# Freundlich equation

## Contents

Example of the Freundlich isotherm, showing the amount adsorbed, q (e.g., in mol/kg), as a function of equilibrium concentration in the solution, c (e.g., in mol/L). The graph is for the values of the constants of K=4 and 1/n=0.6.

The Freundlich Adsorption Isotherm is mathematically expressed as

$\frac{x}{m} = Kp^{1/n}$

It is also written as

$\log\frac{x}{m} = \log K + \frac{1}{n} \log p$

or

$\frac{x}{m} = K c^{1/n}$

It is also written as

$\log \frac{x}{m} = \log K + \frac{1}{n} \log c$

where

p = Equilibrium pressure of adsorbate
c = Equilibrium concentration of adsorbate in solution.

K and n are constants for a given adsorbate and adsorbent at a particular temperature.

At high pressure 1/n = 0, hence extent of adsorption becomes independent of pressure.

It is used in cases where the actual identity of the solute is not known, such as adsorption of colored material from sugar, vegetable oil etc.

## Limitation of Freundlich adsorption isotherm

Experimentally it was determined that extent of adsorption varies directly with pressure until saturation pressure Ps is reached. Beyond that point rate of adsorption saturates even after applying higher pressure. Thus Freundlich Adsorption Isotherm failed at higher pressure.

## References

Freundlich HMF. Uber die adsorption in losungen. Z Phys Chem. 1906;57(A):385–470

Adsorption on heterogeneous surfaces: the exponential equation for the overall adsorption isothermM Jaroniec - Surface Science, 1975 Elsevier

Binary Langmuir and Freundlich isotherms for ideal adsorbed solutionsMD LeVan… - The Journal of Physical Chemistry, 1981 - ACS Publications