Physical Chemistry Third Edition

276 6 The Thermodynamics of Solutions

Sm,∗i−Rln(xi)−Rln

(

γi(I)

)

−RT

⎛

⎝

∂ln

(

γi(I)

)

∂T

⎞

⎠

P,n

S(ideal)i −Rln

(

γ(iI)

)

−RT

⎛

⎝

∂ln

(

γ(iI)

)

∂T

⎞

⎠

P,n

(6.5-3)

The partial molar enthalpy is given by

Hiμi+TSi

μ∗i +RTln

(

γi(I)xi

)

+T

⎡

⎣Sm∗(i)−Rln

(

xiγ

(I)

i

)

−RT

⎛

⎝

∂ln

(

γi(I)

)

∂T

⎞

⎠

P,n

⎤

⎦

Hm,∗i−RT^2

⎛

⎝

∂ln

(

γi(I)

)

∂T

⎞

⎠

P,n

(6.5-4)

An expression for the partial molar volume is

ViVm,∗i+RT

⎛

⎝

∂ln

(

γi(I)

)

∂P

⎞

⎠

T,n

(6.5-5)

Exercise 6.22

Carry out the steps to obtain Eq. (6.5-5).

The partial molar quantities can also be expressed in terms of the activity coefficients

using convention II, the molality description, or the concentration description.

Exercise 6.23

Write an expression for the partial molar entropy of a component of a solution using the molality

description.

Thermodynamic Functions of Nonideal Solutions

The thermodynamic functions of solutions are generally expressed in terms of the

changes produced by mixing the pure components to form the solution at constant

temperature and pressure. From Euler’s theorem and Eq. (6.3-6), the Gibbs energy of

a nonideal solution is given by

G(soln)

∑c

i 1

ni

[

μ◦i(I)+RTln

(

a(iI)

)]

(6.5-6)