Fugacity

In chemical thermodynamics, the fugacity of a real gas is an effective pressure which replaces the true mechanical pressure in accurate chemical equilibrium calculations. It is equal to the pressure of an ideal gas which has the same chemical potential as the real gas. For example, nitrogen gas (N₂) at 0°C and a pressure of 100 atm has a fugacity of 97.03 atm. This means that the chemical potential of real nitrogen at a pressure of 100 atm is less than if nitrogen were an ideal gas; the value of the chemical potential is that which nitrogen as an ideal gas would have at a pressure of 97.03 atm.

Fugacities are determined experimentally or estimated from various models such as a Van der Waals gas that are closer to reality than an ideal gas. The ideal gas pressure and fugacity are related through the dimensionless fugacity coefficient .

For nitrogen at 100 atm, the fugacity coefficient is 97.03 atm / 100 atm = 0.9703. For an ideal gas, fugacity and pressure are equal so is 1.

The contribution of nonideality to the chemical potential of a real gas is equal to RT ln . Again for nitrogen at 100 atm, the chemical potential is μ = μ_id + RT ln 0.9703, which is less than the ideal value μ_id because of intermolecular attractive forces.

The fugacity is closely related to the thermodynamic activity. For a gas, the activity is simply the fugacity divided by a reference pressure to give a dimensionless quantity. This reference pressure is called the standard state and normally chosen as 1 atmosphere or 1 bar, Again using nitrogen at 100 atm as an example, since the fugacity is 97.03 atm, the activity is just 97.03 without units.

Accurate calculations of chemical equilibrium for real gases should use the fugacity rather than the pressure. The thermodynamic condition for chemical equilibrium is that the total chemical potential of reactants is equal to that of products. If the chemical potential of each gas is expressed as a function of fugacity, the equilibrium condition may be transformed into the familiar reaction quotient form (or law of mass action) except that the pressures are replaced by fugacities.

For a condensed phase (liquid or solid), the chemical potential is equal to that of the vapor in equilibrium with the condensed phase, and therefore the fugacity is equal to the fugacity of the vapor. This fugacity is approximately equal to the vapor pressure when the vapor pressure is not too high.

The word "fugacity" is derived from the Latin for "fleetness", which is often interpreted as “the tendency to flee or escape”. The concept of fugacity was introduced by American chemist Gilbert N. Lewis in 1901.