Langmuir theory for multicomponent adsorption

Of the three theories we will discuss, the Langmuir multicomponent expression is a more or less direct extension of a theory we have previously seen, i.e. of the Langmuir equation for binary systems that was presented in Chapter 7. 

There have been smdies of the impact of heterogeneity and improvements have been proposed but they lead to cumbersome equations. Consequently, the Langmuir equation is typically used in the simple form shown here. For a more detailed discussion of the various extensions of Langmuir equation, see the review by Shapiro and Stenby (2002). 

Despite these drastic assumptions, the Langmuir equation is often applied in the areas where assumptions behind it do not hold (e.g. adsorption of asphaltenes, surfactants or polymers). 

The popularity of the Langmuir equation is explained by the fact that it is the simplest dependence predicting linear (Henry-type) behaviour at low partial pressures and the appearance of saturation of the surface at high pressures, which is the expected physical behaviour for most of the systems. 

For multicomponent systems, the Langmuir equation is written for the j component as (using either adsorbed volumes or adsorptions in general)  

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