Now since the adsorption is limited to complete coverage by monolayer, the surface can be divided in two parts:

1. 1. fraction θ covered by adsorbed molecule

2. fraction (1- θ ) which is bare

Since only those molecules that strikes the uncovered part of the surface can adsorb, the rate of adsorption per unit of total surface will also be proportional to (1- θ ). Therefore the rate of adsorption is . Rate of desorption on the other hand is proportional to fraction of covered surface that is

At equilibrium ,

or

or

where .

Further θ can be written as

where v = volume of gas adsorbed and v_m = volume of gas adsorbed at monolayer coverage.

[5]

This is known as the Langmuir isotherm. Among the empirical isotherms, only Type I isotherm ( Fig.1) agrees with the Langmuir equation. The Langmuir equation is valid for less than monolayer coverage and therefore more suited for chemisorption as chemisorption is limited to monolayer coverage. Deviations for other isotherms are mainly due to certain assumptions such as

1. 1. sites are of equal activity

2. no interaction between adsorbed molecules

These assumptions correspond to constant heat of adsorption. However for real systems, the heat of adsorption changes with surface coverage. The adsorption of H₂ on metal films of Fe, Ni, W, drops with the increase in surface coverage. Two other well known isotherms, namely Temkin isotherms and Freundlich isotherm, may be derived in terms of dependency of heat of adsorption on fraction of surface coverage. The Temkin isotherms may be derived from the Langmuir isotherm by assuming that the heat of adsorption decreases linearly with increasing surface coverage θ. The result is where k₁ and k₂ are constant at given temperature. The Freundlich isotherm can be derived assuming a logarithmic decrease in heat of adsorption with surface coverage, i.e . The isotherm is in the form of . The value of ‘n' is generally greater than unity. The adsorption of H₂ gas on tungsten follows this isotherm.