Chemistry > Surface Chemistry > 4.0 Adsorption Isotherms
Surface Chemistry
1.0 Introduction
2.0 Adsorption
3.0 Factors affecting adsorption of gases by solids
4.0 Adsorption Isotherms
5.0 Applications of Adsorption
6.0 Types of Solutions
7.0 Colloidal System
7.1 Different Colloidal Systems
7.2 Classification of Colloidal System
7.3 Preparation of Colloidal System
7.4 Purification of Colloidal System
7.5 Properties of colloidal system
8.0 Coagulation of colloidal solutions
9.0 Emulsions
10.0 Catalysis
11.0 Zeolites as shape-selective catalysts
12.0 Enzyme as catalysts
12.1 Characteristics of Enzymes
12.2 Mechanism of enzyme catalysis
12.3 Autocatalysis
12.4 Induced catalysis
4.2 The Langmuir adsorption isotherm
7.2 Classification of Colloidal System
7.3 Preparation of Colloidal System
7.4 Purification of Colloidal System
7.5 Properties of colloidal system
12.2 Mechanism of enzyme catalysis
12.3 Autocatalysis
12.4 Induced catalysis
Langmuir deduced a theoretical relationship which has been found to be more in agreement with many experimental facts over a wide range of pressure than the Freundlich isotherm.
Actually, Freundlich adsorption isotherm is only a special case of Langmuir isotherm for intermedial pressures. The main points of Langmuir's theory of adsorption are summarised below:
1. 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.
2. Adsorption consists of two opposing processes, namely
- condensation of the gas molecules on the solid surface
- evapouration (desorption) of the gas molecules from the surface back into the gaseous phase.
3. 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 evapouration depends upon the covered surface and hence increases as more and more of the surface is covered. Ultimately an equlibrium will be set up at a stage when the rate of condensation becomes equal to the rate of evapouration.
4. The rate of condensation also depends upon the pressure of the gas since according to kinetic theory of gases, the number of molecules striking per unit area is proportional to the pressure. Mathematically,$$\frac{x}{m} = \frac{{ap}}{{l + bp}}$$
The values of the constants $a$ and $b$ depend upon the nature of the gas (adsorbate), nature of the solid adsorbent and the temperature. Their values can be determined from 
the experimental data.
the experimental data.Case I: If pressure $p$ is very high then $bp > > > 1$, hence $1 + bp \approx bp$ $$\frac{x}{m} = \frac{{ap}}{{bp}} = \frac{a}{b} = {\text{constant}}$$ This indicates saturation point as shown along $BC$ in the figure.
Case II: At very low pressure
$$bp < < 1$$ $$\therefore 1 + bp \approx 1$$$$\frac{x}{m} = ap$$ $$\frac{x}{m} \propto p$$ This is shown along $OA$ in the figure.
Limitation of Langmuir's theory
Langmuir's theory of unimolecular adsorption is valid only at comparatively low pressures and high temperatures. As the pressure is increased or temperature is lowered, additional layers are formed. This has led to the modern concept of multi layer adsorption.
