```Lecture 20.
Adsorption is the accumulation of atoms
or molecules on the surface of a material.
This process creates a film of the
adsorbate (the molecules or atoms being
It is different from absorption, in which a
substance diffuses into a liquid or solid to
form a solution. The term sorption
encompasses both processes, while
desorption is the reverse process of
Isotherms
isotherms, that is, the amount of adsorbate
on the adsorbent as a function of its
pressure (if gas) or concentration (if liquid)
at constant temperature.
some of these isotherms are:
• Langmuir
• BET
Langmuir
Langmuir derived a relationship for q; weight
concentration in fluid based on some quite
reasonable assumptions. These are: a
uniform surface, a single layer of adsorbed
material, and constant temperature. The rate
of attachment to the surface should be
proportional to a driving force times an area.
The driving force is the concentration in the
fluid, and the area is the amount of bare
surface. If the fraction of covered surface is
F , the rate per unit of surface is:
Langmuir
rate going on = k1 C ( 1 - ϕ )
The evaporation from the surface is
proportional to the amount of surface
covered:
rate leaving = k2 ϕ
where k1 and k2 are rate coefficients
C = concentration in the fluid
ϕ = fraction of the surface covered
Langmuir
At equilibrium, the two rates are equal,
and we find that:
A plot of
versus should indicate a
straight line of slope
and an
intercept of
. The graph shows data
points and lines fitted to both Freundlich
and Langmuir equations.
Langmuir Isotherm
BET Theory
BET theory is a rule for the physical
adsorption of gas molecules on a solid
surface and serves as the basis for an
important analysis technique for the
measurement of the specific surface area
of a material. The concept of the theory is
an extension of the Langmuir theory,
which is a theory for monolayer molecular
the following hypotheses:
BET Theory
(a)gas molecules physically adsorb on a
solid in layers infinitely;
(b) there is no interaction between each
(c) the Langmuir theory can be applied to
each layer.
BET Theory
The resulting BET equation is expressed
by:
P and P0 are the equilibrium and the
saturation pressure of adsorbates at the