6.1 Ideal Solutions
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If an expression for one thermodynamic variable is obtained, the expressions for
other thermodynamic variables can be obtained by the use of thermodynamic identities.
The entropy of a system is given by Eq. (4.2-20):
−S
∂G
∂T
P,n
(6.1-12)
Using Eq. (6.1-10), the entropy of an ideal solution is
S −
c
i1
n i
∂µ ∗
i
∂T
P
+ R ln(x i )
(ideal solution)
(6.1-13)
For the unmixed components, using Euler’s theorem
S(unmixed) −
c
i1
n i
∂µ ∗
i
∂T
P
(6.1-14)
so that
∆S mix −R
c
i1
n i ln(x i ) (ideal solution)
(6.1-15)
This is the same as the formula for an ideal gas mixture, Eq. (3.3-20).
The enthalpy change of mixing for a solution is given by
∆H mix ∆G mix + T ∆S mix
(6.1-16)
so that
∆H mix RT
c
i1
n i [ln(x i ) − ln(x i )] 0 (ideal solution)
(6.1-17)
This is the same formula as for ∆H mix of an ideal gas mixture. It can also be shown
that
∆V mix 0 (ideal solution)
(6.1-18)
Exercise 6.3
Show that Eq. (6.1-18) is correct.