JEE Main & Advanced Chemistry Surface & Nuclear Chemistry / भूतल और नाभिकीय रसायन Adsorption Isotherms

A mathematical equation, which describes the relationship between pressure (p) of the gaseous adsorbate and the extent of adsorption at any fixed temperature, is called adsorption isotherms.

The extent of adsorption is expressed as mass of the adsorbate adsorbed on one unit mass of the adsorbent.

Thus, if x g of an adsorbate is adsorbed on m g of the adsorbent, then

\[\text{Extent}\,\text{of}\,\text{adsorption}\,=\frac{x}{m}\]

Various adsorption isotherms are commonly employed in describing the adsorption data.

(1) Freundlich adsorption isotherm

(i) Freundlich adsorption isotherm is obeyed by the adsorptions where the adsorbate forms a monomolecular layer on the surface of the adsorbent.

\[\frac{x}{m}=k{{p}^{\frac{1}{n}}}\] (Freundlich adsorption isotherm) or

\[\log \frac{x}{m}=\log k+\frac{1}{n}\log p\]

where x is the weight of the gas adsorbed by m gm  of the adsorbent at a pressure p, thus x/m represents the amount of gas adsorbed by the adsorbents per gm  (unit mass), k and n are constant at a particular temperature and for a particular adsorbent and adsorbate (gas), n is always greater than one, indicating that the amount of the gas adsorbed does not increase as rapidly as the pressure.

(ii) At low pressure, the extent of adsorption varies linearly with pressure. \[\frac{x}{m}\propto p'\]

(iii) At high pressure, it becomes independent of pressure. \[\frac{x}{m}\propto {{p}^{0}}\]

(iv) At moderate pressure \[\frac{x}{m}\] depends upon pressure raised to powers \[\frac{x}{m}\propto {{p}^{\frac{1}{n}}}\]

(2) The Langmuir - adsorption isotherms 

(i) One of the drawbacks of Freundlich adsorption isotherm is that it fails at high pressure of the gas. Irving Langmuir in 1916 derived a simple adsorption isotherm, on theoretical considerations based on kinetic theory of gases. This is named as Langmuir adsorption isotherm.

(a) Adsorption takes place on the surface of the solid only till the whole of the surface is completely covered with a unimolecular layer of the adsorbed gas.

(b) Adsorption consists of two opposing processes, namely Condensation of the gas molecules on the solid surface and  Evaporation (desorption) of the gas molecules from the surface back into the gaseous phase.            

(c) The rate of condensation depends upon the uncovered (bare) surface of the adsorbent available for condensation. Naturally, at start when whole of the surface is uncovered the rate of condensation is very high and as the surface is covered more and more, the rate of condensation progressively decreases. On the contrary, the rate of evaporation depends upon the covered surface and hence increases as more and more of the surface is covered ultimately an equilibrium will be set up at a stage when the rate of condensation becomes equal to the rate of evaporation (adsorption equilibrium).

(d) The rate of condensation also depends upon the pressure of the gas since according the kinetic theory of gases, the number of molecules striking per unit area is proportional to the pressure.

Mathematically, \[\frac{x}{m}=\frac{ap}{1+bp}\], where a and b are constants and their value depends upon the nature of gas (adsorbate), nature of the solid adsorbent and the temperature. Their values can be determined from the experimental data.

Limitation of Langmuir theory

(a) Langmuir’s theory of unimolecular adsorption is valid only at low pressures and high temperatures.

(b) When the pressure is increased or temperature is lowered, additional layers are formed. This has led to the modern concept of multilayer adsorption.