# Freundlich equation

Freundlich's original data for adsorption of acetic acid (page 392 in [2]) and a fit according to Freundlich's exponential law

The Freundlich adsorption isotherm is mathematically expressed as

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

It is also written as

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

or

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

It is also written as

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

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 gas adsorption varies directly with pressure and then it directly varies with pressure raised to the power 1/n until saturation pressure Ps is reached. Beyond that point, the rate of adsorption saturates even after applying higher pressure. Thus, the Freundlich adsorption isotherm fails at higher pressure.