Fugacity

Fugacity is a thermodynamic property of a real gas or liquid that effectively replaces pressure in accurate calculations of chemical potential. It is a measure of the "escaping tendency" of a substance from a phase. Because real gases and liquids deviate from ideal behavior, particularly at high pressures and low temperatures, using pressure directly in thermodynamic calculations can lead to significant errors. Fugacity accounts for these non-ideal behaviors.

In essence, fugacity is a corrected pressure that allows the use of ideal gas equations and relationships with greater accuracy for real substances. It has units of pressure (typically Pascals or atmospheres).

Definition:

The fugacity f of a substance is defined such that the chemical potential μ is related to fugacity by:

μ = μ⁰(T) + RT ln(f)

where:

• μ is the chemical potential of the substance.
• μ⁰(T) is the standard chemical potential of the substance at temperature T (a reference state).
• R is the ideal gas constant.
• T is the absolute temperature.

For an ideal gas, fugacity is equal to the pressure (f = P). The deviation from ideality is quantified by the fugacity coefficient (φ), defined as:

φ = f/P

Therefore, the fugacity coefficient represents the ratio of the fugacity to the pressure. For an ideal gas, φ = 1. For real gases, φ can be greater than or less than 1, depending on the specific gas, temperature, and pressure.

Significance and Applications:

Fugacity is crucial in chemical engineering, thermodynamics, and physical chemistry for accurately modeling and predicting phase equilibria, reaction equilibria, and other thermodynamic properties of real systems. It is used in:

• Phase equilibrium calculations: Determining the conditions (temperature, pressure, composition) under which different phases (e.g., liquid and vapor) of a substance can coexist in equilibrium.
• Reaction equilibrium calculations: Calculating the equilibrium constant for chemical reactions involving real gases or liquids.
• Separation processes: Designing and optimizing separation processes such as distillation, absorption, and extraction.
• High-pressure processes: Modeling the behavior of substances at high pressures, where deviations from ideal gas behavior are significant.
• Supercritical fluids: Predicting the properties and behavior of supercritical fluids, which have unique solvent characteristics.

Determination of Fugacity:

Fugacity can be determined experimentally or from equations of state. Experimental methods involve measuring the pressure-volume-temperature (PVT) behavior of the substance. Equations of state, such as the van der Waals equation, the Peng-Robinson equation, and the Soave-Redlich-Kwong equation, are used to calculate fugacity coefficients and subsequently fugacities. The choice of equation of state depends on the substance, the range of temperatures and pressures, and the desired accuracy.