Page 141 - Introduction to Colloid and Surface Chemistry

The solid-gas interface 131

The BET equation for multimolecular adsorption

Because the forces acting in physical adsorption are similar to those
operating in liquefaction (i.e. van der Waals forces), physical
adsorption (even on flat and convex surfaces) is not limited to a
monomolecular layer, but can continue until a multimolecular layer
of liquid covers the adsorbent surface.
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The theory of Brunauer, Emmett and Teller is an extension of
the Langmuir treatment to allow for multilayer adsorption on non-
porous solid surfaces. The BET equation is derived by balancing the
rates of evaporation and condensation for the various adsorbed
molecular layers, and is based on the simplifying assumption that a
characteristic heat of adsorption A//! applies to the first monolayer,
while the heat of liquefaction, A// L, of the vapour in question applies
to adsorption in the second and subsequent molecular layers. The
equation is usually written in the form
P == 1 + (c-1) p
: 77- T; (5.ii)

where p 0 is the saturation vapour pressure, V m is the monolayer
capacity and c «* exp [ (A// L — A/fi)//?T|.
The main purpose of the BET equation is to describe type II
isotherms. In addition, it reduces to the Langmuir equation at low
pressures; and type III isotherms are given in the unusual circum-
stances, when monolayer adsorption is less exothermic than liquefac-
tion, i.e. c < 1 (see Figure 5.11).
The BET model can also be applied to a situation which might be
applicable to porous solids. If adsorption is limited to n molecular
layers (where n is related to the pore size), the equation

l
V = ^ - ( „. ^ (5,2)

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is obtained , where x = p/p 0. This equation is, in fact, a general
expression which reduces to the Langmuir equation when n = I and
to the BET equation when n — °°.