Though fugacity is a property unrelated to solutions, its close analogy with activity renders this the appropriate place for its discussion:

Fugacity is used to replace the pressure of a gas in thermodynamically exact expressions.

It is best viewed as a kind of effective pressure (in the same way that activity is an effective mole fraction or effective molality); the pressure adjusted to take into account the fact that gases are not perfect, and that their particles do interact with each other. Use of the fugacity allows us to preserve the form of the expressions derived for the simple case of a perfect gas. Thus the chemical potential of a perfect gas at any pressure p is given by:

whereas the chemical potential of a real gas is given by:

where f is the fugacity of the gas at the given pressure. The chemical potentials of real and ideal gases vary differently with pressure, as shown:

To consider the properties of gases it is necessary to define their standard state, which for all real gases is taken as being at a pressure of pº (1 bar) with the gas behaving perfectly. The chemical potential of this state is, by definition, μº. Note this is a hypothetical standard state - no real gas behaves perfectly at 1 bar.

The advantage of this definition is that it ensures the standard state has the (very simple) properties of a perfect gas. By setting the interactions between particles to zero in this way, we ensure that differences between the standard chemical potentials of different gases arise solely from the internal structure of the molecules.

We write the fugacity as:

where Φ is the dimensionless fugacity coefficient, which depends upon the identity of the gas, the pressure and the temperature. Inserting this into the equation for the chemical potential of a perfect gas gives:

Since μº refers to the hypothetical state in which only the kinetic energy (due to the motion of the molecules) is considered, and the ln p term is the same as that in the equation for the chemical potential of a perfect gas, it follows that the ln Φ term must contain all the effects due to interactions between particles. i.e. it is this term which contains all the deviations from ideal behaviour.

Since all gases approach ideal behaviour in the limit of low pressure, we can conclude it must be the case that:

It is possible to derive an expression for the fugacity coefficient of a gas at a pressure p, but for our purposes it is sufficient to merely quote the result:

where Z is the compression factor of the gas (Z = pV_m / RT), introduced in the discussion of gases, here.

For most gases, Z < 1 up to moderate pressures. If Z is less than one throughout the range of integration, the integrand in the above equation is negative, which implies that Φ < 1 (so that its logarithm is negative). This in turn implies that the fugacity is less than the pressure (attractive forces within the gas dominate), and hence the chemical potential of the gas is less than that of a perfect gas would be.

At higher pressures, where Z > 1 , the integrand may give a positive value for ln Φ. This implies the fugacity is greater than the pressure (repulsive forces in the gas dominate, tending to drive the particles apart) and the chemical potential of the gas is greater than that of a perfect gas under the same conditions.