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) 
Solving