Real gases and the definition of fugacity

The standard state for a real gas is thus a hypothetical state in which the gas is at a pressure of p° = 1 bar and behaving ideally. 

Purely phenomenological as well as physically based equations of state are used to represent real gases. The deviation from perfect gas behaviour is often small, and the perfect gas law is a natural choice for the first term in a serial expression of the properties of real gases. The most common representation is the virial equation of state  

The coefficients B and C are the second and third virial coefficients, respectively, the first virial coefficient being 1. 

For an ideal gas Z = 1. Departures from the value of unity indicate non-ideal behaviour. Z 1 can be related to dominating attractive forces, whereas Z 1 relates to repulsive forces being dominant. 

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