~1660 
C=N 3 2100-2260 
6-6 
C. Predicting wavenumbers: Employing k:;/ along with the bond order, wavenumbers of 
stretching modes of the CHON family can be predicted. 
I k:; · bond order 
vpre =--
2nc µ 
(5) 
D. Evaluating the performance of the model: By plotting v
0
bs vs. vpre and fitting a straight 
line (passing through the origin), the performance of the model is evaluated. If the model 
predicts perfectly, the slope of the line should be 1. The first approximation to k':;/ may result 
in significant error in the prediction of vpre . Therefore, optimization of k:J/ should take place 
in the next stage of this study. 
E. Optimization of the model: The model can be optimized in a number of ways and trial 
and error is one of the approaches. By systematically varying k':J/ a new set of vpre is 
obtained and plotted against vobs until a fit with a slope of 1 is obtained. 
v pre = m . v obs (6) 
where m is the slope. 
If the predicted wavenumber is not equal to observed wavenumber (slope is not equal to 1), 
using the slope of the fitted line a correction factor, f3, can be calculated to optimize the 
effective force constant, k:J' . The relations of k'J' and f3, and f3 and m are shown in Eqs. 
(7), (8), and Eqs. (9), (10), respectively. Multiplying the unrefined wavenumbers by fji , a 
set of refined wavenumbers is obtained and optimization is continued till a slope of 1.00 ± 
0.01 is achieved. 
k opt = j3. k ave 
eff eff 
- opt 1 -
V pre = ·Vobs 
V pre m' V ohs 
=---
- opt 1 -
V pre ·Vobs 
and using Eqs. 5 and 7, 
(7) 
(8) 
(9) 
6-7 
kave l 
eff = m and f3 = -
R k ave m 2 
JJ elf 
(10) 
Table 2. shows the group frequencies for organic compounds. 
Note: This study is modeled for only stretching motion of two atoms and it -vv'ill not work for 
bending and other complicated motions of vibrations. 
6-8 
Tabel 2. Group frequencies for organic compounds.4 
Bond Type of Compound Frequency Intensity 
Ranae, cm-1 
C-H Alkanes 2850-2970 Strong 
1340-1470 Strong 
C-H Alkenes ()c=c(H) 3010-3095 Medium 
675-995 Strong 
C-H Alkynes (-C=C - H) 3300 Strong 
C-H Aromatic rings30 I 0-3100 Medium 
690-900 Strong 
0 -H Monomeric alcohols, phenols 3590-3650 Variable 
Hydrogen-bonded alcohols, phenols 3200-3600 Variable, 
sometimes 
broad 
Monomeric carboxylic acids 3500-3650 Medium 
Hydrogen-bonded carboxylic acids 2500-2700 Broad 
N-H Amines, amides 3300-3500 Medium 
C=C Alken es 1610-1680 Variable 
C=C Aromatic rings 1500-1600 Variable 
C=C Alkynes 2 100-2260 Variable 
C-N Amines, amides 1180-1 360 Strong 
C=N Nitrites 2210-2280 Strong 
C-0 Alcohols,ethers, carboxylic acids, 1050-1300 Strong 
esters 
C=O Aldehydes, ketones, carboxylic acids, 1690-1760 Strong 
esters 
6-9 
The Fourier Transform Infrared Spectroscopy 
The Fourier Transform (FT) is a mathematical process converting intensity and time 
information to intensity and frequency. FTIR conveniently records the same spectrum a 
number of times, since recording a spectrum is on the order of a second, and displays an 
averaged spectrum. Using averaged spectrum a reasonable signal to noise ratio can be 
obtained even with a little amount of sample. 
There are two methods used to resolve an IR spectrum in modern IR instruments. The 
first method (dispersion) consists of a monochromator with a diffraction grating blazed for the 
IR region. The second method, FT-IR, uses the Fourier Transform on the interferogram 
produced by different IR wavelengths that constructively /destructively interfere causing a 
signal at the detector. The Michelson interferometer, a device which is used to split 
electromagnetic radiation and recombine it to cause an interference pattern, is employed to 
create the interferogram which is recorded as signal pattern as a function of time. This 
interference pattern undergoes a Fourier Transformation from the time to the frequency 
domain and the frequency spectrum, this is the final product. 
FT-IR (instrument is shown in Fig. 4) has several advantages over the classical 
dispersion methods: 1) Scan times are much shorter since all frequencies are monitored at 
once. 2) Since more scans can be performed in a shorter amount of time, the signal to noise 
ratio can be increased as the ratio increases proportionally to the square root of the number of 
scans performed. The intensities of each scans can be added together digitally. 3) The 
resolution of a properly tuned FT-IR instrument can be as accurate as 0.125 cm·1•1 
Interferometer 
flat mirror 
HeNe 
windows 
Adjustable 
toroidal 
window 
detector 
Figure 4: A single beam FTIR spectrometer. 1 
2. Laboratory Procedure 
Sample a rea 
Shield 
rR 
detector 
\ 
Purge cover 
6-10 
The following organic liquids will be analyzed using FTIR spectrometer and their 
spectra will be recorded: Acetone, methanol, acetonitrile, cyclohexene, 1-butanamine (n-
butylamine). Use the K.Br (NaCl) plates provided. Note: Do not use water in these cells since 
they are made out of salt. 
Part 1. Experimental determination of stretching modes. 
1. Clean the two KBr salt plates by placing a couple drops of acetone on both sides of the 
plates and wipe them out by kimwipes. It is important to properly clean the salt plates before 
each run, and to wear gloves when handling the plates. 
2. Place the two clean and dry plates in front of the light beam (make a sandwich) and take 
their background spectrum. Once the background spectrum is taken, FTIR spectrometer 
6-11 
corrects the real sample spectrum for the background absorption before recording sample 
spectrum. 
3. Prepare the sample. Place several drops of solvent on the K.Br salt plate that you have just 
taken the background spectrum. Then place the second plate on top of the first plate to evenly 
distribute the liquid as a thin layer between the plates. 
4. Take the FTIR spectrum of the sample. On a typical spectrum you should average at least 
four spectra. Be sure you average a similar number of background spectra. 
5. Record the spectra. 
6. Find frequency of stretching modes by using software. Use Table 2 as reference. Record 
frequency. 
Part 2. Visualization of stretching modes. 
7. To calculated and visualize modes of the molecules studied using Gaussian, go to the 
Chemistry Department computer laboratory in 207 Whitmore. 
8. Log onto the computer. 
9. To access Gaussian, you must log onto the high performance computer Hammer by running X 
term Software. To run this program from the Windows Start Menu select: 
I All Programs/Internet Applications/Communications/Cygwin/Cygwin Bash Shell 
This command will open a new terminal window. Once the prompt appears, type the command: 
Xwin -multi window 
Then run the program "Secure Shell Clinet" from the Windows Start Menu: 
I All Programs/Internet Applications/Communications/SSH Secure Shell/Secure Shell 
Client 
The first time you run this program you will need to check/change settings under: 
/Edit/Settings/Tunneling 
Make sure that "Tunnel XI 1 Connections" (Profile Settings/Tunneling) and "Enable SSH2 
Connections" (Profile Settings/ Authentication) are both checked. 
6-12 
From the SSH Secure Shell window, choose /File/Connect and enter the host computer you wish 
to connect to: hammer.aset.psu.edu and your user name (the same name and password as your 
PSU Access account). 
To access Gaussian, on the SSH Secure Shell window, type the follO\\-ing 
[yourPSUaccessID@ritchie ~] $ module load gaussian 
[yourPSUaccessID@ritchie ~] $ module load gview 
[yourPSUaccessID@ritchie ~] $ gview 
10. Two new windows should appear on the screen entitled "GaussView 4.1.2" and "Gl:Ml:Vl 
-New". 
11. Start drawing a molecule of interest. You should be able to learn how to build molecules 
using the Help menu, especially by stepping through some of tutorials available. 
12. Once the molecule is constructed adjust the geometry of the molecule based on defined set of 
rules by using menu EDIT->CLEAN. This adjustment is only first rough approximation. 
13. Now you are ready to perform a calculation. Your goal is to obtain IR frequencies. However, 
the first step in the calculation is to optimize the geometry of the molecule. To enter the 
parameters of the calculation go to the menu CALCULA TE->GAUSSIAN. 
14. A new window, "Gaussian Calculation Setup", will pop up. Choose the Job Type tab and 
OPT +FREQ as job type. Go to Method tab and change basis set to 6-31 G++. 
15. Go to the Title tab and type the molecule name and description of job you are running. 
16. Go to the NBO tab and choose CHECKPOINT SA VE: DON'T SA VE. 
17.Go to SOL VA TION tab and ensure that MODEL is set to NONE. 
Now you are ready to run calculation! 
6-13 
18. Press the SUBMIT button. The program will ask you to save the input file. Click the SAVE 
button. Type an appropriate file name using extension " .com". Check the box WRITE 
CARTESIAN and then click SA VE button. 
19. Click OK to submit file to Gaussian. 
20. Wait until program reports that your job has completed. (depends on molecule size it may 
take 5 to 15 minutes) Click YES to open the result file. Choose FILE TYPE as Gaussian Output 
Files and than choose your file (the output file has the same name as the input file but with the 
extension changed to ".log"). 
21. Go to menu RESULTS-> VIBRATIONS, which bring up a table with calculated IR 
frequencies. Choose a frequency you want to visualize. Check box Show Displacement Vector. 
Click the Start button. You can see the vibrational motion that corresponds to the IR frequency 
selected. Find stretching modes. You need a total of two nice images of normal modes for the 
report to illustrate the assumptions of the proposed model. You may save more than 2 images. 
Before saving an image click Stop button. To save an image go to the menu FILE->SA VE 
IMAGE. Type a filename, choose File Types as JPEG Files, choose Save As as JPEG FILE. You 
have to check box WHITE BACKGROUND. Click the SA VE button. 
22. Go back to the frequency table and choose the next IR frequency ofinterest, visualize it and 
save the image if you need. 
23. Calculated IR frequencies should be scaled to match experimental frequencies. The scale 
factor is 0.897 (J Phys. Chem., 100, 16502 (1996)) 
24. To transfer JPEG files to the local computer use program ~'SSH Secure File Transfer". Click 
"Quick Connection" and type hammer.aset.psu.edu as "Host Name'', your PSU ID as "Name", 
click the CONNECT button. Move files to Desktop for example and ensure that they are good. 
25. To close Xwin software type "exit". 
6-14 
3. In Lab Questions 
I. What is the usual IR region used in the infrared spectroscopy? (Hint: The IR region includes 
not only stretching modes). 
2. Describe the type of vibration motions. 
3. What is the importance of fingerprint region? 
4. What is a normal mode? 
5. Visualize the vibrational modes of acetone in Gaussian. Identify each stretching mode. 
Determine the symmetry and IR activity of each of these modes. 
4. Data Analysis 
I. Draw each molecule to be analyzed and find their individual stretching modes. Using 
infrared interpretation tables determine their stretching frequencies. Make a table or fill the 
data table below to list the stretching modes of each compound analyzed. 
6-15 
Table l. Calculation of Effective Force Constants 
Mode Bond Mass l Mass2 Reduced Observed Calculated k ke1T (Nm-1) 
Order Mass (kg) frequency frequency (Nm-') 
(cm·1) (cm·1) 
C=O 
C-H 
(spJ) 
C-N 
N-H 
C=C 
C-H 
(spl) 
C-0 
O=N 
0-1-1 
k a""= 
eff 
2. Write down the experimentally observed frequencies into the data table. You may average 
the C-H stretching modes involving sp3 carbon and the ones involving sp2 carbon. Record the 
stretching mode and the corresponding ·stretching frequency on the spectrum. Do not try to 
analyze the C-C bond stretching modes, since they are not identifiable in infrared spectra due 
to their weak intensity. 
3. Using Eq. (3) and the assumption that "vibration is associated with a molecule of two 
atoms'', calculate the force constant for each stretching mode~ 
4. Using the assumption "the force constant for a given bond is directly proportional to the 
bond order", divide the calculated force constants by the bond order to find the effective 
single-bond force constants, k eff . Averaging k eff values obtain k:;e for modeling which 
should be in the order of 102 N m·1. 
6-16 
5. Plotting v
0
bs vs vpre, obtain a best-fitted line which passes through the origin. If the slope 
of this best fitted line is 1.00, there is a good match between the observed and the predicted 
frequencies, which means that model is working perfectly. If the slope is different than 1.00, 
the slope needs to be optimized until the slope of the linear regression line is equal to 1.00 ± 
0.01. 
6. For optimization please follow section Modeling part E. 
7. Discuss in your report the influence of model assumptions on prediction of stretching 
frequency. 
8. Estimate the uncertainty of effective force constant from linear regression analysis. 
5. Report Questions 
1. What is the selection rule for normal mode to be infrared active? 
2. What is the method that Gaussian 09 software is using to calculate infrared frequency? 
3. If you were to use k:;/ and compute the frequency of C-H stretching modes using the 
model, they would show a single peak. As you saw in acetone, this is not the case. Explain. 
4. Overlay the experimental spectrum of acetone with the calculated IR active modes. 
(identified during the In-Lab questions) Discuss the differences between calculated and 
experimental results. 
References: 
6-17 
1. Skoog, D. A.; Holler F. J.; Nieman, T. A., Principles of Instrumental Analysis, 5th Ed.; 
Brooks: Cole, 1998. 
2. Pavia, D. L.; Lampman, G. M.; Kriz, Jr., G. S. Introduction to Spectroscopy: A Guide for 
Students of Organic Chemistry, W. B. Saunders Co.: Philedelphia, 1979, p. 21. 
3. Pamis, J.M.; Thompson, M. G. K. ; J Chem. Educ. 2004, 81, 1196. 
4. Silverstein, R. M.; Bassler, G. C.; Morrill, T. C. Spectroscopic Identification of Organic 
Compounds; 5th Ed.; Wiley: New York, 1991. 
5. Atkins, P.; de Paula, J. Physical Chemistry; gth Ed.; W. H. Freeman and Company: New 
York, 2006, p.461. 
General Reading: 
McQuarrie, D. M. Quantum Chemistry; University Science Books: Mill Valley, CA, 1983, 
Chapter 5. 
7-1 
Resonance Energy of Naphthalene by Bomb Calorimetry 
Objectives 
• To determine the heat of combustion of naphthalene and compare it to the 
literature value 
• To calculate the theoretical heat of combustion of solid naphthalene using bond 
energies, the heat of sublimation of naphthalene and the heat of vaporization of 
water 
• To relate the heat of combustion of naphthalene determined from bond energies to 
the literature value and discuss the reason for the differences as well as the what 
this difference tells us about the resonance energy in naphthalene 
1. Introduction 
The purpose of this experiment is to measure the standard enthalpy of combustion 
of naphthalene, t"lH0comb using a Parr oxygen bomb calorimeter. The enthalpy of 
combustion is useful for calculating other thermochemical information of such as heats of 
formation, bond energies and resonance stabilization energies for aromatic molecules. 
Naphthalene (C10Hs) is one such aromatic compound and its resonance energy will be 
determined indirectly in this experiment. The structure of naphthalene is shown below. 
Figure 1: Structural Formula for Naphthalene 
Theoretical Background The study of the heat produced or required by chemical reactions is 
called thermochemistry.6 It involves the measurement of temperature changes that result from 
the evolution of heat during the course of the reaction. The changes in internal energy (AU) or in 
7-2 
enthalpy (Ml) for chemical reactions can be determined from such measured temperature 
changes. These values can then be used to gain insight into the nature of the chemical bonding in 
the compounds involved in the reaction. 
Complete combustion of hydrocarbons in the presence of excess oxygen generally 
produces only two products, C02 and H20. Combustion reactions are conventionally 
written for the combustion of one mole of material. Therefore, for benzene: 
C6H6(l) + 7 Yz 02(g) 7 6 C02(g) + 3 H20(l) 
AH°comb = - 3268 kJ /mol 
(1) 
The conditions of phase must be specified. This is particularly important for compounds 
such as water which can exist in more than one phase under common conditions. 
