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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 159
D5F.6 �e term B in the extended Debye–Hückel law, [5F.30a–189], and the Davies
equation, [5F.30b–189], can be interpreted as an indicator of the distance of
closest approach of the ions. However, both B and the parameter C in the latter
equation are best thought of as empirical parameters to be obtained by �tting
experimental data.
Solutions to exercises
E5F.1(b) �e activity in terms of the vapour pressure p is given by [5F.2–183], a = p/p∗,
where p∗ is the vapour pressure of the pure solvent. �e vapour pressure of
pure water at 100 ○C, the normal boiling point, is 1 atm.�erefore a = p/p∗ =
(90.00 kPa)/[(1 atm) × (101.325 kPa)/(1 atm)] = 0.8882 .
E5F.2(b) On the basis of Raoult’s law, the activity in terms of the vapour pressure pA is
given by [5F.2–183], aA = pA/p∗A, where p∗A is the vapour pressure of the pure
solvent. With the data given aA = pA/p∗A = (0.02239 atm)/(0.02308 atm) =
0.9701... = 0.9701 .
�e activity coe�cient is de�ned through [5F.4–183], aA = γAxA. �e mole
fraction of solvent water (A) is computed as
xA =
nA
nA + nA
= (0.920 × 103 g)/(18.0158 gmol−1)
(0.920 × 103 g)/(18.0158 gmol−1) + (0.122 × 103 g)/(241 gmol−1)
= 0.990...
Hence γA = aA/xA = (0.9701...)/(0.990...) = 0.980 .
E5F.3(b) On the basis of Raoult’s law, the activity in terms of the vapour pressure pJ is
given by [5F.2–183], aJ = pJ/p∗J , where p∗J is the vapour pressure of the pure
solvent.�e partial vapour pressure of component J in the gas is given by pJ =
yJptot. In this case
aA =
pA
p∗A
= yAptot
p∗A
= 0.314 × (1.00 atm) × [(101.325 kPa)/(1 atm)]
73.0 kPa
= 0.435...
�e activity of A is therefore aA = 0.436 . �e activity coe�cient is de�ned
through [5F.4–183], aJ = γJxJ, therefore γA = aA/xA = 0.435.../0.220 = 1.98 .
For the other component the mole fractions are yB = 1 − yA = 0.686 and xB =
1 − xA = 0.780.�e rest of the calculation follows as before
aB =
pB
p∗B
= yBptot
p∗B
= 0.686 × (1.00 atm) × [(101.325 kPa)/(1 atm)]
92.1 kPa
= 0.754...
�e activity of B is therefore aB = 0.755 and its activity coe�cient is given by
γB = aB/xB = 0.754.../0.780 = 0.968 .