Physical Chemistry Third Edition

266 6 The Thermodynamics of Solutions

Since the activities and activity coefficients of a solute in two different descriptions

are not necessarily equal to each other, we have attached superscripts to specify which

description is being used. We will sometimes omit these superscripts, relying on the

context to make clear which description is being used. In a sufficiently dilute solution,

the activity coefficients in all of these descriptions approach each other in value.

PROBLEMS

Section 6.3: Activity and Activity Coefficients

6.23 Assume that a 1.000 mol kg−^1 solution of naphthalene in
benzene is ideal. Calculate the value of the activity
coefficient of naphthalene in the molality description and
in the concentration description.

6.24 Find the activity of pure liquid water at 1250 bar and 25◦C.

6.25 Find the activity coefficient of gaseous nitrogen at
298.15 K and 20.00 atm, using whatever information you
need from earlier chapters of this book.

6.26 Find the activity of graphite and that of diamond at the
coexistence pressure at 298.15 K. Assume that the molar
volumes are constant.

6.27 In a certain binary mixture, the vapor pressure of substance
2 is given by
P 2 (0.689 atm)x 2 ifx 2 ≤ 0. 100
P 2 (0.754 atm)x 2 if 0. 95 ≤x 2
P 2  0 .435 atm ifx 2  0. 600

a.Find the Henry’s law constantk 2.

b.Find the vapor pressure of pure substance 2.

c.Find the activity and activity coefficient of substance 2

atx 2  0 .0500, 0.600, and 0.95 by convention I and by

convention II, treating substance 2 as a solute.

6.28 Naphthalene is a solid near room temperature, but it forms
a nearly ideal liquid solution with benzene or with toluene.
Show that the mole fraction of naphthalene in a solution
that is equilibrated with solid naphthalene (a saturated
solution) has the same mole fraction of naphthalene,
whether the solvent is benzene or toluene.

6.29 a.From data on enthalpy changes of formation in
Table A.8, find the standard-state differential heat
of solution of KOH at 298.15 K.
b.From data on Gibbs energy changes of formation in
Table A.8, find the value ofμ◦i(m)−G∗m(solid)for KOH
at 298.15 K.

6.30 a.From data in Problem 6.39, find the activity coefficient

of chloroform in acetone for the solution of Problem

6.39, using the molality description and regarding

acetone as the solvent.

b.Find the activity coefficient of acetone in the solution of

Problem 6.39, using the molality description and

regarding acetone as the solvent.

6.31Aregular solutionis one for which the Gibbs energy is

given by

G(T,P,n 1 ,n 2 )n 1 G◦m,1+n 2 Gm,2◦+RTn 1 ln(x 1 )

+n 2 ln(x 2 )+w

n 1 n 2

n 1 +n 2

wherewdepends only onPandT.

a.Find the expression forμ 1 , the chemical potential of

substance 1. Write the expression forμ 2 by analogy

with your expression forμ 1.

b. Show that your expressions conform to Euler’s

theorem.

6.32 The maximum solubility of I 2 in water at 1.000 atm and

298.15 K is equal to 1. 42 × 10 −^3 mol kg−^1. Find the value

ofμ◦i(m)−μ∗(solid)for I 2. State any assumptions.

6.33Assume that the activity of the solvent in a two-component

solution obeys the formula

ln(a 1 )ln(x 1 )+

∑∞

n 1

Cnxn 2

where theC’s are constants. Derive an expression for the

activity coefficient of substance 2, using convention II.

6.34 In a certain solution, the activity of substance 1 (the

solvent) is given by

ln(a 1 )ln(x 1 )+Bx 22

whereBis a constant. Derive an expression fora 2 using

convention II.