The **key difference** between Freundlich and Langmuir adsorption isotherms is that **Freundlich adsorption isotherm is empirical, whereas Langmuir adsorption isotherm is theoretical. **

The adsorption isotherm is a primary method that we can use to predict the adsorption capacity of a particular substance. There are two primary methods for this: Freundlich and Langmuir adsorption isotherms. These are very important in dealing with environmental protection and adsorption techniques.

### CONTENTS

1. Overview and Key Difference

2. What are Freundlich Adsorption Isotherms

3. What are Langmuir Adsorption Isotherms

4. Side by Side Comparison – Freundlich vs Langmuir Adsorption Isotherms in Tabular Form

5. Summary

## What is Freundlich Adsorption Isotherms?

Freundlich adsorption isotherm is the measurement of variation in the quantity of gas adsorbed by a unit mass of solid adsorbent with the change in pressure of a system for a given temperature. That means; the variables, in this case, are quantity of gas and pressure, while the mass of solid adsorbent and the temperature remain constant. The mathematical expression of the Freundlich adsorption isotherm is as follows:

**x/m = kP ^{(1/n)}**

Where x is the mass of the gas adsorbed, m is the mass of the adsorbent used, P is the pressure of the system, k and n are constants. Usually, the Freundlich adsorption isotherm is given in a graphical representation. Therefore, we first need to rearrange the above equation to make it suitable for a graph. There, we can take the logarithm of all the values. Then the equation is as follows.

**Log(x/m) = log k + (1/n) log P**

Therefore, the x-axis of the graph is log(x/m), y-axis is log P, and the slope is (1/n). The intercept of the graph is log k.

## What is Langmuir Adsorption Isotherms

Langmuir adsorption isotherm is the method used to predict linear adsorption at low adsorption densities and a maximum surface coverage at higher solute metal concentration. It is a theoretical expression and the chemical equation for this term is as follows:

**X/M = abc(1 + ac)**

Where, X is the weight of solute sorbed, M is the mass of the adsorbent, c is the equilibrium concentration of the solute, a and b are constants. Moreover, the Langmuir adsorption isotherm is applicable for monolayer adsorption on to a homogeneous surface. However, there should not be any interaction between adsorbed species.

## What is the Difference Between Freundlich and Langmuir Adsorption Isotherms?

There are two primary adsorption isotherms as Freundlich adsorption isotherm and Langmuir adsorption isotherm. Freundlich adsorption isotherm is the measurement of variation in the quantity of gas adsorbed by a unit mass of solid adsorbent with the change in pressure of a system for a given temperature. Langmuir adsorption isotherm is the method used to predict linear adsorption at low adsorption densities and a maximum surface coverage at higher solute metal concentration. The key difference between Freundlich and Langmuir adsorption isotherms is that Freundlich adsorption isotherm is empirical, but Langmuir adsorption isotherm is theoretical. Moreover, the former is a graphical representation while the latter is a mathematical expression by equation.

The following infographic summarizes the difference between Freundlich and Langmuir adsorption isotherms.

## Summary – Freundlich vs Langmuir Adsorption Isotherms

Freundlich adsorption isotherm is the measurement of variation in the quantity of gas adsorbed by a unit mass of solid adsorbent with the change in pressure of a system for a given temperature. Langmuir adsorption isotherm, on the other hand, is the method used to predict linear adsorption at low adsorption densities and a maximum surface coverage at higher solute metal concentration. The key difference between Freundlich and Langmuir adsorption isotherms is that Freundlich adsorption isotherm is empirical whereas Langmuir adsorption isotherm is theoretical.

##### Reference:

1. “Adsorption Isotherms – Freundlich Adsorption Isotherms, Langmuir Adsorption Isotherms & BET Adsorption Isotherms.” BYJUS, Byju’s, 17 Dec. 2019, Available here.

2. “Freundlich Equation.” Wikipedia, Wikimedia Foundation, 13 Nov. 2019, Available here.

##### Image Courtesy:

1. “Freundlich acetic acid” By Toshiyouri – Own work (CC BY-SA 4.0) via Commons Wikimedia

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