Page 139 - Introduction to Colloid and Surface Chemistry

The solid-gas interface 129

where k is a proportionality constant - i.e.

VIV
(1-V/VJ
where AJ/ ads. = E~ E' = heat of adsorption (negative).
Assuming that the heat of adsorption, A// atj S., is independent of
surface coverage,

where a is a constant dependent on the temperature, but independent
of surface coverage. Therefore,
v/v,
ap = — m- (5.5)

_
or V = (5>6)
(l + ap)

or (5.7)

i.e. a 'plot ofp/V versus p should give a straight line of slope l/V m and
an intercept of l/aV m on the p/V axis.
At low pressures the Langmuir isotherm equation reduces to V=
V map - i.e. the volume of gas adsorbed varies linearly with pressure.
At high pressures a limiting monolayer coverage, V- V m, is reached.
The curvature of the isotherm at intermediate pressures depends on
the value of the constant a and, hence, on the temperature.
The most notable criticism of the Langmuir adsorption equation
concerns the simplifying assumption that the heat of adsorption is
independent of surface coverage, which, as discussed in the next
section, is not likely to be the case. Nevertheless, many experimental
adsorption isotherms fit the Langmuir equation reasonably well.
When the components of a gas mixture compete for the adsorption
sites on a solid surface, the Langmuir equation takes the general form