The variation of adsorption with pressure at a constant temperature is called adsorption isotherm.
(1) Freundlich adsorption isotherm
Freundlich, in 1909, gave an empirical relationship between the quantity of gas adsorbed by unit mass of solid adsorbent and pressure at a particular temperature. The relationship can be expressed by the following equation.
At constant temperature x/m = k · P1/n
where `x' is the mass of the gas adsorbed on a mass `m' of the adsorbent at a pressure P. k and n are constants which depend on the nature of the adsorbent and the gas at a particular temperature.
At low pressure, the amount of the gas adsorbed per unit quantity of adsorbent is proportional to the pressure. At high pressure, the amount of adsorbed gas is independent of pressure. At intermediate pressures, Freundlich adsorption isotherm is expected to hold
Langmuir Adsorption Isotherm :-
According to Langmuir —
(a) There is adsorption of gas molecules on the surface of the solid.
(b) There is desorption of the adsorbed molecules from the surface of the solid.
(c) There is formation of unimolecular layer and thus it is chemisorption
(e) A dynamic equilibrium is attained when rate of adsorption = rate of desorption.
(f) Based on the above facts, langmuir adsorption isotherm is represented as
Case-I At very high pressure
bp >>> 1, hence 1 + bp ≈ bp
Case-II At very low pressure
bp <<< 1
1 + bp ≈ 1
θ = ap,
θ ∝ p
This is shown along OA