Chemical Potential

For a statistical system, the chemical potential is the change in internal energy per change in number of particles for constant entropy and volume. That is to say, the internal energy of a statistical system is given by:

\[ dU = T dS - P dV + \sum_{i=1}^{n} \mu_i\: dN_i \]

for \(n\) species with chemical potentials \(\mu_i\), respectively.

Fugacity

For an ideal gas, the change in chemical potential is

\[ d\mu = RT\: d\log P \]

For a real gas, this no longer holds. However, for a real gas with fugacity \(f\), it holds that

\[ d\mu = RT\: d\log f \]

Hence, the fugacity serves as an effective pressure with respect to the chemical potential.