6.5 Thermodynamic Functions of Nonideal Solutions
277
For convention I the standard states are the pure components, so that
G(unmixed)
c
i1
n i µ
∗
i
c
i1
n i µ
◦(I)
i
(6.5-7)
where we neglect a small difference between µ ∗
i and µ ◦
i due to a possible difference
of the pressure from P ◦ . The change in Gibbs energy for producing the solution (the
Gibbs energy change of mixing) is
∆G mix
c
i1
n i µ
∗
i + RT
c
i1
n i ln
a
(I)
i
−
c
i1
n i µ
∗
i
∆G mix RT
c
i1
n i ln
a
(I)
i
RT
c
i1
n i ln(x i ) + RT
c
i1
n i ln
γ
(I)
i
(6.5-8)
The first sum in the right-hand side of the final version of this equation is the same as
for an ideal solution, and the second sum represents a correction for the nonideality of
the solution. This contribution is called the excess Gibbs energy and is denoted by G E :
∆G mix ∆G
(ideal)
mix + G
E
(6.5-9)
so that
G
E
RT
c
i1
n i ln
γ
(I)
i
(6.5-10)
The excess entropy can be defined for a nonideal solution:
S
E
∆S mix − ∆S
(ideal)
mix
(6.5-11)
The excess enthalpy and the excess volume are equal to the mixing quantities, since
∆H mix and ∆V mix both vanish for an ideal solution.
Exercise 6.24
a. Show that
S E −R
c
i1
n i ln γ
(I)
i − RT
c
i1
n i
⎛
⎝
∂ ln
γ
(I)
i
∂T
⎞
⎠
P,n
(6.5-12)
b. Show that
H E ∆H mix −RT 2
c
i1
n i
⎛
⎝
∂ ln
γ
(I)
i
∂T
⎞
⎠
P,n
(6.5-13)
c. Show that
V E ∆V mix RT
c
i1
n i
⎛
⎝
∂ ln
γ
(I)
i
∂P
⎞
⎠
T ,n
(6.5-14)