Experimental heats of combustion are usually determined in a bomb calorimeter. 
In the Parr bomb calorimeter, a sample is burned completely in excess 02 gas at a 
relatively high pressure (25-30 atm). The bomb is flushed with oxygen prior to firing to 
displace any nitrogen present and to eliminate the formation of nitric acid that forms at 
high temperatures in the presence of nitrogen, oxygen and water. 
The heat produced upon combustion is transferred to the water in which the bomb 
is immersed, as well as to the other parts of the calorimeter, though the water is the 
greatest heat sink. The _heat capacity of water (Cw) is. taken as 4.1798 Jg-1K·1 in the 
temperature range of interest. The heat capacity of the entire calorimeter (Ccalorimeter), 
including the water, will be determined in this experiment, usirig a standard sample with a 
known enthalpy of combustion. According to the First Law of Thermodynamics: 
13.U = Q+W (2) 
where the heat, Q, is negative if it is lost by the system and the work, W, is negative if it 
is done by the system. Since the combustion in the bomb is carried out at constant 
volume, the p-V work, defined as -f pdV is zero. Assuming no other type of work (such 
as electrical work) is done, then W = 0 and equation (2) becomes: 
13.Uv = Qv (3) 
Thus, the heat (Qv) released during combustion is equal to the change irI the internal 
energy for the reaction. The direct experimental measurement yieldsthe value of '3.Ubomb, 
the heat of reaction as carried out in the bomb at constant volume and elevated pressure. 
7-3 
The enthalpy change for the process is related to the observed internal energy 
change, ~U, by: 
M! = ~u + ~(pv) (4) 
where ~{p V) = (p V )products - (p V )reactants • For reactions involving only solids or liquids, 
the term ~(p JI) is negligible. However, if gases are involved in the reaction, the term can 
be significant, leading to an ideal gas behavior: 
As a result, ~(pV)= ~n(g)RT , where W(g) is equivalent to moles of gaseous products 
minus the moles of gaseous reactants. This ~n(g) is used in Eq. (6). 
Mf = ~u +~n(g)RT (6) 
where T is the temperature, T60%, as defined in Figure 2. This equation will be used 
when carrying out the calculations for this experiment. It should be noted that the Mf 
is at constant volume, Mfv, in Eqs. (4) and (6). 
Another factor to consider is the pressure of 25-30 atm inside the bomb, which is 
far from the standard pressure of one atmosphere. The enthalp)'. of a gas varies with its 
pressure as shown below. 
1 (8HJ = V -T(oV) 
op r 8T P 
(7) 
Using ideal gas equation p V = nRT, and one mole equation (7) becomes: 
( oHJ = V -T( R J = V -V = 0 op T p 
(8) 
Thus for a process where gases are assumed to act ideally, the Mf of the .reaction is not 
dependent on the magnitude of the pressure. Though oxygen and carbon dioxide do not 
behave ideally at 25-30 atm, the difference between Affv and ~Hp is very small, and can 
be neglected in this experiment. 
7-4 
Ignition of the sample in the bomb causes combustion, and heat is released. This 
energy is transferred from the system (the reactants) to its surroundings (the calorimeter 
with all its parts, including the water) as described by Eq. (9). 
Q reaction = -Qcalorimeter (9) 
The reaction temperature is over 2000°C, the calorimeter is at room temperature and will 
absorb a specific amount of heat per unit mass for every 1°C change in its temperature. 
This specific quantity is known as the heat capacity of the calorimeter (CcaJorimeter), and 
includes the constant volume of water surrounding the bomb. fthe calorimeter heat 
capacity must be determined experimentally by combusting a massed sample with a 
known enthalpy of reaction in the calorimeter, and measuring the resulting change in 
temperature (AT) of the water in the calorimeter. Thermal equilibrium between the 
bomb and the water is assumed so that t:.T is considered to be the same for both. Using 
the definition of heat capacity at constant volume: 
Cv = (-)( dUtherma/) 
dT v 
(10) 
Assume Cv to be independent of T over the small temperature range being used, and 
integrated Eq. (10) to give: 
!::.U = -Cv!::.T = - Cv(Tjinal -T,nilial) (11) 
where Cv is equal to Ccalorimeter· This value is specific for the calorimeter used. 
The amount of heat generated from the complete combustion of the standard 
sample (benzoic acid) and the partial burning of the nickel alloy fuse wire is calculated 
from their known heats of combustion (found on their containers). The total heat 
generated by the sample and the fuse is equivalent to t:.U in Eq. (1 1). Knowing this, 
Cca1orimeter for a given calorimeter can be calculated from the following equation. 
[ ( t:. Vwmple m sample ) + ( t:. u fuse t:.m fu.~e ) J 
Cca1orime1er = (-) !:lT 
(12) 
where t:.U is heat of combustion of the sample or fuse, in Jig, m is mass of the sample 
combusted, D.m is difference between the initial mass of fuse and final mass of fuse after 
7-5 
combustion, and tiT is difference between final and initial temperatures of water. NOTE that 
these are negative values, since combustion is an exothermic process 
In considering t!.T, assume that the bomb calorimeter being used is only 
approximately adiabatic. The calorimeter is normally assembled with the water 
temperature being slightly below room temperature; therefore, heat leaks to the 
calorimeter from the surroundings and there is a slight rate of increase in temperature 
over time. When the sample is ignited the temperature inside the bomb increases. As the 
heat from the bomb is transferred to the water and the calorimeter bucket, their 
temperature rises until they are all at thermal equilibrium, i.e. the same temperature. The 
temperature usually goes through a maximum, and then a slightly negative slope is 
observed in the temperature vs. time graph due to heat leaking from the calorimeter to the 
surroundings. One other factor to conside:r: is that there is usually a stirrer present to 
hasten thermal equilibration. The mechanical work done on the system by the stirrer 
results in the continuous addition of energy to the system at a small, approximately 
constant rate. 
Absorption of heat by or loss of heat from the calorimeter is minimized by having 
the water temperature in the calorimeter close to the surrounding room 
temperature. As observed in Figure 6, the temperature variation as a function of time 
(dT/dt, drift rate) is approximately linear. Therefore, in our system we can reasonably 
assume that the rate of gain or loss of energy by the system resulting from the stirrer 
work and the heat leakage is reasonably constant with time at any given temperature. In 
the same figure, it can also be observed from the sl-opes of the pre-ignition (dT/dt)i and 
post-ignition (dT/dt)r lines that the drift rate is quite small. 
The vertical line, t60%, is placed at the time when the temperature has reached 60% 
of the maximum value for the reaction. This somewhat arbitrary choice is made to 
account for the heat produced by the stirrer and the loss from heat transfer. The value of 
160% (6.5 min.) is then used in each of the best-fit line equations to determine Ti and Tr and 
!!. T. The point of intersection of t6o% and the ignition curve provides the temperature, 
T6o%, for Eq. (6). 
When collecting data for this experiment, one should follow the temperature 
variation before and after the reaction for a period long enough to allow a good 
7-6 
evaluation of (dT/dt)r and (dT/dt)r. This is usually between 5 and 10 minutes. A plot, 
like shown in Figure 6, must be constructed. The best value for t6o% should then be 
determined and used to calculate the values of T f and Ti from the equations of the pre-
and post-ignition lines. f). T can then be calculated from Tr - Ti. It should be noted that 
the slope of each the pre- and post-ignition lines provide the uncertainty for the value of 
the calculated temperatures. Of course the tolerance level of the temperature-
measuring device must also be taken into account and whichever yields the greater 
uncertainty should be the uncertainty used in determinations of propagated uncertainties 
or error. 
27.0 
26.5 
() 
0 26.0 
i Tso% :J 
~ 
25.5 cu ... 
Cl) 
a. 
E 25.0 Cl) 
t-
24.5 
24.0 
0.00 5.00 
y_ = -0.0019x + 26.586 
- - - - - y = 0.0004x + 24.197 
10.00 15.00 
time, min. 
l 
l ---- pre-ignition line 
I 
I -+-Ignition of BA 
I I __...,_post-ignition line 
- - Linear (post-
ignition line) 
- - - - Linear (pre-ignition 
line) 
20.00 
Figure 2. Temperature-time plot for the combustion ofbenzoic acid standard. 1 
Though the majority of the discussion thus far has pertained to the acquisition of 
thermochemical data directly from experimental work in the lab, there are some reactions 
that are not suited for direct calorimetric measurement. The thermochemical 
information for such reactions can be determined indirectly using Hess's law of 
J 
7-7 
constant enthalpy summation or estimated from the manipulation of bond energies if the 
structural formulas for all species involved in the reaction are known. 
If the structure of the molecules involved in a chemical reaction are known, it is 
possible to express the enthalpy for that reaction as an additive property of the bond 
energies of the bonds being broken (positive bond energies) and being formed(negative 
bond energies) in the course of the reaction. Bond energy is defined as the amount of 
energy needed to break one mole of a particular bond in a gaseous molecule to give 
electrically neutral fragments. Bond energies are specified in two ways. 
The average bond energy is the average molar enthalpy change when all similar 
bonds in a gaseous molecule are cleaved under standard thermodynamic conditions. The 
true bond dissociation energy is the L\H0 needed to break one mole of a specific 
chemical bond. Consider the difference in these energies for the C-H bonds in methane. 
In gaseous methane (CR4) the breaking of all four C-H bonds to form gaseous carbon and 
hydrogen atoms requires a total of 1661 kJ mo1·1 of CH4, giving an average bond energy 
of 415 kJ mo1·1 for the C-H bond in methane. 
CH4cg> ~ CH3(g) + Hcg> 
CHJ(g) ~ CH2cg) + H(g} 
CH2cg) ~ CHcg> + Hcg) 
L\H0 = 427 kJ moi-1 
L\H0 = 460 kJ mol 
L\H0 = 435 kJ mo1-1 
L\H0 = 339 kJ mo1-1 
1661 kJ mo1·1 
Average bond energies are usually tabulated from experiments involving many 
hydrocarbons and can be used in determining estimates for enthalpies of reactions. 
Some common average bond energies are shown in Table l . These energies are not 
taking into account the molecular environment of the bond in most cases. The one 
exception is the C=O values given. 
It is possible to estimate the stabilization or resonance energy of aromatic 
compounds using bond energies. For example, in benzene (with 6 C-H bonds, 3 C-C 
bonds and 3 C=C bonds) the conjugated carbon-carbon bonds are thermodynamically 
more stable than three isolated C=C and three isolated C-C bonds in a cyclic system. 
This increased stability of benzene is called the "resonance energy" and is associated 
with the delocalization of the six n-electrons occupying the six carbon 2pz atomic orbitals. 
7-8 
This resonance stabilization energy can be estimated by comparing the experimental heat 
of combustion (which takes into account the molecular environment of the chemical 
species in the reaction) to the theoretical heat of combustion (determined from the 
relevant bond energies and does not take the molecular environment of the bonds into 
account). 
Table 1. Average Bond Energies, LlH0 , at 25°C (in gaseous state)4 
Diatomic Molecules (kJ mol-1) Polyatomic Molecules (kJ mol-1) 
H-H 436 C - H 414 C - F 485 
F-F 157 C- C 347 C-Cl 339 
Cl-Cl 243 C = C 610 C-Br 284 
Br-Br 194 C=C 836 C - 1 213 
I-I 153 C - 0 359 0 - H 464 
H-F 568 C= oa 803 0-0 146 
H - Cl 431 C= Ob 694 0 - Cl 217 
H - Br 365 C = o c 736 0 - Br 201 
H-I 299 C= Od 748 N-H 389 
O = O 498 C-N 305 N - N 163 
N=N 945 C =N 615 N-0 221 
C = N 890 N=N 418 
S - H 339 N=O 606 
S - S 229 
8carbon dioxide; bformaldehyde; caldehydes; dketones. 
Experimental (The Parr Calorimeter) 
Oxygen bomb calorimetry involves the burning of a known amount of a substance 
in an excess of oxygen in a rigid (constant volume) vessel. The heat of combustion is 
determined from the change irI the temperature of the cooling water in the calorimeter 
bucket before and after combustion. The Parr 1341 Oxygen Bomb Calorimeter is shown 
below in Figure 3 and 4. 
IJ.4t Cak:orimfJlttt 
with lgniOO:ri Urtit 
Figure 3. 1341 Parr Calorimeter with Ignition Unit.2 
7-9 
To become familiar with the parts of the calorimeter, look at the following cross-section 
diagram of the calorimeter and locate the following parts: 
l. Oxygen combustion bomb, where the sample will be placed and filled with oxygen, 
2. oval bucket, which will hold the water, and the bomb, thermometer, thermistor, and 
stirrer will be immersed, 
3. stirrer and its pulley, 
4. ignition wires, and, 
5. calorimeter jacket and cover. 
As seen in Figure 4, the oxygen combustion bomb (or "bomb") sits in a oval 
calorimeter bucket which will hold 2 L of water when the sample in the bomb is ignited. 
It is the temperature of this water that is monitored to measure the flow of heat from the 
combustion occurring inside the bomb.2•3 
In the set-up that you will be using there is a thermistor attached to the 
thermometer and a multimeter. The multimeter transfers voltage data corresponding to 
the temperature of the water in the calorimeter to the bomb calorimeter software in the 
PARTS FOR THE 1341 CALORIMETER 
l<ey No. Part No. Description 
1603 Tbennometer, 19-35° C. 
• 2 A39C Thermometer bracket 
3 52C Th.umometer support waah.er 
4 3003 Thermometer reading lens 
5 SC Thermollltlter support rod 
6 A30M3 Mowr a.oeembly with pulley 
7 36M4 Motor pulley 
8 37M2 Stirrer drive ~I• 
9 37C2 Stirrer pulley 
10 AZT A Stirrer bearing assembly 
11 A468E Ignition wire 
12 A30A2 Stiner shaft with propeller 
13 A391DD Oval bucket 
14 A461E Calorimeter jacket with cover 
-15 1108 Oxygen combustion bomb 
6 
12----Y-1~ 
13-----fll---
14--~ 
15----1~-1.1--11----+--1 
Figure 4. Cross-section of the Parr 1341 Calorimeter.2 
7-10 
computer. This software in turn converts the voltages to temperatures in degrees Celsius 
and collects the data electronically in the computer. 
The bomb consists of a high-pressure cell made up of a cylindrical body and a 
head piece, which are held together by a large threaded cap. A check valve for filling the 
bomb with oxygen and a needle valve for venting the bomb are found on the top of the 
head piece (see Figure 5). The head piece also contains a pair of electrical terminals. A 
7-11 
short length of fuse wire that is in contact with the sample is connected to these terminals. 
Electrical ignition of this wire serves as a means of initiating the combustion of the 
sample, which is placed in the small metal pan (the combustion pan) (see Figure 6). 
Electrical -~-_..... 
terminals 
1108 Oxygen Bomb 
Figure 5. Parr oxygen bomb.2 
Fuse wire 
Figure 6. Cross-section of Parr 
oxygen bomb.2 
The bomb is expensive (~$3500) and must be handled carefully. In particular, 
care must be taken not to dent, scratch or strip the threads on the screw cap. When the 
bomb is unloaded after a run, the head piece should be placed on its support stand and the 
screw cap should be placed on a clean, folded paper towel and wiped clean. 
2. Laboratory Procedure 
1. Check if your bomb is clean and dry otherwise rinse with acetone. There should be 
no leftover fuse wire on the terminals of the bomb head piece. Inside of the 
calorimeter pail should also be dry. 
2. Weigh a preformed benzoic acid pellet (for standardizing the calorimeter, Parr cat. 
No. 3413). Its mass should not be greater than 1.2 grams. If it is, the tablet should 
be shaved to reduce its mass to 1.2 grams. 
