1 (566)

Prévia do material em texto

558 16MOLECULES INMOTION
16B Motion in liquids
Answers to discussion questions
D16B.2 �e Grotthuss mechanism for conduction by protons in water is described
in Section 16B.2(a) on page 701 and illustrated in Fig. 16B.2 on page 703. It
seems plausible that such a mechanism could also occur in the relatively open
hydrogen bonded structure of ice.
Solutions to exercises
E16B.1(b) �e temperature dependence of the viscosity η is given by [16B.1–699], η =
η0eEa/RT , where η0 is viscosity in the limit of high temperature and Ea is the
associated activation energy. Taking the natural logarithm gives ln η = ln η0 +
Ea/RT . Hence
ln η1 − ln η2 = (ln η0 + Ea/RT1) − (ln η0 + Ea/RT2) =
Ea
R
( 1
T1
− 1
T2
)
Rearranging gives an expression for the activation energy
Ea = R
ln (η1/η2)
(T−11 − T−12 )
= (8.3145 JK−1mol−1) ln [(1.554 cP)/(1.450 cP)]
[(293.15 K)−1 − (313.15 K)−1]
= 2.64 kJmol−1
E16B.2(b) According to the law of independent migration of ions, the limiting molar
conductivity Λ○m of an electrolyte is given by the sum of the limiting molar
conductivities λ i of the ions present, [16B.6–701], Λ○m = ν+λ+ + ν−λ−; in this
expression ν+ and ν− are the numbers of cations and anions provided by each
formula unit of electrolyte. For each of the given electrolytes it follows that
Λ○KF = λK+ + λF− Λ○KCH3CO2 = λK+ + λCH3CO2−
Λ○Mg(CH3CO2)2 = λMg2+ + 2λCH3CO2−
�ese expressions are manipulated to give Λ○MgF2
Λ○MgF2 = λMg2+ + 2λF−
= (Λ○Mg(CH3CO2)2 − 2λCH3CO2−) + 2(Λ
○
KF − λK+)
= Λ○Mg(CH3CO2)2 + 2Λ
○
KF − 2(λCH3CO2− + λK+)
= Λ○Mg(CH3CO2)2 + 2Λ
○
KF − 2Λ○KCH3CO2
= [18.78 + 2(12.89) − 2(11.44)]mSm2mol−1 = 21.68 mSm2mol−1