Thermodynamics and Chemistry

CHAPTER 7 PURE SUBSTANCES IN SINGLE PHASES

7.9 STANDARDMOLARQUANTITIES OF AGAS 185

HereBis the second virial coefficient, a function ofT. With this equation of state, Eq.
7.8.16becomes

ln

Bp

RT

(7.8.18)

For a real gas at temperatureTand pressurep, Eq.7.8.16or7.8.18allows us to evaluate
the fugacity coefficient from an experimental equation of state or a second virial coefficient.
We can then find the fugacity fromf Dp.

As we will see in Sec.9.7, the dimensionless ratioDf=pis an example of an

activity coefficientand the dimensionless ratiof=pis an example of anactivity.

7.8.2 Liquids and solids

The dependence of the chemical potential on pressure at constant temperature is given by
Eq.7.8.5. With an approximation of zero compressibility, this becomes

CVm.pp/ (7.8.19)

(pure liquid or solid,

constantT)

7.9 Standard Molar Quantities of a Gas

Astandard molar quantityof a substance is the molar quantity in the standard state at the
temperature of interest. We have seen (Sec.7.7) that the standard state of a pureliquidor
solidis a real state, so any standard molar quantity of a pure liquid or solid is simply the
molar quantity evaluated at the standard pressure and the temperature of interest.
The standard state of agas, however, is a hypothetical state in which the gas behaves
ideally at the standard pressure without influence of intermolecular forces. The properties
of the gas in this standard state are those of an ideal gas. We would like to be able to relate
molar properties of the real gas at a given temperature and pressure to the molar properties
in the standard state at the same temperature.
We begin by using Eq.7.8.7to write an expression for the chemical potential of the real
gas at pressurep^0 :

.p^0 /D(g)CRTln

f .p^0 /

p

D(g)CRTln

p^0

p

CRTln

f .p^0 /

p^0

(7.9.1)

We then substitute from Eq.7.8.14to obtain a relation between the chemical potential, the
standard chemical potential, and measurable properties, all at the same temperature:

.p^0 /D(g)CRTln

p^0

p

C

Zp 0

0



Vm

RT

p



dp (7.9.2)

(pure gas)

Note that this expression foris not what we would obtain by simply integrating dD
Vmdpfromptop^0 , because the real gas is not necessarily in its standard state of ideal-gas
behavior at a pressure of 1 bar.