7-12 
3. Make note of the heat of combustion for the benzoic acid standard that is given 
on the pellet container. This should be in units of MJ/kg. This will be needed for 
later calculations. 
4. Using tweezers, place the pellet into the combustion pan, close to its center. 
5. Cut 10 cm of the nickel alloy fuse \Vire (Parr 45C10), wire should have no kinks or 
sharp bends in it. Weigh it accurately. Record the wire's heat of combustion. 
6. Set the bomb head on its support stand, if it not already there. Insert one end of the 
wire into the eyelet at the end of the stem of the electrode and wrap the fuse wire 
around the stem of the electrode several times to ensure good electrical contact. 
Then push the cap downward to pinch the wire into place. Repeat with the other 
end of the wire and the other electrode stem. 
7. Be sure that the combustion pan is sitting snugly in its holder and that it is level. 
Then bend the fuse wire so that the loop bears down firmly against the top of the 
pelleted sample so that it will not slide against the side of the combustion pan. Be 
sure that the fuse wire does NOT touch the metal pan at any point or it will short out 
before causing the sample to combust. Figure 7 illustrates how this is to be done. 
. ,-J 
Figure 7: Attaching the fuse3. 
8. Using a pipetteand 10 mL graduated cylinder, carefully place 1.0 mL of distilled 
water in the bottom of the bomb, below the combustion pan (not in the 
combustion pan!!!). This is to saturate the atmosphere in the bomb with water 
vapor, so that the water produced by the combustion will all be in the liquid state. 
7-13 
9. Closing the bomb. Care must be taken not to disturb the sample when moving the 
bomb head from the support stand to the bomb cylinder. Gently set the head into 
the cylinder and push it down as far as it will go. Make sure it is level. 
10. Set the screw cap on the cylinder and turn it down firmly by hand. Do not use a 
wrench. Hand tightening should be sufficient to secure a tight seal. 
11. Charging the bomb with oxygen. Carefully carry your closed bomb to the lab 
bench to the left of the entrance to the calorimetry room. Have a TA fill the bomb 
\.Vith oxygen for you. They will filJ it to 15 atm. twice and vent it and then will 
finally fill it to 30 atm. and it will be ready to use. Why must the bomb be flushed 
with oxygen before filling it? 
12. Assembly of the calorimeter. Be sure that the bucket in the calorimeter is sitting 
so that the raised points correspond to the plastic knobs under the bucket. If they 
don't, turn the bucket around. If there are problems or questions about this, see a 
TA. 
13. Set the bomb in the bucket in the calorimeter, making sure it is centered on the 
raised circle in the bucket. The bomb should not touch the walls of the bucket. 
14. Insert the electrical connections into the electrode terminals at the top of the bomb 
and make sure they are tight. 
15. Fill a 2.0 L volumetric flask with deionized water to its marked level at room 
temperature. Use the water from the carboys in the calorimetry room to fill the 
bucket. Carefully pour the water into the bucket and over the bomb, so none of the 
water splashes out. The water should completely cover the bomb when it is all 
poured into the bucket. Use the same amount of water every time the calorimeter is 
used and not to lose any in the transfer. Why? 
Important NOTE: If you see bubbles continually rising from the bomb at this time, seek 
a TA. DO NOT continue, until a TA has looked at the bomb. 
16. Refill the 2.0 L volumetric flask to the mark for the next run. 
17. Put the calorimeter lid fmnly in place with the stirrer m the back and the 
thermometer in the front. Check to be sure that the thermometer/thermistor are in 
7-14 
the bulk of the water. NOTE: Be sure to pick up the paper on the ledge above the 
sink about the thermistor and its tolerance levels. 
18. Turn the stirrer by hand to check it runs freely; then slip the drive belt onto the 
pulleys and start the motor. 
Collection of Data via the Computer and the Multimeter 
19. Open the bomb calorimetry program using one of the following: 
a) double-click the bomb calorimetry icon on the PC desktop (upper left) 
OR 
b) the program may already be running 
20. When ready to initiate the run, click on the ST ART button on the bottom of the 
computer screen. 
21. A Dialog Box will appear and ask you to choose a File Name where your data will 
be saved at regular time intervals during the run. Choose to save your file in the 
appropriate folder for your section on the desktop. Choose a File Name such that 
you can identify it as yours AND you will know what sample is being combusted, 
for example, BA for benzoic acid and naph for naphthalene. 
Once you have saved the file name, the digital read-out on the multimeter should 
convert to degree Celsius readings. 
22. Do not perform any other tasks on the computer while your data is being collected 
otherwise you might lose data. 
23. At this point, the run will be~ started. It will take about five seconds to show 
readings on the screen. Then it will take readings every five seconds until you stop 
the run. 
24. Take readings for five minutes or until you have a temperature change at a very 
slow linear rate (on the order of 0.00l°C per minute) for at least 5 minutes. This 
will give you the pre-ignition line for later calculations, see Figure 2. 
25. When you are ready to ignite the sample, make note of which calorimeter you are 
using, have everyone leave the room, shut the door, and press the ignition button 
/ 
7-15 
for the calorimeter you want to ignite for about 5 seconds. You should see a brief 
flash of light at the ignition box, indicating the passage of current for the instant 
required to bum through the fuse wire. In nearly all cases the burning wire will 
ignite the pellet, and after a period of about 20 s the measured water temperature 
will begin to rise. Wait outside the room for 30 seconds before reentering. 
26. The rise in temperature "'ill be very rapid for the first few minutes; then it will 
become slower as the temperature approaches a stable ma."Ximum. The total increase 
in temperature will be 1. 5 - 3 degrees C over a period of 5-10 minutes. 
27. After the temperature reaches a maximum, continue to take readings for at least five 
more minutes, so that you have a very slow linear rate of temperature change for 
your post-ignition line in Figure 2. 
28. Click on the STOP button at the bottom of the computer screen ONCE when you 
are finished with the run. The programs will run for several seconds longer, then 
stop and save your last few data points. The data is saved continually during the run, 
so if some problem occurs you will have your data saved up to that point. 
29. Transfer your data from the PC to a flash drive. The data can be open in Microsoft 
Excel. 
30. Go back to the bomb calorimetry program so that the other lab group can carry out a 
run, while you prepare your apparatus for the naphthalene run. 
Disassembling the Calorimeter 
31. Tum off the stirrer motor, remove the belt and lift the cover from the calorimeter. Set 
it on its support stand. 
32. Gently dry off the thermometer, thermistor and stirrer with a paper towel. 
33. Lift the bomb out of the bucket, remove the ignition leads and wipe them, dry the 
bomb with a paper towel. 
34. Set the dried bomb on the lab bench and open the needle valve on the bomb head 
slowly to release the gas pressure BEFORE attempting to remove the cap. This release 
should proceed slowly over a period of at least one minute. 
7-16 
35. After all the pressure has been released, unscrew the cap; lift the head out of the 
cylinder and place it on its support stand. You may have to wiggle the head back and 
forth slightly to loosen it enough to pull it out of the cylinder. Examine the interior of the 
bomb for soot or other evidence of incomplete combustion. Make note of what you see. 
If it is apparent that combustion was grossly incomplete, discard this run and do another 
with the same substance. 
36. Wipe to dry all bomb parts. Wipe clean inside of the bomb and the combustion pan 
using acetone in the fume hood. 
37. Remove and weigh any unburned fuse wire; ignore globules unless attempts to 
crush them reveal that they are fused metal rather than oxide. Subtract the mass of the 
unburned fuse wire from the initial fuse wire mass to obtain the net mass of the fuse 
wire combusted. After weighing, discard the unburned wire to garbage. 
38. Dump the water out of the calorimeter bucket and dry it thoroughly. Dry the inside of 
the calorimeter jacket before placing the bucket back in. Remember to line up the bumps 
in the bucket with the knobs in the calorimeter. 
Naphthalene Combustion 
3 9. Repeat step # I. In step #2, weigh 0.6 grams of naphthalene crystals on a tarred piece 
of weighing paper. (Do NOT obtain more than 0.7 grams.) Transfer the naphthalene to a 
mortar and pestle and grind to a fine powder. The mortar and pestle is either in the 
fume hood or on the lab bench near the bulletin board in the main lab room next to the 
pellet press. 
40. Refer to the paper next to the pellet press showinghow to make a pellet with the 
pellet press. Transfer the naphthalene powder to the die and form a firmly pressed 
pellet. Once you have removed the pellet from the die, use forceps to pick up the tablet 
and weigh it on a tarred weighing paper. Record this mass. 
Rinse all equipment and glassware that has contacted the naphthalene with acetone 
over a funnel inserted into the acetone-naphthalene waste bottle in the fume hood. 
Return cleaned equipment to its proper location for someone else to use. 
41 . Continue on with steps #4 through #42 
7-17 
CLEANING AND ORDER: 
1. Calorimeter is dismantled and its parts are cleaned and dried. 
2. All extraneous paper and unburned fuse wire is.in the garbage. 
3. Volumetric flask is filled to the 2.000 L mark with room temperature distilled 
water. 
4. Get approval of your TA that everything is m an order to not to get any 
deductions from your lab grade. 
3. In Lab Questions 
1. Why is it important to keep from interchanging parts between the two calorimeters 
available to use during the experiment? Would the same concern arise from using 
different amounts of water in the calorimeter bucket for each run? 
2. Why must the bomb be flushed with oxygen gas before it is finally filled for the 
combustion? If it is not flushed with oxygen, do you think it would affect the quality 
of your results? 
3. In a bomb calorimetry experiment where a bomb was immersed in water at 25°C, the 
following data were obtained: on calibration by combustion of 0.771g of benzoic 
acid (C6HsCOOH, the temperature of the water rose by l.97°C; and on combustion of 
1.214 g of solid naphthalene (C10Hs) the temperature of the water rose by 4.78°C. 
Calculate the standard heat of combustion for naphthalene in MJ mo1·1. For benzoic 
acid, ~H0combustion = -26 430 Jg·1 at 25°C (combustion to liquid water). NOTE: You 
can assume ~H = ~U in this problem under stated conditions. 
4. If benzene is made up of 6 C-H bonds, 3 C-C bonds and 3 C=C bonds, estimate the 
resonance stabilization energy for benzene vapor in kJ mo1·1. Use the average bond 
energies from Table 1 for the different chemical bonds in benzene and its combustion 
reactants and products to estimate benzene's enthalpy of combustion. The 
7-18 
experimentally measured enthalpy of combustion of liquid benzene at 25°C to give 
carbon dioxide gas and water vapor is -3135.6 kJ mo1·1• The standard enthalpy of 
vaporization of benzene at 25°C is 33.62 kJ mo1·1• Comment on the difference 
between the measured and estimated (theoretical) enthalpy of benzene combustion. 
4. Data Analysis 
1. Construct a graph in Excel like is shown in Figure 6, using your data for each 
run. This is accomplished on Excel by the following: 
a) Highlight all data, click on chart wizard and choose the x-y scatter with 
the smooth lines connecting the points. 
b) At step 2 - Chart Source Data choose series 
c) Then click on add. Use name = pre-ignition line; choose x-values by 
highlighting time values up to the ignition time (where the temp. begins to 
rise more rapidly); choose the corresponding y-values by highlighting 
them. 
d) Then add series three using name = post-ignition line; choose the x-
values for the time when the temperature begins to level off and choose 
the corresponding y-values. 
e) Go back to series 1 in the left menu and highlight it. Give it the name = 
ignition line, then choose the x-values by highlighting the last time value 
for the pre-ignition line to the first value of the post-ignition line. Choose 
the corresponding y-values. 
f) Click on next and continue by adding the title and axes labels. 
g) Double-click on any point on the graph to change its color; shape or series 
line color as well as ordering the series list. It is best to have the series 
listed in the same order that they appear on the graph. 
7-19 
h) Lastly, to do the linear regression on the pre- and post-ignition lines, 
which will be needed for determining Ti and Tr, go to the menu at the top 
of the screen. Under chart choose add trendline, choose the linear for 
either the pre- or post-ignition line. Go to the options tab and check 
display equation on chart. Do this for both the pre- and post-ignition 
lines 
i) ti = 160% shown in Figure 2. In placing this vertical line on your graph, 
you have several options for choosing the estimated Ti and Tr. You may 
use the last point of the pre-ignition line as the estimated Ti and the first 
point of your post-ignition line as the estimated T f OR you can use the y-
intercept of the pre- and post-ignition lines as the estimated Ti and Tr 
values. Find the difference of these values (Ti and Tr) and then take 60% 
of this difference and add it to the estimated Ti to determine T 60% = T d. 
The value of t6o% is best determined using your Excel spreadsheet of the 
numerical data and finding the time that corresponds to your T 60% value. 
To add the t6o% line to your graph, go to the Autoshapes or drawing 
feature of Excel and place the vertical line so that it intersects at 60% of 
the rise. 
j) Make any other adjustments you wish to make your graph easier to 
interpret. 
2. Calculate the instantaneous values of Ti and T fat the time of ignition, by using the 
160% value in the equations of the best-fit pre- and post-ignition lines. Report the 
value of Ti, T f and 160% and explain how each was determined in the results 
section of your report. 
NOTE: The slope of the best-fit line is an indication of the heat lost from the calorimeter 
and the heat gained by the calorimeter from sources other than the combustion of the 
sample in the bomb. These slopes should be quite small and are generally smaller than 
the tolerance limit of the thermistor used to measure the temperatures. IF you had to 
carry out uncertainty analysis on this experiment, you would have to use the larger of the 
7-20 
two values (slope of the best-fit line and the thermistor tolerance limit) as the uncertainty 
in Ti and T f that would be propagated. 
3. Calculate the heat capacity of the calorimeter. 
4. Calculate the heat of combustion of naphthalene, AU in kJ g-1• 
5. Calculate the molar heat of combustion of naphthalene, AUmo1arin kJ mo1-1• 
6. Using the molar heat of combustion of naphthalene, calculate the experimental 
enthalpy of combustion of naphthalene, AHcombustion naph(s) in kJ moJ-1 usmg 
equation 6. Reference to the caption of Figure 6 may be helpful here. 
7. Find the value for the enthalpy of sublimation of naphthalene as well as the 
enthalpy of combustion, &II°, by referring to: 
http://webbook.nist.gov 
click on: NIST chemistry webbook 
then click on: search options 
then click on: name 
put in naphthalene and check phase change and condensed phase boxes 
Use the average .Mlsub for naphthalene that you come to at the bottom of the 
first table. 
Use the average .Mlc0 for naphthalene. This will be considered the literature 
value for AH0 combustion, naph(S). 
8. Determine the theoretical AHcombustion.naph(g) from the bond energies given in Table 1. 
Keep in mind these values are for gaseous molecules only. Write the result as a 
thermochemical equation. 
9. Using Hess's law with the LlRsub, naph found on the NIST website, the heat of 
vaporization of water as 40.67 kJ/mol and the thermochemical equation determined in 
data analysis #8, calculate the theoretical AHcombustion,naph(S) starting with solid 
naphthalene reacting with gaseous oxygen and producing gaseous carbon dioxide and 
7-21 
liquid water. Show the summation of thermochemical equations and the net 
thermochemical equation for this determination. 
10. Compare the experimentally determined Affcombustion, naph(s) to the literature value for 
~Hcombustion,naph(s) found on the NIST website. 
11. Calculate the absolute value of the difference between the theoretical 
~Hcombustion,naph(s) calculated in data analysis #9 and the literature valuefor 
Affcombustion,naph(s) found on the NIST website. 
12. Be sure that you have shown detailed sample calculations for each different kind of 
calculation. If unsure of what is expected here, refer to your introductory material for 
the course or ask one of the T As or the instructor. 
13. Calculate uncertainty of all experimental values you reported. 
5. Report Questions 
1. Convince that the uncertainty in ~ T is the single major source of error in the final 
result. A concrete example such as, showing how much the experimental 
Aff0 combustion,naph( s) changes if you change ~ T by 0 .1 K is expected. 
