Fits which Yield Relative Numbers for the Surface Area

ISOTHERM FITS WHICH YIELD RELATIVE NUMBERS FOR THE SURFACE AREA 

The Langmuir isotherm is most appropriately suited for the description of chemisorption. The underlying assumption is that the adsorbate from the gas is in equilibrium with a bonded or tightly held species on the surface. A reaction such as 

The general shape of this curve is presented in Fig. 39 with different values of K. The value of % is set to 1 in this figure. The value of Hq approaches as P oo. For subsequent discussions one could say for this figure that estimating % by looking at where the knee , at least on this scale, give a correct value within 50%. (This is deceptive due to the approximate invariance of the scaling.) 

Using the Langmuir isotherm one cannot obtain a surface area number, unless one knows how the surface sites are distributed. If one knows that the approximate area required for one bonding location is 0.2 nm then one can conclude from a calculation of % what the area is. An assumption implied in this is that the activity of the surface site is proportional to the number of sites available divided by the original number, i.e. the mole fraction of species on the surface. In bulk calculations, this is referred to as the saturation limit. The assumption that full saturation is the same as the number of original sites may not be valid either in the bulk or on surfaces. 

As useful as the Langmuir isotherm is, due to the site assumption, it is impossible to use it for physisorption. There have been some derivations which assume that the sites do not exist however, these derivations suffer from the unrealistic assumption of localized forces without localization. Implicit in chemical bonding is the assumption of directional, local bonds. 

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