278
6 The Thermodynamics of Solutions
The expressions for ∆G mix , ∆S mix , and ∆V mix can be expressed in terms of the
activity coefficients using convention II, the molality description, or the concentration
description.
Exercise 6.25
Write an expression for ∆G mix using convention II activity coefficients.
The enthalpy change of mixing is often expressed in terms of the heat of solution
or enthalpy change of solution. For a two-component solution, the molar integral heat
of solution of component 1 in a solution with component 2 is defined by
∆H int,1
∆H mix
n 1
(6.5-15)
and the molar integral heat of solution of component 2 is defined by
∆H int,2
∆H mix
n 2
(6.5-16)
The same enthalpy change of mixing occurs in both equations, but it is divided by the
amount of a different substance in each case.
E X A M P L E 6.16
If 2.000 mol of ethanol (substance 2) and 10.000 mol of water (substance 1) are mixed at a
constant temperature of 298.15 K and a constant pressure of 1.000 atm, the enthalpy change
is equal to −9.17 kJ. Find the molar integral heat of solution of ethanol in 5.000 mol of water
and the molar integral heat of solution of water in 0.200 mol of ethanol.
Solution
∆H int,2 −
9.17 kJ
2.00 mol
−4.58 kJ mol −1
∆H int,1 −
9.17 kJ
10.00 mol
−0.917 kJ mol −1
Using Euler’s theorem for a two-component system,
∆H mix n 1 ¯
H 1 + n 2 ¯
H 2 −
n 1 H ∗
m,1 + n 2 H ∗
m,2
(6.5-17)
the integral heat of solution of a component of a two-component solution can be written in
terms of the partial molar enthalpies:
∆H int,2
1
n 2
n 1
¯
H 1 − H ∗
m,1
+ n 2
¯
H 2 − H ∗
m,2
n 1
n 2
¯
H 1 − H ∗
m,1
+ ¯
H 2 − H ∗
m,2
(6.5-18)
This integral heat of solution is the enthalpy change per mole of substance 2 for the process
of making the solution, starting with the pure substances. A similar equation can be written
for ∆H int,1 .