2. a) Comment on the meaning of the difference between the theoretically determined 
~Hcombustion, naph(S) and the literature value for Affcombustion,naph(S) found on the 
NIST website. 
b) Look up the resonance energy of benzene in reference 5 and see how it compares 
to the resonance energy of naphthalene. Is this what you expected? Explain. 
7-22 
References: 
1. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in Physical 
Chemistry, 6th ed., McGraw-Hill Co., Inc., 1996, p. 145-158. 
2. Instructions for the 1341 Plain Jacket Oxygen Bomb Calorimeter, Manual No. 
147, Parr Instrument Co., Moline, Ill. 
3. Operating Instructions for the 1108 Oxygen Combustion Bomb, Sheet No. 205M, 
Parr Instmment Co., Moline, Ill. 
4. Pine, S. H. Organic Chemistry, 5th Ed., McGraw-Hill: New York, 1987. 
5. McMurray, J. Organic Chemistry, 5th ed, Brooks/Cole Publishing Co.: CA, 2000, 
p. 564-566 
6. Atkins, P.; de Paula, J. Physical Chemistry, 7th Ed. , W. H. Freeman and 
Company: New York, 2002, p.55. 
8-1 
Pyrene Excimer Formation Kinetics 
Objectives 
• To study the complex photophysics (luminescent properties) of pyrene using fluorimetry. 
• To explore a complex kinetic system comprising two parallel and two consecutive 
reactions, that is, to determine the kinetic rate constants associated with pyrene excimer 
formation and decay using time-resolved laser photolysis. 
Introduction 
Polycyclic aromatic molecules, such as pyrene (Py), in the singlet excited state can react 
with a ground state molecule of the same type forming an excited state dimer called an 
excimer[ll. This laboratory exercise will explore the excited state 
of pyrene (*Py) and its excimer (*Ex) to determine the rate 
constants associated with the various steps in this complex kinetic 
system. 
Pyrene excimer formation 
Pyrene is a planar, polycyclic aromatic hydrocarbon 
Figure 1. Structure ofpyrene. 
(Figure 1 ). Pyrene and its derivatives are used commerciall]'.'. to 
produce dyes and as molecular probes in fluorescence spectroscopy due to its high quantum yield 
and long lifetime. The emission spectrum of pyrene is sensitive to solvent polarity; therefore, 
pyrene has been used as a probe to assess solvent microenvironments. 
The pyrene absorption spectrum lies in the UV region of electromagnetic radiation; 
therefore, UV light will excite pyrene (Py) from its ground state to a singlet excited state (*Py). 
The quantum yield for pyrene fluorescence is relatively high, so the resulting emission is intense, 
and due to the relatively long lifetime it is easy to detect. The emission spectrum sho\.\n in 
figure 4 varies depending upon the concentration of pyrene, suggesting multiple luminescent 
species, which makes the emission decay rate wavelength-dependent. We will use interference 
filters to observe each of the species (*Py and *Ex) separately during laser photolysis as their 
emission is well resolved. The pyrene monomer has structured emission at a shorter wavelength 
than the broad structureless emission of the excimer. The absorption spectrum of highly 
concentrated pyrene solutions is a near mirror image of the pyrene emission. This emission and 
8-2 
absportion corresponds to the 1Lb (Platt notation, see ref 2) excited state of pyrene, which is the 
lowest energy excited state. This is not seen for the ~ 10 µM solution because it is weak due to 
symmetry. The absorption seen for that low concentration solution corresponds to the transition 
from the 1 A ground state to the 1La excited state. 
1.2 U) 
t 
*Ex -2.285mM :t= - 2rnM c 8 
-1.725 mM ::J - l.5mM 
w 1.0 - 0.973mM .0 tLb il - t rnM 
-0.506mM ..... - 0.5m11 () ~ I! - 0.0098mM e z 
~ 
-0.0l mM 0.8 ~ 4'. ·u; 
Ill c 
Cl'.'.: 
0.6 (!) 4 ....,, I \ c 0 (/) 0.4 c 0 2 Ill ' ii) 
<{ fl) 02 E i) w 0 ,l 
0.0 
310 320 330 340 350 360 370 380 390 3!;'.) 400 4~0 500 55C eoo C.fil 1~-0 
WA V E L E N GT H (nm) WAVELENGTH (nm} 
Figure 4. Left: Absorption spectra (left) of pyrene in decane with wavelength resolved pulse profiles of our dye 
(366 nm) and nitrogen (337 nm) lasers. Right: Emission spectra ofpyrene in decane 
As mentioned previously, excited pyrene (*Py) can react with ground state pyrene (Py) to 
form an excited state dimer (*Ex), referred to as the pyrene excimer. The reaction mechanism is 
described by the following reactions: 
Py + hv --. *Py (excitation) (1) 
• ko Py--. Py+ hVM (singlet pyrene decay accompanied with fluorescence) (2) 
rfn addition to processes l and 2, at high pyrene concentration the following reactions occur: 
.. k1 * 
Py+ Py Oil k-~ Ex (excimer formation) (3) 
k1 
*Ex ~2Py + hvE (excimer decay accompanied with fluorescence) (4) 
The rate constants~ and kz also include nonradiative decay mechanisms (not show in scheme). 
Photo-induced chemical reactions differ from thermally-induced ones. In the case of 
photochemical reactions, the reaction will not occur if the reactants do not encounter each other 
within the lifetime of the excited state. This is why Py and *Py do not react in dilute solutions. 
In sufficiently concentrated solutions (where the collision frequency is high enough), *Ex 
formation competes with *Py luminescence decay. For these concentrated solutions, the 
absorbance at 337 nm is so high (Figure 4) that laser excitation creates a concentration gradient 
8-3 
of *Py within the cell. The absorption spectrum of the concentrated pyrene solution can be used 
to identify a different wavelength for which the absorbance is in the right range (0.2<A<0.4). In 
this case, 366 nm is appropriate, and an approximately homogeneous distribution of excited state 
molecules results from excitation at that wavelength. 
Rate constants describing the pyrene photophysics and photochemistry 
The complex kinetics of the pyrene system involves a number of rate constants (Figure 2). 
The first order decay of *Py fluorescence to the ground state is described by ko. The second-
order rate constant for the formation of *Ex is k1 and the first-order rate constant for the 
dissociation of *Ex to Py and *Py is k- 1. The fluorescence decay rate constant of *Ex is k1. 
Py + *Py 
*Ex 
hvl hvo 
absorption 1 fluorescence 
ko 
Distance 
Figure 2. Jablonski diagram for pyrene photochemistry. 
Using Figure 2 and using that k1 is negligibler3•4J, the rate equations that describe the 
time-dependent concentrations of *Py and *Ex can be written: 
d[*Py]=-(k +k[Py]\f*Py] (5) 
dt 0 l JI. 
d[* Ex] =-(k2 ~* Ex]+k1[Py] (*Py] (6) dt 
By assuming pseudo-first order kinetics, the system can be solved analytically by first solving 
equation 5 and substituting into equation 6. Applying the conditions that the initial 
concentrations of *Py and *Ex are [*Py]o and zero, respectively, gives: 
[*Py]= [*PyJoe-x' (7) 
[*Ex]= (k1 [Py][*PyL )(e-x' _ e-k11) (S) 
k2 - X 
WhereX= ko+ k1[Py]. 
Laboratory Procedure 
The instructor or the teaching assistant will 
provide detailed directions for the use of the Horiba 
Scientific Fluorolog FL-3 spectrofluorimeter, the 
Cary 4000 Varian UV-VIS spectrophotometer, and 
the laser photolysis apparatuses with lasers from SRS 
(model NL-100, A.em= 337.1 nm, pulse width= 3.5 ns) 
and OBB (model, ~m = 366 nm, pulse width = 0.8 ns 
half width), a photodiode from Electro-Optics 
sample 
Holder 
• I 
I 
D 
Nitrogen 
Laser8-4 
Photodiode 
Optical 
filter 
Oscilliscope 
(50-0terminator) 
Figure 3. Laser photolysis setup. 
Technology, Inc (model 23-2618A, rise time= 0.5 ns), (400 ± 5) nm optical interference filter, 
500 nm band-pass optical filter, and a Tektronix 200 MHz and 500 MHz storage oscilloscope 
(model TDS 2022B and TDS 3022B). To obtain sufficient data to determine the reaction rate 
constants for pyrene excimer formation, measure the luminescence decays of nitrogen-purged 10 
µM, 0.5 mM, 1.0 mM, 1.5 mM, and 2 mM pyrene in decane solutions. The samples are 
nitrogen-purged to prevent quenching by oxygen. In addition, absorption and emission spectra 
of the pyrene solutions are needed. A 2.0 rnM solution of pyrene in decane will be provided. 
Important: In order to finish this lab in the allotted time, your group will need to be organized 
and split up to complete several e~eriments at a time. The steps do not need to be done in order. 
The absorption spectra can be{aicen before purging with nitrogen, but the laser photolysis and 
fluorimetry must be done after purging with nitrogen. 
1. Dilute the 2 rnM pyrene in decane solution provided to create 10 µM, 0.5 rnM, 1.0 mM, 
and 1.5 mM solutions. Use the density of decane (0.73 g/rnl) to determine the 
appropriate masses of decane to add. 
2. Take an absorption spectrum of each of the pyrene solutions between the wavelengths 
300 and 400 nm. The literature extinction coefficient for pyrene is 8335 = 5.40 x 104 
M·1cm·1 (1). Determine and record the optical density (O.D.) at 337. l and 366 nm from 
the absorption spectrum. 
3. Deoxygenating the pyrene solutions. The samples will be purged and sealed in advance. 
8-5 
4. Take an emission spectrum of each pyrene solution. The TA will have the instrument 
and lamp on and ready to run samples. Please do nor touch any switches or shutters on 
the instrument. The measurement will be that of an emission scan with A.excitation= 337.1 
nm for the 10 µM solution and 366 nm with the others. The emission scan range will be 
from 350 to 500 nm for the 10 µM sample and 375 to 700 nm for the other samples. 
5. A laser pulse profile is required as a test of the detection system to ensure that results of 
luminescence decays for samples are not artifacts from continuous excitation within the 
laser pulse. This is especially true at short time scales. To take a laser pulse profile, 
remove the filters from in front of the photodiode. Use the 5 ns/division time scale. 
NOTE: When using the laser photolysis apparatus, EVERYONE near the setup MUST be 
wearing eye protection (protection goggles for 366 nm can be found in the laser dark 
room)! UV light can cause irreversible damage to the eye, plastic and amorphous glass 
will not transmit UV light at 3 3 7 .1 nm. Place a piece of aluminum foil in front of the 
laser (at a 45 degree angle with respect to the photodiode). The instructor or TA will 
start the laser. The small black knob on the laser controls the laser pulse rate. Turn on the 
oscilloscope, press ACQUIRE then SAMPLE then RUN. At this point you may want to 
adjust the pulse rate. The signal on the oscilloscope is the laser pulse profile. Press 
SA VE/RECALL and save as a .CSV file to a USB flash drive located on the front of the 
oscilloscope. Note the file name given on the oscilloscope screen. 
6. Remove the aluminum foil and carefully tape a 400 nm filter to the front of the 
photodiode. Take a luminescence decay of each pyrene solution with this filter by 
placing the cuvette in front of the laser pulse and photodiode with A.excitation = 337.1 run 
for the 10 µM solution and A.excitation= 366 nm for all others. 
7. For all of the solutions other than the 10 µM, take a luminescence trace using the 500 nm 
filter. Use an excitation wavelength of 366 nm. 
Data Analysis 
1. Plot the absorption spectra and identify the 337 nm and 366 nm excitation wavelengths 
on the graph. The comparison indicates the need to use different excitation wavelengths. 
8-6 
2. Normalize the emission spectra with respect to the third vibrational peak in the monomer 
spectrum. The increase in the intensity of excimer fluorescence on increasing the pyrene 
concentration indicates that the pyrene ground state is involved in excimer formation. 
3. Determining ko. Plot the luminescence decays (Figure 5) for all pyrene solutions on the 
same graph (obtained with a 400 nm filter), normalize them, and fit them with single 
exponential decays. From the fit of the luminescence decay for the 10 µM pyrene 
solution, determine kobs,o (this is ko) and from the fits of the other luminescence decays, 
determine kobs values for each concentration of pyrene. 
o,ot 
.......... - 0,01mlil 
en - 0.51111! -4 
±! - 1mM ~ c ocs "' 
- -:i. :" 0"1.! 
-.:...:!~;!. 
-·e~ 
::i ... 
_o 
_Q '- 00! ro .. . , 
"'"-' "' 
z. s ·w oo:; ~ 
c 
Q) ....... 
c 
o~A 
-~ 
c 
0 
·w 0 ·J' ~ (/) 
1~ 
w 
0 00 
0 1 O\l 200 3Xl !OQ soc 600 ;-oo 
T I M E (ns} 
Figure S. Fluores~ence decays of the pyrene monomer with single exponential fits over a range of concentrations. 
The natural logs are plotted in the inset. 
4. Determining kJ. Plot the values of kobs versus pyrene concentration. Apply a linear fit to 
these data to show that pseudo-first order kinetics is obeyed and detennine the value of 
k1 from the slope. 
5. Determining k-1. Explain why the value of k-1 is negligible in comparison to the other 
rate constants at room temperature using the emission spectrum of concentrated pyrene 
(Hint: Look at the Jablonski diagram and try to approximate the binding energy of the 
excimer). Also, plot the natural log of the luminescence decays of the pyrene solutions 
with the 400 nm filter and explain how these results also suggest k-1 is negligible. 
6. Plot the laser pulse profile and luminescence build up (5 ns/division) of concentrated 
pyrene obtained with the 500 nm filters on the same graph (Figure 6). This will show 
that the laser is fast enough to monitor excimer formation. 
8-7 
,,........ 
rn 0,;)~ 
/ 
±:: 
c 
::J 
-
..Q () ,;) 4 .__ 
ro 
~ 0!.)3 /' 
(/) 
c 
Q} ....... 
0 .02 -- pulse profile c 
c -- 1 mM , i_ = ~.oo nm ..... 
0 
(/) ·) !) 1 
(/) 
"E~ w 0 .') •) 
- <O 1J tO 20 30 40 5·) 60 
T I M E (ns) 
Figure 6. Luminescence decay taken with 500 nm filter and laser pulse. 
7. Determining ki. Use a mathematical fitting program such as MATLAB and Equation 8 
to fit the excimer fluorescence traces using the rate constants already determined in steps 
3 and 4. A MATLAB script will be provided by your TA. If necessary for a good fit, ko 
and ki may be adjusted within experimental error. Average the values obtained and use 
their range as an approximate experimental error in the rate constant. 
Report Question: Why is it important to have an approximately homogeneous distribution of 
excited state pyrene molecules when performing laser photolysis to study the kinetics of the 
system? 
References 
1. Birks, J.B. Photophysics of Aromatic Molecules; Wiley-Interscience: London, 1970. 
2. Platt, J. R. J Chem. Phys. 1949, 17, 484-495. 
3. Hanlon A.D. and Milosavljevic B.H., Photochem. Photobiol. Sci. , 12 (5), 787-797 (2013) 
4. Hanlon A.D. and Milosavljevic B. H., J Lumin., 157, 16-20 (201 5) 
Polypropylene Phase Transitions 
Studied by Differential Scanning Calorimetry (DSC) 
Objectives 
• To determine and compare the phase transitions of amorphous and isotactic 
polypropylene. 
• To determine the enthalpy of crystallization of isotactic polypropylene. 
• To calculate the degree of crystallinity of the "supposed" amorphous and isotactic 
polypropylene samples. 
9-1 
• To determine the glass transition temperatures (T g) of amorphous PP and prove that there 
is no glass transition in isotactic polypropylene. 
• To calculate the entropy of crystallization of the isotactic polypropylene. 
