Adsorption using the Langmuir equation

Langmuir derived his famous adsorption theory based on the assumption that the adsorption rate is proportional to the concentration in the solution and the fraction of free non-covered area of the adsorbent. The desorption rate, on the other hand, is considered to be proportional to the fraction of surface covered by adsorbate molecules. At equilibrium, the adsorption and desorption rates are equal. The Langmuir theory is derived based on many simplifying assumptions  

These assumptions could, in theory, very much restrict the applicability of Langmuir s equation. However, surprisingly, the Langmuir theory is of wide applicability in numerous adsorption phenomena, especially chemical adsorption and physical adsorption at low pressures and high temperatures. This is possibly due to cancellation of errors, and the fact that the Langmuir equation can fit a plateau shaped curve, which many monolayers and in general many adsorption phenomena follow. In brief, Langmuir is an excellent correlative model. 

In the case of gas-solid adsorption, the mathematical representation of the Langmuir equation is often given as the fraction of occupied active centres (or volume per mass of solid) over the total active centres (or the volume of monolayer) against pressure. The equation and its linear form are shown in Equation 7.1  

The volume V is expressed in, for example, em g (solid). P is the pressure, wMle V and B are adjustable parametCTs, respectively, the volume of the monolayer and the affinity parameto. The higher the B-parameter is, the highCT is the affinity of a gas for the soUd. 

Note that a plot of P/V versus P gives a straight line. The slope is 1/Vm and the intereept is lIBVm-At low pressures, Langmuir approaehes the Henry equation (V = BV P). 

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