Thermodynamics and Chemistry

CHAPTER 7 PURE SUBSTANCES IN SINGLE PHASES

7.8 CHEMICALPOTENTIAL ANDFUGACITY 183

p



0 pÆ f.p^0 / p^0

Æ(g) b

b b

A

C B

Figure 7.6 Chemical potential as a function of pressure at constant temperature, for

a real gas (solid curve) and the same gas behaving ideally (dashed curve). Point A is

the gas standard state. Point B is a state of the real gas at pressurep^0. The fugacity

f .p^0 /of the real gas at pressurep^0 is equal to the pressure of the ideal gas having the

same chemical potential as the real gas (point C).

If a gas isnotan ideal gas, its standard state is a hypothetical state. Thefugacity,f, of
a real gas (a gas that is not necessarily an ideal gas) is defined by an equation with the same
form as Eq.7.8.6:

D(g)CRTln

f

p

(7.8.7)

(pure gas)

or

f

def

D pexp



(g)

RT



(7.8.8)

(pure gas)

Note that fugacity has the dimensions of pressure. Fugacity is a kind of effective pressure.
Specifically, it is the pressure that the hypothetical ideal gas (the gas with intermolecular
forces “turned off”) would need to have in order for its chemical potential at the given
temperature to be the same as the chemical potential of the real gas (see point C in Fig.7.6).
If the gas is an ideal gas, its fugacity is equal to its pressure.
To evaluate the fugacity of a real gas at a givenT andp, we must relate the chemical
potential to the pressure–volume behavior. Let^0 be the chemical potential andf^0 be
the fugacity at the pressurep^0 of interest; let^00 be the chemical potential andf^00 be the
fugacity of the same gas at some low pressurep^00 (all at the same temperature). Then we
use Eq.7.8.5to write^0 (g)DRTln.f^0 =p/and^00 (g)DRTln.f^00 =p/, from
which we obtain

^0 ^00 DRTln

f^0

f^00

(7.8.9)