36.2.3 |
Langmuir Adsorption Isotherm
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In the Langmuir model, the adsorbent surface is considered to possess a number of active interaction sites for adsorption. Langmuir derived a relation between adsorbed material and its equilibrium concentration. His assumption are: |
1. |
There are fixed adsorption sites on the surface of the adsorbent. At a given temperature and pressure, some fraction of these sites are occupied by adsorbate molecules. Let this fraction be
 . |
2. |
Each site on the surface of the adsorbent can hold one adsorbate molecule. |
3. |
The heat of adsorption is the same for each site and is independent of . |
4. |
There is no interaction between molecules on different sites. |
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Considering the processes of adsorption and desorption of the molecules on the surface, the Langmuir adsorption isotherm may be obtained as follows: |
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Rate of adsorption of molecules on the surface of the adsorbent = k aCe(1 - ) |
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where x and Xm are the amount of the adsorbent adsorbed at equilibrium concentration Ce and maximum amount of adsorbate for the formation of monolayer, respectively. |
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rearranging equation (36.2.2), we get |
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If we plot  vs  , we will get a straight line. Slope of which will be  and intercept as  . |
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Therefore, from values of intercept and slope of the plot values of Xm and KL could be calculated. In the case for the adsorption of gaseous substrate, Ce, X, and Xm will be replaced by p.V, and Vm, respectively.
For chemisorption too, Langmuir’s equation works very well but fails for the cases where multilayer formation takes place. |
