Physical Chemistry Third Edition

186 4 The Thermodynamics of Real Systems

In a one-component system any partial molar quantity is equal to the corresponding

molar quantity.The most important examples are

μGGm

G

n

(one-component system) (4.5-19)

and

VVm

V

N

(one-component system) (4.5-20)

Partial Molar Quantities of a One-Component Ideal Gas

As with any pure substance the partial molar volume of a one-component ideal gas is

equal to the molar volume:

VVm

V

n



RT

P

(ideal gas) (4.5-21)

The chemical potential of a one-component ideal gas is equal to the molar Gibbs energy.

From Eq. (4.4-5),

μGGmG◦m(T)+RTln

(

P

P◦

)

(ideal gas) (4.5-22)

whereG◦mis the molar Gibbs energy in the standard state. It is equal toμ◦, the chemical

potential in the standard state. The standard state for the Gibbs energy of an ideal gas

is the ideal gas at pressureP◦(exactly 1 bar). The relation of Eq. (4.5-22) is the

same as

μμ◦+RTln

(

P

P◦

)

(ideal gas) (4.5-23)

The partial molar entropy of an ideal gas is obtained by use of Eq. (4.2-20):

Sm−

(

∂Gm

∂T

)

P

−

(

∂G◦m

∂T

)

P

+Rln

(

P

P◦

)

SmSm◦−Rln

(

P

p◦

)

(ideal gas) (4.5-24)

whereS◦mis equal to−(∂μ◦/∂T)P. The partial molar enthalpy of a one-component

ideal gas is obtained from Eq. (4.1-14):

HHmGm+TSm

G◦m+RTln

(

P

P◦

)

+T

[

S◦m−Rln

(

P

P◦

)]

HG◦m+TSm◦Hm◦ (ideal gas) (4.5-25)

The partial molar enthalpy of an ideal gas does not depend on pressure.