Physical Chemistry Third Edition

242 6 The Thermodynamics of Solutions

EXAMPLE 6.2

Calculate the Gibbs energy change of mixing, the entropy change of mixing, the enthalpy

change of mixing, and the volume change of mixing for a solution of 1.200 mol of benzene

and 1.300 mol of toluene at 20.00◦C. Assume the solution to be ideal.

Solution

∆GmixRT[(1.200 mol) ln(0.4800)+(1.300 mol) ln(0.5200)]−4219 J

∆Smix−R[(1.200 mol) ln(0.4800)+(1.300 mol) ln(0.5200)] 14 .39JK−^1

∆Hmix 0

∆Vmix 0

We can obtain expressions for other partial molar quantities from the expression for

the chemical potential. For example, Eq. (4.5-14) for the partial molar entropy is

S ̄i−

(

∂μi

∂T

)

P,n

(6.1-19)

Application of this equation to Eq. (6.1-1) gives

S ̄i−

(

∂μ∗i

∂T

)

P,n

−Rln(xi)

S ̄iS∗m,i−Rln(xi) (ideal solution) (6.1-20)

whereS∗m,iis the molar entropy of pure substancei.

Exercise 6.4

In the same way that Eq. (6.1-20) was derived, obtain the relations for the partial molar volume

and partial molar enthalpy of components of an ideal solution:

V ̄iVm,∗i (ideal solution) (6.1-21)

H ̄iHm,∗i (ideal solution) (6.1-22)

Molecular Structure and Ideal Solutions

It is found experimentally that Raoult’s law applies most nearly to liquid solutions in

which the substances have molecules of similar size, shape, and polarity. The expla-

nation for this fact is that if two substances have similar molecules, a molecule of one

substance attracts or repels molecules of the other substance in much the same way as

molecules of the same substance. The similarity of interaction allows the molecules

to mix randomly in a solution without changing the volume or the enthalpy just as

noninteracting molecules mix randomly in a dilute gas mixture.