# What is the Difference Between Activity Coefficient and Fugacity Coefficient

Activity coefficient and fugacity coefficient are useful terms in thermodynamics and physical chemistry, particularly in the context of solutions or mixtures. The difference between activity coefficient and fugacity coefficient lies in their respective applications within thermodynamics.

What is the difference between activity coefficient and fugacity coefficient? Activity coefficient, denoted by γ, is used in the context of solutions, especially non-ideal solutions, while fugacity coefficient, denoted by φ, is used in the context of gases, especially non-ideal gases.

### Key Areas Covered

1. What is Activity Coefficient
– Definition, Features, Calculation
2. What is Fugacity Coefficient
– Definition, Features, Calculation
3. Similarities Between Activity Coefficient and Fugacity Coefficient
– Outline of Common Features
4. Difference Between Activity Coefficient and Fugacity Coefficient
– Comparison of Key Differences
5. FAQ: Activity Coefficient and Fugacity Coefficient

### Key Terms

Activity Coefficient, Fugacity Coefficient

## What is Activity Coefficient

Activity coefficient is a measure of the deviation of a solution’s behavior from ideal behavior. In an ideal solution, the interactions between solvent and solute molecules are assumed to be equivalent to those between solvent-solvent and solute-solute molecules. However, in real solutions, especially when the solute concentration is high or when the solute molecules are significantly different in size or polarity from the solvent molecules, deviations from ideal behavior occur.

The activity coefficient (γ) is defined as the ratio of the actual concentration of a species to its concentration as predicted by an ideal solution. Mathematically, it is expressed as:

a = γc

Where:

• a is the activity of the species,
• c is its concentration,
• γ is the activity coefficient.

Activity coefficient accounts for the non-ideality of a solution by adjusting the concentration term to reflect the true behavior of the solution. When

γ=1, the solution behaves ideally. However, when

γ≠1

the solution deviates from ideal behavior, and the activity coefficient becomes necessary to correct the concentration term.

Activity coefficients are influenced by various factors such as temperature, pressure, and the nature of the solute and solvent molecules. They are typically determined experimentally through measurements of colligative properties, such as osmotic pressure, vapor pressure, or freezing point depression.

## What is Fugacity Coefficient

Fugacity coefficient is a crucial concept in thermodynamics and chemical engineering, particularly in the study of phase equilibria and the behavior of real gases and liquids. It is denoted by the symbol φ and is defined as the ratio of the fugacity of a component in a mixture to its partial pressure under the same conditions of temperature, pressure, and composition. The fugacity of a component is a measure of its tendency to escape or vaporize from a mixture, analogous to pressure for ideal gases.

In simpler terms, the fugacity coefficient accounts for deviations from ideal behavior in gases and liquids. For ideal gases, the fugacity coefficient is equal to 1, indicating that the gas behaves according to the ideal gas law. However, real gases and liquids often deviate from ideal behavior due to intermolecular interactions and non-ideal conditions.

The fugacity coefficient varies with changes in temperature, pressure, and composition of the mixture. It is often determined experimentally or calculated using thermodynamic models such as the Van der Waals equation of state or the Redlich-Kwong equation. These models incorporate correction factors to account for deviations from ideal behavior and provide more accurate predictions of phase equilibria.

Understanding fugacity coefficients is essential in various industrial processes, such as chemical reactions, separation processes, and gas purification. Engineers use fugacity coefficients to design and optimize processes, ensuring efficient operation and accurate prediction of equilibrium conditions. Additionally, fugacity coefficients play a crucial role in environmental studies, particularly in modeling gas-phase reactions and predicting pollutant behavior in the atmosphere.

## Similarities Between Activity Coefficient and Fugacity Coefficient

1. Both activity coefficient (γ) and fugacity coefficient (φ) are correction factors used to adjust for deviations from ideal behavior in solutions or mixtures.
2. In both cases, these coefficients affect equilibrium calculations.

## Difference Between Activity Coefficient and Fugacity Coefficient

### Definition

• Activity coefficient (γ) measures the non-ideality of a solution, specifically how the activity of a component differs from its concentration in an ideal solution. Fugacity coefficient (φ) quantifies the deviation from ideal gas behavior in gases, representing how the fugacity of a gas differs from its pressure in an ideal gas.

### Measurement

• Activity coefficient is often determined experimentally using methods like vapor pressure measurements, osmotic pressure measurements, or activity coefficients of a solute in different solvents. Meanwhile, fugacity coefficient can be calculated using equations of state, such as the van der Waals equation or the Redlich-Kwong equation, along with experimental data to correlate the behavior of real gases.

### Deviation

• Activity coefficient reflects the deviation of the solution’s behavior from ideal behavior due to interactions between solute and solvent molecules, including effects like solute-solvent interactions and solvent-solvent interactions. However, fugacity coefficient accounts for deviations from ideal gas behavior caused by factors such as molecular volume, intermolecular forces, and compressibility of the gas molecules. It provides a measure of the non-ideality of gases under non-standard conditions.

## Conclusion

In conclusion, while both activity coefficient and fugacity coefficient serve to correct for deviations from ideal behavior in solutions and gases respectively, they operate in distinct domains. Activity coefficient addresses non-ideality in solutions, reflecting interactions between solute and solvent molecules. Conversely, fugacity coefficient pertains to deviations from ideal gas behavior, considering factors like molecular volume and intermolecular forces. Both coefficients play pivotal roles in understanding and predicting thermodynamic properties, guiding industrial processes, and environmental studies.

## FAQ: Activity Coefficient and Fugacity Coefficient

### 1. What is the coefficient of fugacity?

• The coefficient of fugacity, often denoted by φ, represents the ratio of the fugacity of a substance to its pressure. It serves as a correction factor that accounts for deviations from ideal gas behavior.

### 2. What is the purpose of activity coefficient?

• The activity coefficient is used to measure how much a solution’s properties differ from those of an ideal solution with the same composition. It’s a practical tool in thermodynamics for understanding how real-world solutions deviate from ideal behavior. By considering interactions between components, the activity coefficient helps predict properties like vapor pressure, osmotic pressure, and solubility more accurately.

### 3. What does the activity coefficient represent?

• The activity coefficient in chemistry represents the ratio of the chemical activity of a substance to its molar concentration. It quantifies how the behavior of a substance in a solution differs from what would be expected based solely on its concentration.

### 4. What are the factors affecting fugacity?

• Fugacity is influenced by factors such as pressure, temperature, volume, and composition. Equations like the van der Waals equation or the Redlich-Kwong equation help calculate the fugacity coefficient, which indicates how far from ideal gas behavior a substance behaves. Intermolecular forces and molecular size also impact fugacity.

### 5. What is meant by fugacity=1?

• When the fugacity coefficient equals 1, it implies that the gas behaves ideally, meaning there are no significant interactions between its molecules. In other words, the gas follows ideal gas laws closely, with properties like pressure, volume, and temperature behaving as predicted by ideal gas behavior.
##### Reference:

1. “Fugacity.” Wikipedia. Wikipedia Foundation.
2. “Activity Coefficient.” Wikipedia. Wikipedia Foundation.

##### Image Courtesy:

1. “UNIQUACRegressionChloroformMethanol” By WilfriedC – Own work (CC BY-SA 3.0) via Commons Wikimedia

### About the Author: Hasini A

Hasini is a graduate of Applied Science with a strong background in forestry, environmental science, chemistry, and management science. She is an amateur photographer with a keen interest in exploring the wonders of nature and science.