Page 138 - Introduction to Colloid and Surface Chemistry

128 The solid—gas interface

Isotherm equations

Numerous attempts have been made at developing mathematical
expressions from postulated adsorption mechanisms to fit the various
experimental isotherm curves. The three isotherm equations which
are most frequently used are those due to Langmuir, to Freundlich,
and to Brunauer, Emmett and Teller (BET).

The Langmuir adsorption isotherm

Before 1916, adsorption theories postulated either a condensed liquid
film or a compressed gaseous layer which decreases in density as the
distance from the surface increases. Langmuir (1916) was of the
opinion that, because of the rapidity with which intermolecular forces
fall off with distance, adsorbed layers are not likely to be more than
one molecular layer in thickness.' This view is generally accepted for
chemisorption and for physical adsorption at low pressures and
moderately high temperatures.
The Langmuir adsorption isotherm is based on the characteristic
assumptions that (a) only monomolecular adsorption takes place, (b)
adsorption is localised and (c) the heat of adsorption is independent
of surface coverage. A kinetic derivation follows in which the
velocities of adsorption and desorption are equated with each other
to give an expression representing adsorption equilibrium.
Let V equal the equilibrium volume of gas adsorbed per unit mass
of adsorbent at a pressure p and V m equal the volume of gas required
to cover unit mass of adsorbent with a complete monolayer.
The velocity of adsorption depends on: (a) the rate at which gas
molecules collide with the solid surface, which is proportional to the
pressure; (b) the probability of striking a vacant site (1 — V/V m); and
(c) an activation term exp [—E/RT], where E is the activation energy
for adsorption.
The velocity of desorption depends on: (a) the fraction of
the surface which is covered, V/V m; and (b) an activation term
exp [—E'/RT\, where E' is the activation energy for desorption.
Therefore, when adsorption equilibrium is established,

~ VI V m )exp[-E / RT] = k(V I V m )exp[-£' / RT]