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.
Accurate calculations of chemical equilibrium for real gases should use the fugacity rather than the pressure.
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.
The differential change of the chemical potential between two states of slightly different pressures but equal temperature (i.e., dT = 0) is given by
where ln p is the natural logarithm of p. For real gases the equation of state will depart from the simpler one, and the result above derived for an ideal gas will only be a good approximation provided that (a) the typical size of the molecule is negligible compared to the average distance between the individual molecules, and (b) the short range behavior of the inter-molecular potential can be neglected, i.e., when the molecules can be considered to rebound elastically off each other during molecular collisions.
[2]: 248–249 If a reference state is denoted by a zero superscript, then integrating the equation for the chemical potential gives
[1] This means that the molar Gibbs energy of real nitrogen at a pressure of 100 atm is equal to the molar Gibbs energy of nitrogen as an ideal gas at 97.03 atm.
The contribution of nonideality to the molar Gibbs energy of a real gas is equal to RT ln φ.
The fugacity of a condensed phase (liquid or solid) is defined the same way as for a gas:
When calculating the fugacity of the compressed phase, one can generally assume the volume is constant.
At constant temperature, the change in fugacity as the pressure goes from the saturation press Psat to P is
This equation allows the fugacity to be calculated using tabulated values for saturated vapor pressure.
Often the pressure is low enough for the vapor phase to be considered an ideal gas, so the fugacity coefficient is approximately equal to 1.
[6]: 345–346 [7] Unless pressures are very high, the Poynting factor is usually small and the exponential term is near 1.
Frequently, the fugacity of the pure liquid is used as a reference state when defining and using mixture activity coefficients.
It does not add any new information compared to the chemical potential, but it has computational advantages.
As the molar fraction of a component goes to zero, the chemical potential diverges but the fugacity goes to zero.
In addition, there are natural reference states for fugacity (for example, an ideal gas makes a natural reference state for gas mixtures since the fugacity and pressure converge at low pressure).
The fugacities commonly obey a similar law called the Lewis and Randall rule:
where f*i is the fugacity that component i would have if the entire gas had that composition at the same temperature and pressure.
This is a good approximation when the component molecules have similar size, shape and polarity.
where ΔHm is the change in molar enthalpy as the gas expands, liquid vaporizes, or solid sublimates into a vacuum.
[10] The fugacity can be deduced from measurements of volume as a function of pressure at constant temperature.
This is useful because of the theorem of corresponding states: If the pressure and temperature at the critical point of the gas are Pc and Tc, we can define reduced properties Pr = P/Pc and Tr = T/Tc.
Then, to a good approximation, most gases have the same value of Z for the same reduced temperature and pressure.
However, in geochemical applications, this principle ceases to be accurate at pressures where metamorphism occurs.
[11]: 247 For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is
Since the pressure and the molar volume are related through the equation of state; a typical procedure would be to choose a volume, calculate the corresponding pressure, and then evaluate the right-hand side of the equation.
In the sense of an "escaping tendency", it was introduced to thermodynamics in 1901 by the American chemist Gilbert N. Lewis and popularized in an influential textbook by Lewis and Merle Randall, Thermodynamics and the Free Energy of Chemical Substances, in 1923.