Fugacity

Fugacity is a thermodynamic property that is used to describe the tendency of a substance to escape or expand. It is particularly useful in the study of chemical equilibrium and phase equilibrium in thermodynamics. Fugacity is analogous to pressure in an ideal gas but is applicable to real gases and liquids.

Definition

Fugacity is defined as the effective pressure exerted by a species in a mixture of gases or liquids. It is introduced to account for deviations from ideal behavior. The fugacity of a substance in a given phase is related to its chemical potential and can be expressed mathematically as:

\(\mu = \mu^\circ + RT \ln(f)\)

where:

• \(\mu\) is the chemical potential,
• \(\mu^\circ\) is the standard chemical potential,
• \(R\) is the universal gas constant,
• \(T\) is the temperature,
• \(f\) is the fugacity.

Fugacity Coefficient

The fugacity coefficient (\(\phi\)) is a dimensionless number that quantifies the deviation of a real gas from ideal gas behavior. It is defined as the ratio of the fugacity to the pressure:

\(\phi = \frac{f}{P}\)

where:

• \(f\) is the fugacity,
• \(P\) is the pressure.

For an ideal gas, the fugacity coefficient is equal to 1.

Applications

Fugacity is used in various fields of chemical engineering, physical chemistry, and environmental science. It is essential for:

• Calculating the equilibrium constant for reactions involving gases.
• Determining the vapor-liquid equilibrium in mixtures.
• Modeling the behavior of pollutants in the environment.

Calculation

Fugacity can be calculated using different methods depending on the system under consideration. For real gases, the Peng-Robinson equation of state or the van der Waals equation can be used to estimate fugacity. For liquids, activity coefficients and excess Gibbs free energy models are often employed.

Related Concepts

• Activity (chemistry)
• Partial pressure
• Chemical potential
• Equilibrium constant
• Phase diagram

See Also

• Thermodynamics
• Chemical equilibrium
• Phase equilibrium
• Ideal gas law
• Real gas