Fugacity

The fugacity is a quantity that corresponds to the pressure for a non-ideal gas. Fugacity can be used in expressions of the equilibrium constant exactly as pressure is used. The relationship between fugacity and pressure is analogous the relationship between activity and mole fraction (or molarity depending on the units used in describing the equilibrium). To understand fugacity we begin with the standard Gibbs energy. In general we know that:

At constant temperature we can see that:

for an ideal gas. To include deviation from ideality we can use the virial expansion.

Using the virial expansion we can substitute in for the molar volume using the following form:

Thus,

where P^id is an arbitrarily low pressure where the gas behaves ideally. Now we can reference this ideal state to the standard state:

and finally we have:

We define fugacity for a real gas as follows.

Since all gases behave ideally at sufficiently low pressure we have

f à P as P à 0

Note the similarity to activity where

a à x as x à 0.

The fugacity and virial expressions are equivalent provided:

There are some subtle points about the relative standard state that are discussed on page 907 in McQuarrie and Simon.

Here we simply mention that there is a fugacity coefficient, g that is analogous to the activity coefficient.

A general expression for determining the fugacity coefficient can be derived using the compressibility Z, where,

In general

For example, for a van der Waals' gas

Can be expressed in the form of a virial expansion as shown using Eqn. 16-42 on page 672 of McQuarrie and Simon.

Thus,