The **key difference between equation of state and activity coefficient** is that equation of state can be applied for both liquid and gas phases, whereas the activity coefficient is applied only for gases.

Equation of state and activity coefficient are important chemical concepts. Equation of state can be defined as a thermodynamic equation related to state variables describing the state of matter at certain physical conditions. Activity coefficient is a factor useful in thermodynamics for the accounting of deviations that comes from ideal behaviour in a mixture of chemical substances.

### CONTENTS

1. Overview and Key Difference

2. What is Equation of State

3. What is Activity Coefficient

4. Equation of State vs Activity Coefficient in Tabular Form

5. Summary – Equation of State vs Activity Coefficient

## What is Equation of State?

Equation of state can be defined as a thermodynamic equation that is related to the state variables describing the state of matter at certain physical conditions. The physical conditions that can be specified include pressure, volume, temperature, and internal energy. This equation is very important in explaining the properties of fluids, fluid mixtures, solids, etc.

There are no equations of state describing the properties of all substances accurately under all conditions. Therefore, we describe the properties using the ideal state of substances. For example, ideal gas law is a type of equation of state. This equation is approximately accurate for weak polar gases when low pressures and moderate temperatures are considered.

The general form of the equation of state can be given as follows:

**f(p,V,T) = 0**

Here, p is absolute pressure, V is volume, and T is the absolute temperature. Classical ideal gas law, quantum ideal gas law, cubic equations of state, non-cubic equations of state, virial equations of state, SAFT equations of state, multiparameter equations of state, etc., are some types of equations of state.

## What is Activity Coefficient?

Activity coefficient is a factor used in thermodynamics for the accounting of deviations that come from ideal behaviour in a mixture of chemical substances. When considering an ideal mixture, the microscopic interactions between pairs of chemical species are usually similar. Therefore, we can express the properties of the mixtures directly in terms of simple concentrations or partial pressures of the substances present. An example of this is Raoult’s law. We can give the deviations from ideality by modifying the concentration using an activity coefficient. The opposite of the activity coefficient is the fugacity coefficient.

Typically, we can determine the activity coefficient through experimental methods. This is done by making measurements on non-ideal mixtures. The two major methods are the radiochemical methods and the infinite dilution method. For example. We can get the activity coefficient for binary mixtures at the infinite dilution of each component.

## What is the Difference Between Equation of State and Activity Coefficient?

Equation of state and activity coefficient are important chemical concepts. Equation of state is a thermodynamic equation related to the state variables describing the state of matter at certain physical conditions while activity coefficient is a factor used in thermodynamics for the accounting of deviations that comes from ideal behaviour in a mixture of chemical substances. The key difference between equation of state and activity coefficient is that equation of state can be applied for both liquid and gas phases, whereas the activity coefficient is applied only for gases. Moreover, the equation of state is complicated to use whereas the activity coefficient is comparatively simple to use.

The following infographic lists the differences between equation of state and activity coefficient in tabular form for side by side comparison.

## Summary – Equation of State vs Activity Coefficient

Equation of state and activity coefficient are important chemical concepts. The key difference between equation of state and activity coefficient is that equation of state can be applied for both liquid and gas phases, whereas the activity coefficient is applied only for gases.

##### Reference:

1. “Equation of State.” *NASA*.

##### Image Courtesy:

1. “UNIQUAC Regression Chloroform Methanol” By WilfriedC – Own work (CC BY-SA 3.0) via Commons Wikimedia

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