Physical Chemistry Third Edition

278 6 The Thermodynamics of Solutions

The expressions for∆Gmix,∆Smix, and∆Vmixcan 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∆Gmixusing convention II activity coefficients.

The enthalpy change of mixing is often expressed in terms of theheat of solution

orenthalpy change of solution.For a two-component solution, themolar integral heat

of solutionof component 1 in a solution with component 2 is defined by

∆Hint,1

∆Hmix

n 1

(6.5-15)

and the molar integral heat of solution of component 2 is defined by

∆Hint,2

∆Hmix

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.

EXAMPLE6.16

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

∆Hint,2−

9 .17 kJ

2 .00 mol

− 4 .58 kJ mol−^1

∆Hint,1−

9 .17 kJ

10 .00 mol

− 0 .917 kJ mol−^1

Using Euler’s theorem for a two-component system,

∆Hmixn 1 H ̄ 1 +n 2 H ̄ 2 −

(

n 1 Hm,1∗ +n 2 Hm,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:

∆Hint,2

1

n 2

[

n 1

(

H ̄ 1 −Hm,1∗

)

+n 2

(

H ̄ 2 −Hm,2∗

)]



n 1

n 2

(

H ̄ 1 −Hm,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∆Hint,1.