• To calculate the entropy change associated with the glass transition. 
HazardsThe differential scanning calorimeter used in this experiment is extremely sensitive, can be 
damaged easily and repair costs are exorbitant; therefore, extreme care must be used when 
operating the instrument. The following concerns are of special importance: 
• The cell (sample compartment) lid is automated and must not be opened manually 
or severe damage will be done to the instrument. 
• The nitrogen gas must be maintained at a pressure of no higher than 20 psi, or 
again, severe damage can be done to the instrument. 
• The cell and its components get very hot and the thermocouples inside are very 
fragile therefore only use tweezers to load sample pans. 
• If you are unsure of a procedure or want to attempt a new procedure on the DSC, 
you must consult Dr. Milosavljevic or a T.A. 
•Turning on and shutting off of the DSC, along with any maintenance will be 
performed by Dr. Milosavljevic or a T.A. 
Isotactic PP Atactic PP 
1 
Materials and Instrumentation 
• TA Instrument DSC Q200 differential scanning calorimeter 
• Emachines T3300 desktop pc 
•Software: TA Instrument's Explorer and TA Universal Analysis 2000 
• 3 Hermetic Tzero aluminum sample pans and a set of tweezers 
• Amorphous polypropylene, Aldrich (CAS 9003-07-0) 
• lsotactic polypropylene, Aldrich (CAS 25085-53-4) 
•Ultra-high purity nitrogen cylinder (CAS 7727-37-9) 
Introduction 
9-2 
Differential scanning calorimeters are a widely used therm6analytical instruments due to 
their. ease of use, relatively fast data collection times and the ability to use small sample sizes. 1 
DSC has been applied to many fields such as the characterization of materials (especially 
polymers), quality control such as purity determination, biochemical research into the stability of 
proteins, nucleic acids and membranes, kinetic investigations, the evaluation of phase diagrams 
and other areas as well. 
A DSC measures the energy as heat flow to or from a sample at constant pressure during 
a chemical or physical change in the sample.2 The measurement is made by linearly heating the 
sample and a reference at the same rate; to maintain the sample and reference at the same 
temperature when the sample is undergoing a physical or chemical change, more or less energy 
must be supplied to the sample compared to the reference depending on whether sample is 
undergoing an endothermic or exothermic process. This difference in energy being supplied to 
the sample relative to the reference is the measured heat flow. 
The heat transferred to a sample when there is no chemical or physical change is q = 
p 
2 
C LJT, where LJT =T - T and the heat capacity C is assumed to be independent of temperature. 
p 0 p 
During a chemical or physical process there is excess heat transferred q to the sample 
p.ex 
2 
9-3 
2 
compared to the reference, and the total heat transferred is therefore q + q . The excess heat 
p p,ex 
can be viewed as a change in the heat capacity, and the resulting heat capacity is C + C which 
P p,ex 
gives 2 
q + q = (C + C ) L1T thus 
p p,ex p p,e 
C = q. I t1T 
p,ex p,ex 
The DSC data in a thermogram is therefore a plot of C against T. A physical or chemical 
p,ex 
change represented by a peak in a thermogram can be used to find the corresponding enthalpy of 
the transition from 
2 
where T and T are the beginning and ending temperatures of the transition. 
I 2 
In this lab, two types of the polymer polypropylene which have different tacticities will be 
studied by DSC. Tacticity indicates the local stereochemistry of the pendent groups (H, CH3) in 
3 
polymers. 
Polypropylene is a Jong carbon chain in which each backbone carbon atoms has one H 
and CH3 group. In isotactic polypropylene all of the methyl groups ire in the same position at 
each stereocenter in the carbon backbone. Amorphous or atactic polypropylene has a random 
distribution of methyl groups. 
Isotactic polypropylene is able to form a crystalline structure which is geometrically 
ordered in the appropriate temperature range. Due to the random arrangement of the methyl 
groups in atactic polypropylene, it is not able to crystallize and can only form an amorphous 
solid. The degree of crystallinity of a sample of isotactic polypropylene can be found by divi<;ling 
the enthalpy of fusion of the crystalline melting peak by the enthalpy of fusion of a pure sample 
of isotactic polypropylene. 
3 
9-4 
Experimental Procedure 
1. To the right of the desk.top PC, in the top drawer, you will find three bottles labeled PPA, 
PPC and R. These bottles contain your polypropylene samples and reference (PP A = 
amorphous, PPC = isotactic and R =reference). Also, in one of the black TA boxes in the 
same drawer is the tweezers you will use to load the cell. 
2. Check that the pressure gauge on the nitrogen tank reads 20 psi, if it does not, ask a TA to 
adjust the pressure. Exceeding 20 psi can damage the instrument. 
3. On the desk.top pc, open the TA Instrument Explorer program by clicking on its desk.top 
icon. 
4. Next, double click on Q200-1 724 at the left side of the window. 
5. Check that the cell is at room termperature and that the sample purge flow is 50 mL/min 
by looking in the signal pane in the upper right hand side of the window (see figure 
below). 
6. If the cell is not at room temperature, go to control (top left side of window) and in the pull 
down menu click on Go to Standby Temp and check that the temperature adjusts 
accordingly. If the sample purge flow rate is not 50 mL/min, click on the Notes tab at the 
top of the middle pane. Then type 50 in the box labeled Flow Rate and click apply at the 
bottom of the middle pane. 
7. Next you will load the cell with one of the polypropylene samples and the reference. First, 
go to control and in the pull down menu click on lid and then open. (If the cell does not 
open, notify a TA) 
8. Use the tweezers to remove the reference from the R bottle (bottom of pan is not crimped) 
and gently place pan on the top of left rear cylindrical thermocouple. (Caution: the 
thermocouples can be easily damaged) 
9. Place a sample pan (PPA or PPC) on the right.front thermocouple with the tweezers. 
10. Then click on control and in the pull down menu click on lid and then close. 
11. Next, at the top of the middle pane click on summary and check that the mode is 
standard, the test is custom and that the sample size is either 9.3 mg/or PPA or 9.5 mg 
for PPC. Also, take not of the number at the end of the datafile name. Your file will be 
listed as the next higher number. 
12. Click on the procedure tab at the top of the middle pane. Check that the test is custom 
and that the method name is P PA-1 . You should take note of the temperature program in 
the segment description either in the middle procedure pane or in right middle pane 
labeled Running Segment Description. · 
13. After you have checked all your experimental parameters, you can start the experiment 
by clicking on the green circle with the black triangle at the top left of the window. The 
4 
9:.5 
red circle with the black square, to the right, is if you need to stop the experiment 
otherwise the experiment will stop on its own after completing the temperature program. 
14. The status bar at the bottom of the window will indicate when the run is complete. The 
data will be automatically stored. You can then run your remaining sample by following 
the same procedure. / 
Data Analysis. 
I. Minimize the Explorer window and open the TA Universal Analysis program by clicking 
on its desktop icon. 
2. To open your data file follow the path: File--+ Open - DSC - CHEM457--+ "your file". 
3. A check parameters window will appear, click OK, then your DSC thermogram will be 
displayed. 
4. To zoom in on a feature, left click near the feature and drag a box around. Then left click 
in the box. 
5. To find the glass transition temperature, click on the Tg icon or you can find it in the 
analyze pulldown menu at the top of the screen. A red crosshairs should appear, if it does 
not, left click on the thermogram. To move the crosshairs, left click on it and drag. To set 
a marker, double left click on the marker. When you have set the first marker to one side 
of the glass transition, set a marker on the other side by left clicking on the thermogram. 
Then right click to accept limits and temperatures will appear next to the glass transition. 
By convention the inflection point is taken as Tg. 
6 . To integrate a peak, go to analyze and in the pull down menu click on integrate and then 
linear; or you can click on the linear integration icon on the toolbar. Left click on the . 
thermogram next to the peak you want to integrate and then left click on the thermogram 
on the opposite side of your peak. Right click to accept limits. The enthalpy of the 
transition should appear along with the peak temperature. 
7. Create a plot showing the change of entropy versus temperature for amorphous 
polypropylene in the temperature range (Tg- 20 °c, Tg + 20 °c). Follow the instructions 
below: 
Open your data in Excel, where you will see four columns. The second column contains 
temperature data. The third column contains heat flow data. Start by preparing two new 
columns containing 1) Cp and 2) C/f'. 
(Hint: Divide heat flow column by the heating rate to get Cp. Divide Cp column by 
temperature column to get CplT.) 
5 
Plot this column against temperature to get ~ vs T. You are now ready to integrate the 
T 
areas under this curve to obtain .'.18 values at different temperatures. 
T:z 
9-6 
LlS= J ;dr 
--
T. 
Tg-17 
Tg+20 
v 
I 
T~~-;1 
I 
I 
J 
I 
Tg-20\ J ) ,, 
\ ~~ ,, 
L--
1rt Poll'll Int Patig1 
..... '" 3..t ~ .... ,_,_ 
MC 
~a «lt11 pomt 
~ ... 
TEMPERATURE 
To obtain a column for L1S values at different temperatures, you 
will perform 40 separate integral calculations for the 
temperature range (T g - 20 °c, T g + 20 °C). 
The lower boundary condition (Tg- 20 °C) will be the same for 
every integration. The upper boundary condition varies for each 
data point: 
The first data point will range from T g- 20 °c to T g - 19 °c; the 
second data point will range from T g - 20 °c to T g - 18 °c, etc. 
You are increasing the range by I degree Celsius each time. 
When you're finished you should have a column for .'.18 at every temperature from 
(T g - 20 °c, T g + 20 °c). Plot this column as a function of temperature. 
8. Refer to the Atkins handout on ANGEL and compare your plot with the one shown in the 
handout. Comment on the differences in the observed slopes between the two splots and 
explain them using what you know about heat capacity. 
References 
1. Hahne, G.; Hemminger, W.; Flarnmersheim, H.J. Differential Scanning Calorimetry; 
Springer: New York, 1995, p. 3. 
2. Atkins, P.; de Paula, J.; Physical Chemistry, Vol. 1, Oxford University Press: Great 
Britain, 2006, pp. 46, 47. 
3. Anslyn, E. V.; Dougherty, D. A. ; Modern Physical Organic Chemistry, University Science 
Books: U.S.A., 2006, p . 331. 
6 
Fluorom·etric Measurement of the Rate Constant and Reaction 
Mechanism for Ru(bpy)32+ Phosphorescence Quenching by 02 
Objectives 
• To understand the_ basic principles of luminescence spectroscopy.' 
10-1 
• To construct the Stem-Volmer plot m order to detennine the rate constant for 
luminescence quenching. 
• To determine the quenching mechanism 
In trod uctio.n 
Luminescence spectroscopy has been a remarkable tool in the last two decades, 
mostly due to light induced chemical changes observed in many photochemical reactions 
including biological processes. 1•2•3 These chemical changes occur as a result of the 
promotion of molecules from ground-to excited energy levels. While the applicable areas 
for use and the instrumentation of luminescence spectroscopy are getting broader, it 
would be an asset to understand the basic principles of luminescence. 
Molecular Photophysics 
In the ground energy state molecules exists in their lowest energy state, where all 
the electrons are in their most stable orbitals. Upon absorption of light, an electron gets 
promoted from an orbital that is filled in the ground state to a vacant orbital of higher 
energy. The excited molecules prefer to return back to their ground energy states and the 
energy of the excited state may dissipate in a number of ways. An outline of these 
processes are given in Figure 1.2 
Structure of Ru(bpy)32+ 
. 1 
Radiative 
1) Fluorescence 
2) Phosphorescence 
Light 7 Light 
hv 7 hv' 
Absorption of light 
Electronic excitation 
Dissipation mechanisms 
Chemical 
1) Singlet 
2) Triplet 
Light 7 Chemistry 
hv7~G 
Radiationless 
Physical 
1) Internal conversion 
2) Intersystem crossing 
Light 7 Heat 
hv7Q 
Figure 1. Overview of molecular photophysics and photochemistry.2 
10-2 
In the next sections, radiative and radiationless (non-radiative) energy dissipation 
processes are briefly outlined. 
Radiative Mechanism 
In the radiative mechanism, a molecule loses its energy as a photon and goes from 
a higher energy state to a lower state. The type of the radiative process is determined by 
the multiplicity of the states between which transitions are taking place. In the excited 
state, two unpaired electrons in different orbitals can exist with opposed spin or with 
parallel spin orientation. Different spin orientation results in a singlet, and parallel spin 
orientation results in a triplet state multiplicity. Based on the multiplicity of the states, 
there are two major radiative processes: fluorescence and phosphorescence. In 
fluorescence, which is a spin-allowed process, transition takes place between the states of 
the same multiplicity, S1 7 So. In phosphorescence, which is a spin forbidden process, 
transition takes place between the states of different multiplicity T 17 So. Figure 2 shows 
the processes which may take place during absorption and radiative energy dissipation 
processes along with the orientation of the electron spin. 
2 
hv + ~ 
Singlet 
(spins paired) 
hv + ~ 
Singlet 
(spins paired) 
electron jump 
electron jump 
and spin flip 
electron jump 
electron jump 
and spin ftip 
t 
f 
Excited singlet 
(spins paired) 
t 
t 
Triplets 
(spins parallel) 
(Spin allowed 
absorption) 
(Spin forbidden 
absorption) 
+ hv (fluorescence) 
+ ltv 
•Ph?Sphoresa:nce) 
Figure 2. Absorption and radiative energy dissipation processes along with the 
orientation of the electron spin.2 
Radiationless Mechanism 
10-3 
In radiationless or non-radiative mechanisms, a molecule loses its energy without 
any photon emission. The radiationless mechanism can involve both photophysical and 
photochemical processes. Photophysical processes can be categorized as internal 
conversion (transitions between states of the same multiplicity, such as from S2 to S1 or 
from T1 to T1), and intersystem crossing (transitions between states of different 
multiplicity, such as from S1 to T1). In photochemical processes the excited state of one 
molecule and a state (usually the ground state) of another molecule participate into 
radiationless transitions. 
The Jablonski diagram presents the processes that occur between the absorption 
and emission of the light as shown in Figure 3 .1 Radiative and radiationless mechanisms 
are shown by solid and dashed arrows, respectively. In this diagram So represents the 
ground, and S1 and S2 represent the electronic excited energy states. Each one of the 
electronic states has a number of vibrational energy levels shown by 0, 1, and 2. This 
figure shows that upon absorption, molecules get excited to higher vibrational energy 
level of either S1 or S2. Molecules at the upper vibrational energy levels relax back to the 
3 
10-4 
lowest vibrational energy level of S 1 through internal conversion in 10-12 s-1 or less. This 
relaxation is generally followed by the fluorescence emission which takesaround 1 o-8 s-1• 
: Internal 
1 Conversion 
Absorptio n 
2 
50 l 
0 
.::f 
I 
\I 
hv,."" 
Figure 3. Jablonski Diagram. 1 
Quantum Yield 
v Intersystem --- - - - - - -'rossing 
--~ 
Fluorescence 
hVp«' 
I"> hVF 
~ Phosphorescence,. 
, • 
These radiative and non-radiative mechanisms are all governed by individual rate 
constants. These rate constants can all be related to each other by a rate constant ratio, ¢, 
which is called quantum yield. 
Quenching 
¢ = rate of formation of product 
sum of all rates 
Quenching represents the decrease in the fluorescence intensity. Collisional 
quenching, which is one of the quenching mechanisms, occurs due to deactivation of the 
excited-state molecule upon collision with a quencher (another molecule) in solution. As 
a result of the quenching a decrease in the fluorescence intensity is observed and can be 
quantified using the Stern - Volmer equation (as given in Eq. 10).1•4•5 
Ru(bpy)l+ Luminescence and Quenching 
In this experiment, you will be studying the luminescent properties of the 
transition metal complex ruthenium (II) tris-bipyridine, Ru(bpy)32+. Irradiation of 
Ru(bpy)32+ with UV light causes the molecule to absorb energy and get promoted to one 
of its excited singlet states (*Ru(bpy)/+), where Ia shows the absorption rate. 
