Physical Chemistry Third Edition

6.1 Ideal Solutions 241

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

i 1

ni

[(

∂μ∗i

∂T

)

P

+Rln(xi)

]

(ideal solution) (6.1-13)

For the unmixed components, using Euler’s theorem

S(unmixed)−

∑c

i 1

ni

(

∂μ∗i

∂T

)

P

(6.1-14)

so that

∆Smix−R

∑c

i 1

niln(xi) (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

∆Hmix∆Gmix+T∆Smix (6.1-16)

so that

∆HmixRT

∑c

i 1

ni[ln(xi)−ln(xi)]0 (ideal solution) (6.1-17)

This is the same formula as for∆Hmixof an ideal gas mixture. It can also be shown

that

∆Vmix0 (ideal solution) (6.1-18)

Exercise 6.3

Show that Eq. (6.1-18) is correct.