Thermodynamics and Chemistry

CHAPTER 7 PURE SUBSTANCES IN SINGLE PHASES

7.9 STANDARDMOLARQUANTITIES OF AGAS 186

Table 7.5 Real gases: expressions for differences between molar properties and standard molar

values at the same temperature

General expression Equation of state

Difference at pressurep^0 VDnRT=pCnB

UmUm(g)

Zp 0

0

"

VmT



@Vm

@T



p

#

dpCRTp^0 Vm pT

dB

dT

HmHm(g)

Zp 0

0

"

VmT

@V

m

@T



p

#

dp p



BT

dB

dT



AmAm(g) RTln

p^0

p

C

Zp 0

0



Vm

RT

p



dpCRTp^0 Vm RTln

p

p

GmGm(g) RTln

p^0

p

C

Zp 0

0



Vm

RT

p



dp RTln

p

p

CBp

SmSm(g) Rln

p^0

p

Zp 0

0

"

@Vm

@T



p

R

p

#

dp Rln

p

p

p

dB

dT

Cp;mCp;m(g) 

Zp 0

0

T



@^2 Vm

@T^2



p

dp pT

d^2 B

dT^2

Recall that the chemical potentialof a pure substance is also its molar Gibbs energy
GmDG=n. The standard chemical potential(g) of the gas is the standard molar Gibbs
energy,Gm(g). Therefore Eq.7.9.2can be rewritten in the form

Gm.p^0 /DGm(g)CRTln

p^0

p

C

Zp 0

0



Vm

RT

p



dp (7.9.3)

The middle column of Table7.5contains an expression forGm.p^0 /Gm(g) taken from this
equation. This expression contains all the information needed to find a relation between any
other molar property and its standard molar value in terms of measurable properties. The
way this can be done is as follows.
The relation between the chemical potential of a pure substance and its molar entropy
is given by Eq.7.8.3:

SmD



@

@T



p

(7.9.4)

The standard molar entropy of the gas is found from Eq.7.9.4by changingto(g):

Sm(g)D



@(g)

@T



p

(7.9.5)

By substituting the expression forgiven by Eq.7.9.2into Eq.7.9.4and comparing the
result with Eq.7.9.5, we obtain

Sm.p^0 /DSm(g)Rln

p^0

p

Zp 0

0

"

@Vm

@T



p

R

p

dp (7.9.6)