4 
10-5 
la 
Ru(bpy)~+ + hv-0-* Ru(bpy)~+ 
d[*Ru(bpy)j+] = I 
dt a 
(1) 
At this stage *Ru(bpy)32+ can do a number of things: 
1. *Ru(bpy)32+ can undergo rapid (- 10-12 - 10-13 s) relaxation to its lowest excited 
energy state and then fall back to its ground state by emitting a photon (fluorescence). 
This is a first-order fluorescence decay process where the fluorescence rate constant is 
denoted kt-. 
k; 
*Ru(bpy)~+ -0-Ru(bpy)j+ +hvf 
d[*Ru(bpy)j+] = -k [*Ru(bpy)2+] 
dt I 3 
(2) 
2. * Ru(bpy)5+ can lose its energy in a nonradiative fashion through heat transfer to the 
solvent and return to its ground state. These non-radiative transitions of* Ru(bpy)j+ 
in its excited state can be described in a first-order rate process with a rate constant of 
knr· 
knr 
* Ru(bpy)5+ -0- Ru(bpy)5+ +heat 
d[*Ru~py)j+ ] = -knr [*Ru(bpy)J+ ] (3) 
3. * Ru(bpy)j+ can undergo an intersystem crossing to a triplet state and then relax back 
into its ground state through phosphorescence. 
k1sc 
* Ru(bpy)j+ -0- T Ru(bpy)j+ 
kph 
T Ru(bpy)5+ -0- Ru(bpy)j+ + hup 
5 
10-6 
d[*Ru(bpy)~+] = -k (*Ru(bpy)2+] 
dt !SC 3 (4) 
d[T Ru~py)5+] = k1sc[*Ru(bpy)5+]- k ph[T Ru(bpy)j+] 
Phosphorescence in solution is very uncommon, but in the case of Ru(bpy)32+, 
does indeed occur. This luminescence activity can be quenched by molecular oxygen 
according to two proposed schemes: 
kq 
TRu(bpy)5+ ~Ru(bpy)5+ +8 02 Scheme A 
Scheme B 
For Scheme A, the relaxation of singlet oxygen to the ground state triplet form releases a 
photon of 1400 run. This provides a way to test the proposed mechanism using a state-
of-the-art IR detector. 
The situation described above can be simplified to the following scheme for the purposes 
of this lab. 
Ia 
Ru(bpy)5+ + hq ~ * Ru(bpy)5+ 
knr 
* Ru(bpy)~+ ~ Ru(bpy)5+ +heat 
kq 
* Ru(bpy)5+ + 02 ~ Quenching Products 
Excitation 
Luminescence 
Nonradiative 
Relaxation 
Quenching 
(5) 
These reactions come to a steady state if the exciting light intensity is constant and no 
irreversible photochemical reactions exist. 
6 
10-7 
The quantum yield, ¢>0 , is equal to the radiative luminescence decay rate divided by the 
sum of the radiative and nomadiative decay rates. 
* 2+ 
0 k f [ Ru(bpy)J ] 
</> = * 2+ * 2+ 
k j[ Ru(bpy)J ] + knr[ Ru(b!JY)3 ] 
(6) 
(7) 
In the presence of quencher, the quantum yield expression becomes 
The relation of kq with other rate constants and the relative quantum yield are determined 
from Stem-Volmer equation in Eq. (10). 
(10) 
Replacing the relative quantum yield by the relative areas measured from fluorescence 
spectroscopy, (area)0 /(area) vs [02] is plotted. The slope of this plot gives the relation 
between the rate constants of radiative and nonradiative radiations. 
In the absence of a quencher, the rate of disappearance of excited Ru(bpy)32+ can 
be obtained from Eq. (12). 
* 2+ 
d[ Ru~py)3 ] = -ki(Ru(bpy)~+]-knr(Ru(bpy)j+] 
* 2+ = - (k f + knr)[ Ru(bpy)J ] (11) 
* 2+ 
and d~ Ru(bpy;3 ] = -(k f + knr) dt, giving the following equation when 
[ Ru(bpy)J +] 
integrated: 
(12) 
7 
10-8 
The slope of the plot of time vs natural logarithm of Ru(bpy)32+ fluorescence intensity, 
provides kr + knr. Once k 1 + knr is known, the quenching rate constant can be found from 
the slope of the Stem-Volmer plot. 5 
Experimental Procedure 
The instructor or the TA will give detailed directions for the use of the FluroLog 
luminescence spectrometer, the Varian UV-VIS spectrometer, and the laser photolysis 
apparatus. To obtain sufficient data for a Stem-Volmer plot, you will need to measure 
the luminescence of three samples of Ru(bpy)32+: an air-saturated sample, a nitrogen-
saturated sample, and an oxygen-saturated sample. In addition, you will also need to take 
the absorption spectrum of the complex. The TA ""ill provide the Ru(bpy)32+ sample for 
you and will give you the laser photolysis data. 
Absorbance: 
1) The TA will demonstrate how to use the instrument. You will first need to take a 
blank with pure water before you take your spectrum. You will be using a 
specially modified cuvette that allows for attachment of a rubber septum. You 
should scan between 250 and 650 nm. The literature extinction coefficient for 
the complex is E4s1 = 1.41 x 104 M·1cm·1• 
Luminescence: 
2) The TA will have the instrument turned on and ready to run the samples. Please 
do not touch any switches or shutters on the instrument. The measurement will 
be that of an emission scan with A.excitation = 450 nm and the emission scan range 
from 500 to 700 nm. 
3) The first sample will be the air-equilibrated sample. Use the same cuvette used in 
the absorbance measurement. Run the scan and save your file to the appropriate 
folder. You will want the Sl data set (You can also include S l/Rl). Once 
complete, go to Analysis, and then Calculus, and choose Integrate. Record the 
Area and the Amax. You will calculate the oxygen concentration under prevailing 
8 
10-9 
atmospheric conditions (make a note of the current barometric pressure and 
temperature). 
4) The next measurement will be on an oxygen free sample. Take the cuvette to the 
laser photolysis lab table and purge with nitrogen using the set-up there. First 
place the vent needle into the septum and then insert the nitrogen needle all the 
way to the bottom of the cuvette. Let nitrogen bubble through the solution for 5 
minutes and then remove both the nitrogen needle and the vent needle at once. 
Take an emission scan and analyze using the procedure in step 3. 
5) The final measurement will be on an oxygen saturated sample. Place a new 
septum onto the cuvette and bubble pure 0 2 through the solution for 5 min using 
the same procedure as in step 4. Take an emission scan and analyze as you did 
before. You will calculate the (02] for the saturated sample. 
6) On the same sample, you will need to take an IR emission spectrum to test the 
viability of quenching scheme A. The instructor or TA will demonstrate this for 
you. 
Laser Photolysis: 
7) You will obtain laser photolysis data on the Ru(bpy)32+ sample. Please refer to 
pages 11-1 in the lab packet for the theory and data analysis procedure. 
In-Lab Questions 
1. Explain the terms ground and excited states, radiative and nonradiative decays, and 
quantum yield. Give examples of radiative and nonradiative decays. 
2. How does Stem-Volmer plot enable one to determine the rate constant for fluorescence 
quenching? 
3. Why are you using area under the fluorescence spectrum in this calculation? 
9 
10-10 
Data Analysis 
1. Make a table to list the sample number, correspondingconcentration of 02 in M and 
corresponding (area)0 /(area) ratio. 
2. Plot (area)0 /(area) (y-axis) vs concentration of 02 and obtain kq/ (kr + knr) from the 
slope of the Stem-Volmer plot. 
3. Using the data provided in the laser photolysis experiment, plot natural log of 
fluorescence intep.sity vs time and obtain the slope (kr+ knr). 
4. Calculate the quenching rate constant, kq using the results of step 2 and 3. 
5. Estimate uncertainty of quenching rate constant from linear regression analysis. 
Report in appropriate format the quenching rate constant with uncertainty. 
6. The collision rate of A and B reactants in solution can be calculated using Eq. (13) 
k 
_ 8RT 
d -
317 
(13) 
where, kct is the collision rate constant in L·mol·1sec·1, R is the gas constant in 8.314 J 
K·1 mo1·1, T is the temperature in K, and T/ is solvent viscosity ( ry = 1.0020 cP for 
water at 20°C). Calculate the value of kd for water at 20°C. 
Report Questions 
1. What is the importance of kd (the collision rate constant)? (Hint: The reciprocal of kq 
can be considered as the average time it takes for a given excited Ru(bpy)i+ molecule to 
become quenched by 02 at a concentration of 1.0 M 02). 
2 . What is major source of error in calculation of quenching rate constant? 
3. What are three common mechanisms for bimolecular quenching of an excited state? 
10 
Reference 
1. Lakowicz, J. R. Principles of Fluorescence Spectroscopy; 2nd Ed.; Kluwer 
Academic/ Plenum: New York, 1999, pp. 1-12., and pp. 237-259. 
2. Turro, N. Modern Molecular Photochemistry; University Science Books: 
Sausalito, 1991, pp. 1-15. 
10-11 
3. Barltrop, J.; Coyle J. D. Principles of Photochemistry; Wiley & Sons, Inc.: New 
York, 1978, pp. 1-100. 
4. Lagenza, M. W.; Morzzacco, C. J.; J Chem. Educ. 1977, 54, 183. 
5. Stern, O.; Volmer, M.; Physik, Z. 1919, 20, 183. 
11 
11-1 
Determining the Spin-lattice Relaxation (T1) of 1-Hexanol 
using 13C-NMR 
Objectives 
• To determine the spin-lattice relaxation times (T1) of each C atom of n-hexanol 
• To relate -re values to the atomic motion of each C atom on n-hexanol 
1. Introduction 
Nuclear magnetic resonance (NMR) has become one of the primary tools in 
organic and biochemistry for structure elucidation, primarily through routine experiments 
detecting 1H, 13C, or 15N. However, NMR has the capability to far exceed the basics; 
almost e·very nuclei in the periodic table has at least one NMR active nuclei, and many 
possess spin 1/2, making them as straightforward to detect as 13C (figure 1). 
K Ca 
Rb Sr 
Cs Ba 
• Spin 1/2 D Spin>l /2 
Figure 1. Nuclear magnetic resonance periodic table. Black squares contain atoms that have at 
least 1 NMR active isotope having spin 1/2, while white boxes contain atoms that have at least 
1 NMR active nuclei having spin greater than 1/2 (quadrupolar nuclei). 
11-2 
Experiments to determine inter-nuclear distance, through space coupling, 
coordination number and octahedral distortion are available through the use of NMR. 
This laboratory will focus on spin relaxation of a simple organic solvent measured 
through NMR. The data generated from this T l experiment will be fit to a relaxation 
equation using Mathematica. 
Theoretical Background 
Nuclear magnetic resonance (NMR) spectroscopy exploits small energy 
differences in nuclear spin levels when spins are subjected to an external magnetic field 
(figure 2). This energy difference is described by the Boltzmann distribution, 
Ni,upper = e(-r;IJli! kT) 
N i.lower 
(1) 
where N represents the spin population of nuclei i in either the upper or lower energy 
states, y; is the gyromagnetic ratio of nuclei i, B is the external magnetic field in units of 
Tesla (T), h is planck' s constant, k is the Boltzmann constant and Tis the temperature. 
The population difference in a sample of H20 in an external magnetic field of9.4 Tesla 
is: 
N 2.675 l9x l08 s-1-r-1·9.4T·l.05457 x!0-34 J·s 
H ,upper = e 1.38065xW-23 JX-1·293K = 0.999934 
N H,lower 
Since the signal intensity of all spectroscopic techniques relies on population differences 
this extremely small population difference has important consequences for NMR: the 
amount of sample required for NMR experiments is large, thereby increasing the absolute 
number of spins and increasing the absolute population difference. The presence of an 
external magnetic field causes the nuclear spins to align themselves with or against the 
applied magnetic field, dependant upon the initial energy state of the spin (figure 3) with 
the energy difference between the two spin states given by M = rB/z. 
E No Field 
Energy levels for spin 1 /2 (ex: 1 H, 13() 
00 00 m =-1/2 
... ... · .. ... 
'• 
"~ ' .. 
·-.. initial populations determined 
... / by the Boltzmann distribution ... 
•··•·.•. j:. •. •······ 
"-. .. 00000 m = 112 
Applied Magnetic Field (B
0
) 
Figure 2. Energy level diagram for a spin system. 
The magnetization vector along the z-axis is given by the vector addition of 
magnetization of them = 112 and them = - 112 (figure 3). 
z 
----- -- -
---
x 
m = 1/2 
' ' 
, 
~ 
y 
m = -1/2 
z 
x 
l:m; 
---
, 
~ 
y 
Figure 3. Magnetization vectors along +z and -z axis representing the two population 
states, followed by the resultant magnetization vector along the +z axis generated by 
vector addition. 
11-3 
However, in order to measure the difference and generate a spectrum the spin 
system is perturbed from equilibrium (magnetization along the z-axis) by application of 
an RF pulse (figure 4). The applied pulse has a tip-angle 8, which is determined by the 
time length of the applied field is turned on (pulse length). 
z 
x 
' ' 
90 
y 
z 
0 
x 
; 
; 
11-4 
y 
Figure 4. Application of a 90° pulse along the y-axis moves the magnetization vector 
from the z-axis to the x-axis. The tip angle is given by 80 0 the angle between the initial 
magnetization vector (Iz) along the z-axis and the magnetization vector after the applied 
pulse (Ix)-
Once the applied field is removed the magnetization vector relaxes back to 
equilibrium along the z-axis. This relaxation effect is termed spin-lattice relaxation, or Ti 
relaxation (Figure 5). 
z z 
'tl ---
y 
x x 
' ' 
y 
't2 
z 
I 
x 
Figure 5. Spin-lattice relaxation (Tl relaxation). Left: initial magnetization vector after 
a 90° pulse along y-axis; after a time period -r1 the magnetization vector along x has 
diminished and the magnetization along z is growing in. Right: equilibrium 
magnetization after time period -r2. 
Spin-lattice relaxation occurs due to field fluctuations at the nucleus, and may be caused 
by 
• Magnetic dipole-dipole interactions 
• Electric quadrupole interaction 
• Spin-rotation interaction 
• Scalar-coupling interaction 
• Chemical shift anisotropy 
y 
Mathematically, T 1 relaxation is described by the Bloch equation, eq. 2, 
aM . (M - lvf J --• = - y(M xB1 sm( OJ t) + M YB1 cos( OJ t ) - z 0 & ~ (2) 
The T l decay may be modeled quantitatively by setting Mx =My= 0 in eq. 2, 
d~, = { M,;, M, J (3) 
Integration of eq 3 yields, 
-I 
(4) 
which will be used to model the Ti relaxation data. 
Procedure/Data Analysis 
Two pulse sequences may be used to acquire Ti relaxation data: the inversion 
recovery method, tlir, or the T1 saturation recovery, tlsat (figure 6). Note the two 
methods differ in their mathematical fitting equations, we will use the T 1 inversion 
recovery method (Figure 6). 
(180) (90) 
1-t ~ 1 aCXl 
M(t)=M
0
(1-2e -tfT1) 
-Mo .....___ ____ _ 
t 
Figure 6. Pulse sequence and fitting equation for Tl inversion recovery experiment. 
11-5 
11-6 
How does T1 relate to Atomic Motion? 
The Tl tells us the spin-lattice relaxation of a nuclei, in this case, different 
carbon-13 atoms, but it can be extended to give us useful information about th~ molecule. 
NMR active nuclei interact in many ways, but for this experiment it is the dipole-dipole 
couplingwhich is the most important interaction. This depends on the orientation and the 
distance between the two spins. (In this case, both 13C and 1H are NMR active and so 
they interact). 
