Adsorption isotherms have been of immense importance to researches dealing with environmental protection and adsorption techniques. The two primary methods used for predicting the adsorption capacity of a given material are known as the Freundlich and Langmuir isotherms.

An adsorption isotherm is a graph that represents the variation in the amount of adsorbate(x) adsorbed on the surface of the adsorbent with the change in pressure at a constant temperature.

## As we know from Le Chatelier’s principle, the direction of equilibrium in a reaction shifts in the direction in which stress is relieved. So, here we can see that upon application of excess pressure on the system, the equilibrium shifts in the direction where the number of molecules decreases so that the pressure in the system decreases.

From the graph, we also observe that after attaining a pressure Ps, that is the saturation pressure, the variation in the amount of adsorbent adhering to the adsorbate becomes zero. This happens because the surface area available for adsorption is limited and as all the sites are occupied, a further increase in pressure does not cause any difference.

Different adsorption isotherms have been proposed by different scientists namely,

• Langmuir isotherm
• Freundlich isotherm
• BET theory

The graph shown above shows the isotherm proposed by Freundlich.

Freundlich adsorption gives the variation in the quantity of gas adsorbed by a unit mass of solid adsorbent with the change in pressure of the system for a given temperature. The expression for the Freundlich isotherm can be represented by the following equation: where n>1

Where x is the mass of the gas adsorbed, m is the mass of the adsorbent, P is the pressure and n is a constant which depends upon the nature of adsorbent and the gas at a given temperature. Taking the logarithm on both the sides of the equation, we get, The plot of this equation is a straight line as represented by the following curve.

## The Freundlich adsorption isotherm is followed by another two isotherms, Langmuir adsorption isotherms and BET theory. The Langmuir adsorption isotherms predict linear adsorption at low adsorption densities and a maximum surface coverage at higher solute metal concentrations.

The Langmuir adsorption isotherm has the form:

X/M = abc(l + ac)

where

• X is the weight of a solute sorbed by M grams of solid,
• C is the equilibrium solute concentration,
• a and b are constants 1/a equals the concentration when 1/2 of the available adsorption sites.

The Langmuir adsorption is applicable for monolayer adsorption onto a homogeneous surface when no interaction occurs between adsorbed species.

The theory of multilayer adsorption proposed by Brunauer, Emmett and Teller in 1938 (BET Theory) assumes that physisorption results in the formation of multilayer adsorption. The theory also assumes that the solid surface has uniform sites of adsorption and that adsorption at one site does not affect adsorption at neighbouring sites.

After the formation of the monolayer, the adsorption process can continue with the formation of multilayer involving the second layer, third layer and so on.

The equation for BET is 