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)