The di polar interaction ( d) is described by 
d = µo n
2
r1Y2 
47r r 3 
(5) 
where y1 & y2 =gyromagnetic ratio of the nuclei and r is the distance between atoms. The 
Ti relaxation is proportional to d2!h2. As the carbon containing group (CH2 or CH3) 
moves around, these distances between atoms (nearby 1H's change), and these changes 
are transmitted to the carbon through coupling interactions. Thus it has been shown that 
T1 relates to motion of each group in the alkyl chain through a variable -re, the effective 
correlation time for rotational reorientation, through the following equation. 
J_ _ N'( µo ) 2 n2r~r~ - re 
Ti 47r T~H 
(6) 
re= 6.72881x107 s-1 T 1 ; m= 2.67519 x 108 s-1 T 1 
where re & YH are the gyromagnetic ratio of 13C and 1H respectively, Jk = permeability in 
a vacuum, N is number of directly bonded H atoms (to the C of interest), and r cH is the C-
H distance. 1 
The Experiment 
For this experiment, you will be determining the T 1 relaxation of all six carbons 
of 1-hexanol. A degassed sample of 1-hexanol (70% in CDCb, sealed under vacuum) 
was placed in the spectrometer. This sample was tuned, meaning the NMR' s two 
11-7 
channels were tuned to the exact frequency of 13C and 1H respectively. The sample was 
locked to the frequency of the deuterated solvent (CDCb). 
NMR spectrometers are tuned to the frequency of the nuclei they study, in this 
case 13C (the frequency is approximately 100 MHz on this spectrometer). In order to stay 
correctly calibrated, we relate this frequency to another value. Deuterium becomes this 
standard. Deuterium is NMR-active, and so can be used as a comparison. This is what 
'Lock' does, and why it must be done for every experiment. Without lock, your spectra 
wilJ come out unreadable. 
Next the exact 90-times for this sample had to be determined for both 13C and 1H. 
This is the length of time that the spectrometer must pulse to rotate the magnetization 
vector 90 degrees. Hydrogen must be considered because the spectrum will be decoupled, 
and if the exact 90 time is not used for the 1H-channel, you could see splitting (coupling) 
of your 13C signal. You will be given these values in the procedure. 
You will set-up and run the inversion-recovery experiment yourself on the 400 
MHz Bruker spectrometer. The actual run time is approximately 35 mins. After this, you 
will process and analyze your data. Both running and processing your experiment will 
utilize XWIN NMR 3.1 software. 
A T1 experiment is a pseudo-2D experiment, and it will give a 2D spectrum. In 
one direction (x-axis) you will be taking frequency information, this is the 13C-NMR 
spectrum for your sample. You must vary the delay time, 't, this will become the y-axis of 
a 2D spectrum. (see below) 
I I I 
I I I i I I I 
't , secs 
I I I 
Shift, ppm 
Figure 7. Pseudo-2D spectrum you will get from this experiment. 
Fitting the plot of integral vs. twill give you a plot similar to that shown in Figure 
6. This is an exponential function. You will be asked to CHOOSE your values to place in 
11 -8 
a vdlist. What is the best way to sample an exponential function? Where do you want to 
take the most points on the curve (Figure 6)? Think about this as you choose your values. 
The better your picks for the vdlist, the better your Tl fit to the data will be! 
2. Laboratory Procedure 
Experimental Set-up 
1. Welcome to XWIN, a software program designed to run Bruker NMR 
spectrometers. The program should be open. This is the program you will be 
using both to run and to process your NMR T 1 experiment. 
2. First you will want to familiarize yourself with the layout ofXWIN. Notice 
menus are at the top. In this procedure, Menus> "Will be written with arrows for 
the initial menu and the pull-down choices. ( e.g File>Search). All the buttons you 
need later on to process will be on the left side. In these instructions, buttons will 
be underlined. Also, at the bottom of the window is a line where you will type 
commands. In these instructions, "commands" will have quotes. Always hit enter 
after typing a command! 
3. "re filename" 
The filename depends on your section and group, and should be in the form 
chem457 _s#_g% where# = your section number and% = your group number 
(Don't forget underscores!) For example, if you are in section 2, group 1 the 
filename would be: chem457_s2_gl , and you would type "re chem457_s2_gl" 
4. Choose the type of experiment you wish to run. For this experiment, you are 
running an inversion-recovery experiment. This has a pulse sequence of 180-'t-
90. 
"rpar" Choose: c13 _ Chem457 _hex (include underscore). This file contains 
parameters you need to run the experiment. 
11-9 
5. Enter the 90-time for 13C by typing "pl". Then enter the value 7.25. (This is 7.25 
µsec) 
6. You must also enter the 90-time for 1 H since this experiment uses the proton 
channel for decoupling. Because it is the pulse length for decoupling, you must 
type "pcpd2", then enter the value 109. (This is 109 µsec) 
7. Between each pulse on the carbon channel, you must allow time for the spins to 
relax to zero (equilibrium). The common protocol is to wait AT LEAST 5 times 
the longest Tl in the sample. For hexanol, a delay of 30 secs is sufficient. Type 
"dl" then enter the value 30. 
8. "edlist" Choose: vd on the pop-up menu. At the bottom of the pop-up window 
type your filename (see step 3). 
9. This will open a notepad window. In this type 10 values. This is your vdlist (see 
intro), and it will contain your 't values. You will want to make sure you include 
more points at the curve of the function (Figure 6). To do this, values should be 
closer together then spread out as they increase. 
Values of the vdlist must be typed in a certain format. Type one number per line. 
Do NOT include units - the program will assume the values are in SECONDS! 
Values less than 1 must have a zero in front of the decimal. 
See example below for format, but DO NOT use these values, you MUST 
CHOOSE YOUR OWN using the instructions below! 
f' kchex922 - Notepad t;]LQJ~ 
Fde Edit Format View Help 
50 
30 
25 
20 
15 
10 
8 
6 
4. 5 
3 
2. 5 
2 
1 
o. 5 
11-10 
Start with 10., hit enter, continue in the same manner with the next 8 time delays 
(your choice). This list is the vdlist explained in the introduction (p. 6-7). Type 
time delays in decreasing order. For the final (1 oth) point type 0.2. 
You must write down YOUR values in order (with the units). 
10. Choose File>Save, then close the window (or File>exit). 
11 . type "vdlisf' choose the name of the vd list you made in steps 8-10. 
12. "eda" In the open window, type "sol" in the bar at the bottom of the window. 
Look for PR OSOL and make sure the value directly below it says TRUE. If not, 
click it once, and it should change. 
13. "ii" This double-checks your parameters for format errors. Wait until is says ' ii 
finished'. 
14. "rga" wait until is says ' rga: finished' at the bottom of the window. 
11-11 
15. "expt" This will tell you the length of your experiment. Make sure it is not too 
long!! It should be approximately 35 minutes. lfit is much longer, see a TA for 
help. 
16. "zg" You experiment is now running. You can use this time to work on questions 
for the lab. 
Processing Tl Experiment 
1. Once your experiment is finished, you can begin processing. This experiment 
should be processed in the computer lab in Whitmore (rm 207). {Data transfers 
from the NMR computer to the lab computers every 15 minutes.} 
2. Log-on to one of the NMR processing computers (computer lab, left side. There 
are 3 of them.) If they are all full, but you see that someone is doing NON-NMR 
work on one, you may kick them off! Sign-on, then find the X-WINNMR 3.1 
icon and double-click to open the program. 
3. On the top, far left of the screen is the File> menu. Click this, then Search. 
4. For this experiment, choose the following: 
Directory = d:/data user= chem 457 *name= your filename 
*this list is in alphabetical order, search here for your sample name 
Double click the filename, and then click filmly. Now click close 
5. Look underneath the top menu and you should see your filename in the top left of 
the screen. The middle of the screen will be blank except for a message ' type xfb 
to process' Do NOT do this. Type "xt2" 
6. "edtl" Change FCTTYPE to invrec, this tells the program what functions to use to 
calculate the Tl values. 
11-12 
Phasing key 
Should show full rainbow, reds and purples 
Figure 8: The pseudo-2D spectrum. Note the full phasing key is shown. 
7. Click the +/- button 2 times, to give the full rainbow of colors on the phasing 
key(see Figure 8). This should show both the positive and negatively phased 
peaks. If you cannot see any negative peaks, try clicking *2 to enlarge the 
spectrum on the top left several times (more peaks will appear). Similarly, /2 
decreases the spectrum. 
8. Click phase. The screen will become a split-screen. The top left window is your 
full 2D spectrum. All the buttons at the top left relate to this window. The 3 
window on the right are for taking pieces of the spectrum. Buttons at the bottom 
left relate to these. (Figure 9). 
Click in the full 2D window, now click the+/- button 2 times. You can also 
enlarge the spectrum similar to step 6. 
11-13 
9. Look at the peaks on the right side of the full spectrum (these are lower shifts, 
ppm). Click row, then middle-click on the lowest one (on the y-axis). 
10. Move to position 1, by finding mov on the left side of the window, and clicking 
the 1 button. You should see a spectrum appear in box 1, the screen should look 
like Figure 9. 
CD 
c 
C/J ::+ -g 0 
(') :::J 
r+ (/) 
2 O' 3 -, 
2' 
Figure 9: Moving rows, in order to phase. 
11. Now on the original 2D spectrum, find the highest (on the y-axis) peak in the 
same column as you chose before. Click row, then middle-click the highest peak. 
12. Move to position 2, by finding mov on the left side and clicking the 2 button. 
11-14 
13. Find Qig on the left. Click the 2. button next to it. (Figure 10) 
14. Click the phO and HOLD it. While holding move the mouse up and down until 
your spectra looks phased (see Figure 11). All peaks should be above the baseline. 
Also, look at the left and right side of each peak, both should look the same 
(symmetrical). However, if you have more than one peak overlapping, these may 
be unsymmetrical and that is normal. 
15. Use Ph.l (the same way as phO) to make sure all peaks in each spectrum are 
phased. 
Figure 10: Phasing your spectra 
Spectrum Before Phasing Spectrum After Phasing 
\ ' 
-~+)~~~ ~\ ~~-~JJ1~ ~~ \ 
r--r---r--- l 
6.4 6.2 6.0 5.8 5.6 5.4 5.2 5.0 
1H Frequency (referenced from TMS) 
6.4 6.2 6.0 5.8 5.6 5.4 52 5.0 
1H Frequency (referenced from TMS) 
11-15 
Figure 11. On the left is a portion of a spectrum before phasing (unphased). To the right 
is that SAME spectrum after phasing. · 
16. Click return, then save & return 
17. Type "rspc". This will give you a ID spectrum of the first 't value from your 
vdlist. By integrating or picking peaks peaks in this window, the software "''ill 
automatically transfer this information to integrate or pick the same peaks for all 
10 't values from the vdlist! 
18. Click integrate to enter a new window. Integrating will tell you the area under 
each peak. As i; decreases, this will decrease down to null, then become more 
negative. Thus we can use the changing integral values to monitor the change in 
magnetization as a function of the delay time. 
19. Spread out the spectrum so that you can see the peaks well. (See Moving Around 
section below for buttons.) Also you may need to increase the peak size. Make 
sure you can tell where one peak ends and another begins. 
11-16 
Moving Around in XWIN 
For many tasks, you will need to change the view of the spectrwn. Gettug a 
close-up view, spreading peaks apart, increasing or decreasing the size of the peaks, etc. 
To move around in your spectrum, use the following: 
· 11<11>1 1 
Expand to show full spectrum Move to left Move to rig ht 
Expand incrementally Condense incrementally 
INCREASE size of spect , X2 INCREASE size of spectra XS 
DEGRE.A. ~: size of spE. Jra X2 DECREASE size of spectra X8 
20. Cli\, 1< t:1e le;, mouse button once. A white arrow should appear where the pointer 
is: th. is called select mode. Middle click to the left side of (where it is still flat), 
then (where it becomes flat again) on the right side of a peak. Usually a number 
(the integral) will appear on the bottom. 
21. Repeat step 19 for all 6 peaks (NOT the solvent peak, at 77.0 ppm), moving 
around the spectrum as described above. 
22. When you are done integrating, click return button (bottom left). Now click Save 
as ' intmg' and return on the pop-up menu. This will return you to regular mode. 
11-17 
23. For the next step you will need to see all the peaks. First spread out the spectrum, 
so that you can clearly see the tip of each peak, by first clicldng the expand 
button. Left clicking in the spectral window will put you in select mode. Now, 
middle-click to the left of your highest ppm peak in the sample, then middle-click 
to the right of your lowest ppm peak in the sample. This will change your viewing 
window. 
24. Type "basl" to enter a new window. This is where you will tell the program which 
peaks it should find Tl values for. 
25. Click def:·pts on the left side of the screen 
(towards the top). 
26. On the spectrum, left click once to enter select 
mode. For each of the 6 peaks (NOT the 
solvent peak!), middle click at the very tip of 
the peak. A small green arrow will appear to 
indicate a selected peaks. (see Figure 12). 
27. When you have selected all 6 peaks, click 
return, and then save & return. 
28. Click 20 in the bottom Left comer. 
29. "pd" 
Figure 12. basl Screen. Note the 
small arrow above a selected peak. 
30. Analysis> relaxation (tl/t2). This will show the data for the first peak (highest 
shift, ppm). 
11-18 
31. ''ctl" to calculate the Tl value. It will show you the T 1 curve for this peak. If you 
want, you can continue to view each curve by typing "nxtp" and repeating the 
"ct l " command. 
32. You can get a printout of all the ·calculated Tl values, as well as the integrals for 
each value from your vdlist, by typing "datl", and click 'Print' . Turn in this 
printout with your final report. 
3. In Lab Question 
1. The following is a plot of one doublet changing as a function of pulse length (pl). 
Explain what is happening overall and at each point A, B and C. (All peaks ARE 
phased correctly.) 
A 
B 
r. r JJ •• .. , ""' ..... ....,, . - . 
c 
Pulse length (pl , in seconds) 
2. You enter two important parameters for experiment, p 1 and d 1. Explain why they 
are important and what is the meaning of these two parameters? 
3. Write the equation you used to determine Ti times. 
11-19 
4. Data Analysis 
1. At the end of this report, a plot of the final 13C-NMR is given for 1-hexanol. Label 
each peak with the corresponding carbon (letters A-F). Ignore the solvent peak (a 
triplet at 77.0 ppm). Note: the shift of Cc< shift of Co, which is NOT what you 
would expect (this is a special exception for this gamma atom). 
2. Using the data in your printouts, make a plot of "t versus intensity using a program 
other than XWIN. Apply a non-linear fit to these plots. Calculate the error. 
3. Using the Tl data from XWIN, calculate the -re values for each peak. Make a 
chart with this information. 
Peak Letter shift (ppm) T l (s) -re (ps) 
5. Report Questions 
1. Compare the Tl data obtained XWIN to that ofanother program (data compiled 
in Data Analysis #2). What are the differences? What would account for these 
differences? Which do you think is more accurate and why? 
2. Using the spectra and table made in data analysis (#1 & #3), explain the trend of 
'tC values along the backbone of the 1-hexanol molecule. The molecule has been 
modeled and there are movies available in 207 Whitmore (see Dr. Arzhantsev for 
details). What do these tell you about the -re values? 
3. What is hydrogen bonding? How important is hydrogen bonding in this 
experiment? 
References: 
1. Gasyna, Z.; Jurkiewi cz, A. J Chem. Ed 2004, 1038. 
A-1 
Treatment of Experimental Data 
In Chem 457 the following terminology is very important m the evaluation of the 
experimental data. 
Precision: a measure of reproducibility of a set of results from replicate runs. 
The closeness of agreement between independent test results obtained by applying the 
experimental procedure under stipulated conditions. The smaller the random part of the 
experimental errors which affect the results, the more precise the procedure. A measure 
of precision (or imprecision) is the standard deviation. 
Accuracy: a measure of the closeness of an experimental value to the true value or 
accepted value; correctness. The agreement between the values can be determined by 
absolute error or percent error. 
If an error occurs consistently, it affects the accuracy and classified as a systematic error. 
To avoid a consistent error, a standard should be run or a correction factor needs to be 
applied during the experimentation or data analysis. 
If an error occurs inconsistently, it affects the precision and classified as a random error. 
To avoid an inconsistent error, measurements should be taken number of times and 
averaged. 
Uncertainty: Parameter, associated with the result of a measurement, that characterizes 
the dispersion of the values that could reasonably be attributed to the measurand 
(particular quantity subject to measurement). 
Error: anything qualitative or quantitative causing a measurement to differ from the true 
or accepted value. 
Error of measurement: Result of a measurement minus the true value of the measurand. 
Since a true value cannot be determined, in practice the conventional true value is used. 
A-2 
Common Statistical Calculations: 
1) Mean: To select a typical data value or to obtain an average value, all data values are 
added up and divided by the number of data items. 
1 N 
x=-Ix; 
N i=I 
2) Estimated Standard Deviation: The most common way to describe the range of 
variation in the collected data. 
S= I(x;- x)2 
(N -1) 
3) Estimated Standard Deviation of the Mean: Answers the following question: 
How much variation is there in the estimated standard deviation? 
Example Problem: Calculate the a) mean, b) estimated standard deviation, and c) 
estimated standard deviation of the mean for the following sample data. 
Sample Data 
(Length, cm) 
2.5 ± 0.5 
3.2 ± 0.5 
2 .7 ±0.5 
x = 2.5 + 3.2 + 2.7 + 2.4 + 2.2 = .!]_ = 2.6 
5 5 
/')' ( Y . - X)2 Jn n 1 ..L n ~h. ..L n n 1 ..L n nLI. ..L n 1 h. 
2.4 ± 0.5 
2.2 ± 0.5 
A-3 
A-4 
How to Collect and Analyze the Data? 
1. Record measurements properly: 
a) to the correct number of decimal places 
b) with units and 
c) with indication of the uncertainty associated with the measurement (±) 
The uncertainties or the tolerance levels of the common glassware used m the 
laboratories are as given in Table 1. 
Table 1. Glassware Tolerances- for class B glassware (class A glassware tolerances are 
Yz those of class B) 
Transfer Pipettes Volumetric Flasks 
Size, mL Tolerance(±) Size, mL Tolerance (±) 
1&2 0.012 50 0.1 0 
5 0.02 100 0.1 6 
10 0.04 250 0.24 
25 0.06 100 0.60 
50 0.10 2000 LOO 
If tolerance levels are not available, use the rules of thumb to determine the uncertainties. 
Table 2. Estimating the tolerance levels, where they are not available. 
Instruments Tolerance(±) 
Linear scales 0.5 of the smallest division 
Digital readout 1 - 5 in the last digit 
Mettler balances 0.4mg = ± 0.0004 g 
Vernier scales 0.1 of the smallest division on the non-Vernier scale 
In addition, the tolerance level information can be found for most of the instruments from 
their instrument instruction manuals if needed. In case of an assumption on the tolerance 
level estimation, clearly state the conditions under which the measurements were taken 
and clearly explain it in your report. 
A-5 
2. Rejection of Apparently Inconsistent Replicated Data: 
Before replicated data or replicated results can be rejected, a statistical Q test needs to be 
performed to decide whether the points have to be rejected. If the calculated value of Q 
is LARGER than the tabulated value, the data point can be rejected. This test is valid for 
small samples (3-10 data points). 
Q = Difference between the point in question and the next nearest data point 
Range of data points 
Table 3. Critical Q values for rejection of discordant values at 90 percent confidence 
level. 1 
N 3 4 5 6 7 8 
Qc. 0.94 0.76 0.64 0.56 0.51 0.47 
3. Determine Deviations for Each Replicate Measurement 
A) For 20 or more number of data points: 
9 IO 
0.44 0.41 
Random error needs to be statis6cally treated to prevent imprecision. Normal error 
probability function is expressed in the following Gaussian curves as shown in Figure 
1. 1 If large number of data points are available (at least 20 and more) these curves 
provide satisfactory precision. 
Pu -µ) PU'-µ) 
I 
.r - µ-. - 1.96a 0 1.96<1 .r - µ -+ 
(a l !bl 
Figure 1. Integrated probability P for normal error distribution. 1 
a) Standard deviation error limits, ± u 
b) 95% confidence limits, ±l.96u 
A-6 
Table 4 shows the uncertainty values and their corresponding level of confidence.1 
Table 4. Correspondence between uncertainty value and level of confidence.1 
Uncertainty ±cr ±1.64 (j ±1.96 (J ±2.58 (J ±3.29 (j 
Confidence level 68.26 90 95 99 99.9 
B) For less than 20 number of data points: 
For experiments with number of data points between 1 < N < 20, the student t 
distribution curve should be used. 1 
P (t )lk_.,, 
- 3 - 2 - 1 0 2 3 
Figure 2. Student t distribution function curve ( v : number of 
degrees of freedom, P(r): student distribution function).1 
~0.95 represents 95% confidence limit in the mean. 
-t --( s J - 0.95 .,[ii 
To determine the t, critical value, a brief table, Table 5 needs to be used, where P 
is the probability of the mean and v is the degrees of freedom that can be 
calculated by subtracting the number of variables from the number of data points 
as follows: 
A-7 
v = N - l when using a series of replicated measurements, one variable exists. 
v = N -2 Owhen using a series of replicated measurements two variable exists. 
For more complete t tables check the elementary statistics books.2 
T bl 5 a e . . I t b . t cnt1ca va ues o e use d h al If w en c cu a mg unce rt"f am ies. 
v p 0.50 0.80 0.90 0.95 0.98 0.99 0.999 
1 1.00 3.08 6.31 12.7 31.8 63.7 637.0 
2 0.816 I .89 2.92 4.30 6.96 9.92 31.6 
3 0.765 1.64 2.35 3.18 4.54 5.84 12.9 
4 0.741 1.53 2.13 2.78 3.75 4.60 8.61 
5 0.727 1.48 2.02 2.57 3.36 4.03 6.87 
6 0.718 1.44 1.94 2.45 3.14 3.7 1 5.96 
7 0.711 1.41 1.89 2.36 3.00 3.50 5.41 
8 0.706 1.40 1.86 2.31 2.90 3.36 5.04 
9 0.703 1.38 1.83 2.26 2.82 3.25 4.78 
10 0.700 1.37 1.81 2.23 2.76 3.17 4.59 
15 0.691 1.34 J 1.75 2.13 2.60 2.95 4.07 
20 0.687 1.33 1.72 2.09 2.53 2.85 3.85 
30 0.683 1.31 1.70 2.04 2.46 2.75 3.65 
00 0.674 1.28 l.64 1.96 2.33 2.58 3.29 
I 
I 
I 
I 
I 
! 
I 
P is the probability that the mean µ of the population does not differ from the sample 
mean x by a factor of more than t, the critical value corresponding to degrees of freedom. 
4. Reporting Results of Calculations: 
a) "The final result of a calculation should be reported with the estimated uncertainty 
and the proper units". The uncertainty maybe a limit of error (confidence limits), 
standard error, or probable error; it is important to indicate which, to avoid possible 
confusion. A "±" sign without further explanation is generally understood to indicate 
a limit of error. 
b) Reported values and uncertainties are to be expressed in the same notation (either 
both scientific or both in normal notation. 
A-8 
c) If a result will be used in the later calculations, that result should not be rounded until 
the final answer that is to be reported. 
5. Calculate the composite error: 
Composite error (propagation of uncertainties or propagation of error) quantifies the 
precision of the results, identifies the principle error source, and suggests improvement. 
Once the uncertainties of each individual measurement are made, their combined effect 
on the quantity of interest needs to be found. Knowing the uncertainty in x, Ax, the 
uncertainty in some function, F(x), can be estimated as shown below: 
Example: 
Li(F) =l:ILix 
Li(lnx) =ld:xlLix= ~& 
If function depends on several variables, F = F (x, y, z, ... ) a partial derivative method 
can be applied to find the uncertainty of the function as shown. 
(8F)
2 (8FJ 2 (ap)2 Li(F)2 = ax Li(x)2 + 8y Li(y) 2 + oz Li(z)2 + ... 
Helpful Simplifications: 1 
1. For F = ax ± by ± cz, 
2. For F = axyz (or axy/z or ax/yz or a/xyz) 
Li2 (F) Li2 (x) Li2 (y) Li2 (z) 
- -=--+--+--p 2 x2 y2 2 2 
3. For F =ax", 
Li2 (F) 2 ,t:.,.2 (x) Li(F) Li(x) --=n --~--=n--
F 2 x 2 F x 
A-9 
4. For F = aeX, 
5. For F =a ln x, 
6 2 (F) =a: A2 (x)-> A(F) =a L\(x) 
x x 
6. Determining Uncertainty for Values Obtained from Graphical Data: 
In most of the cases, result of an experiment depends on the slope of a straight line in the 
graph. A straight line may be represented by the following equation: 
y = mx+b 
where, m is the slope, and b is the intercept. The best straight line equation can be 
obtained by drawing the best straight line in the graph using Excel or Mathematica (or 
any other mathematics software). In the uncertainty and the graphical analyses for the 
lab reports, linear regression analysis is required. For that reason, it is recommended to 
learn how to do the linear regression analysis using the data analysis tool pack of Excel or 
using Mathematica. 
Linear Regression Using Excel 
Please follow the instructions, to do linear regression analysis on excel using a MAC or a 
PC. 
1. Enter the data into a spreadsheet. For a straight line you may enter the x values 
into column A and the corresponding y values into column B. Place the units in 
the column heading for each set of values and NOT in the individual cells with 
the numerical values. You may use the following example in practicing linear 
regression analysis. 
A-10 
A (x-values) B (y-values) 
1.0 2.1 
2.0 3.9 
3.0 5.8 
4.0 8.3 
5.0 10.3 
6.0 11.9 
2. Go to the Tools menu and select Data Analysis. (If the Data Analysis is NOT in 
the Tools menu, go to Add-ins in the Tools menu and select analysis tools pack. 
Then restart your computer. If it is not on the add-ins menu, it may not have 
been installed. 
3. From the Data Analysis list, scroll down to Regression and select it. 
4. Jn the Regression window, enter the range of the x data (Al:A6 in our example) 
and of they data (Bl:B6). Check the line fit plots box. 
5. Check the confidence level box and set it at 95%. If you are using Excel 98 for 
Macintosh or Excel 97 for Windows, you \Vill need to check the new workbook 
box, due to minor revisions in these versions of Excel. 
6. When you have completed the regression \\<indow, click on OK. In a few 
seconds, the screen will look like the output on the next page. You can print the 
table by using the Print command in the File menu. 
7. Scroll the window to the right and you will see the plot. You can also print this, 
although you should enlarge it first by clicking on it and using the mouse to drag 
on the border to make it bigger. This is easy to do, but hard to describe in print; 
so if you're having trouble, just ask someone for help. 
Table 5 shows a sample linear regression output. 
Table 6. Linear regression analysis output (obtained by excel) 
SUMMARY OUTPUT 
Regression Statistics 
Multiple R 0.998407331 
RSquare 0.996817198 
Adjusted R Square 
Standard Error 
Observations 
ANOVA 
Regression 
Residual 
Total 
0.996021498 
0.238746728 
6 
d[ SS 
l 71.407 
4 0.228 
5 71.635 
Equation of the line 
y = 2.02 x -0.02 
MS F Siwzif!.cance F 
71.407 1252.754 3.80287E-06 
0.057 
~2ofidim~1: limit 
Coefficients Standard Errort Stat P-value Lower 95% Uooer 95% 
Intercept I Y -interc_'Tfb2 I Kl.22226 1108 Sb 
X Variable 1 I Slope D.057071384 
2 02 I Sm 
RESIDUAL OUTPUT 
Observation 
1 
2 
3 
4 
5 
6 
Predicted Y Residuals 
2 0.1 
4.02 -0.12 
6.04 -0.24 
8.06 0.24 
10.08 0.22 
12.l -0.2 
0.08998 0.932625 -0.637097043 0.597097 
35.394273.8E-06 1.861544 107 2.178456 
A-11 
A-12 
References: 
1. Shoemaker, D.P., Garland, C.W., and Nibler, J.W .. , in Experiments in Physical 
Chemistry, 7th Ed., McGraw-Hill Co., 2003. 
2. Downie, N. M. and Starry, A. R. in Descriptive and Inferential Statistics, 
Harper and Row, New York, 1977. 
General Reading: 
Bevington, P. R. and Robinson, D. K. in Data Reduction and Error Analysis for 
the Physical Sciences, 2nd Ed, McGraw-Hill, New York, 1991. 
Mortimer, R. G. in Mathematics for Physical Chemistry, Macmillan, New York, 
1981. 
Chem 457 Error Analysis Problem Set 
Instructions: 
Write down the initial values with uncertainties and units 
Write down what you are determining 
Write down the equation you will be using 
Substitute the values into the equation, including units 
Circle your final answer, which is expressed in correct number of digits with 
uncertainties, and units. 
Problems: 
A-13 
1. Repeated measurements of the mass of a pellet of benzoic acid on a Mettler balance 
with a tolerance limit of ± 0.0004g gave the following results: 
1.0109, 1.0145, 1.0097, 1.0101, and 1.0115 g. 
a) What is the mean for this data set? 
b) What is the estimated standard deviation, S, of this data set? 
c) What is the estimated standard deviation of the mean value, Sm? 
d) How would you report the mass of the sample using the 95% confidence limit? 
2. In order to calibrate the volume of a large bulb it is filled with argon and the 
temperature, pressure, and mass are measured several times producing the following 
results: 
Temperature (K) = 304.7 ± 0.5 
Pressure (mm Hg)= 742.5 ± 1.3 
Mass (grams) = 9.3182 ± 0.0001 
Note: These uncertainties are given in the 95% confidence limit. 
Assuming that argon behaves like an ideal gas with molecular mass of 3 9. 948 g mo1-1, 
what is the best estimate for the volume of the bulb (in L) and the uncertainty in the 
estimate? (The gas constant, R = 0.0820579 L atm K 1moi-1, can be assumed to be 
known exactly, as can the molecular mass.) 
3. Suppose one wants to apply the van der Waals equation of state, 
P= RT a 
(Vm -b) V~ 
to predict the pressure of a non-ideal gas. Assuming that the constants, R = 0.0820579 L 
atm K-1 mo1-1, a= 1.345 atm L2 mo1-2, and b = 0.0322 L mo1-1 are known exactly, what is 
the uncertainty in the predicted pressure P due to the uncertainties in the measured molar 
A-14 
volume, V m = 54.21 ± 0.11 L mo1-1, and temperature, T = 342. 7 ± 0.3 K? Report your 
answer as the calculated P ±AP. 
4. An experiment is performed to determine the force constant k of a spring by 
measuring its length as a function of the applied load. The following data are obtained: 
Mass Length 
fa) (cm) 
10.0 5.1 
20.0 8.8 
30.0 10.9 
40.0 14.3 
50.0 18.0 
Generate a graph along with its best fit Jine using Excel or a similar program. Display the 
equation of the best fit line and its R2 value on the graph. Remember to title the graph 
and label the axes with quantity and unit. The line plotted has the general equation of: 
Length= Lo+ k(mass) 
Use the regressionprogram under the data analysis menu in Excel to carry out the 
regression analysis on your set of graphed data. Use the resulting print-out to determine 
the uncertainties of Lo and k as discussed in the error analysis lecture. Show clearly how 
you used the information on the printout to determine these uncertainties. Include the 
regression printout with your work to be graded. 
Report the values of Lo and k and their associated uncertainties with 95% confidence 
limit. 
CHEM 457 Packet SP17-090 
$7.70 
2 818440 169359 
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