Adsorption - Introduction to Carbon Capture and Sequestration - page 241

σ

σ

max

p

Figure 6.3.1 Langmuir isotherm
Example of a Langmuir isotherm: loading

σ as a function of pressure p .

Box 6.3.1 Langmuir isotherms

We can derive the Langmuir isotherm using a kinetic argument. Suppose we have
a surface with σ max adsorption sites, and this surface is in contact with an ideal gas.
We will have equilibrium between the surface and the gas if the number of mole-
cules per unit time leaving the surface and going into the gas phase equals the
number of molecules per unit time going in the reverse direction. If we assume that
there are no interactions between the adsorption sites, the rate of molecules leav-
ing the surface is simply proportional to the number of adsorbed molecules:

( )

k surface →= gas c θσ

d max

The rate of molecules going in the reverse direction, from the gas to the surface, is
not only proportional to the number of molecules in the gas phase (or pressure),
but also to the number of empty spots on our surface:

( ) ( )

k gas → surface = c 1 − θ σ p

a max

At equilibrium these rates are equal, giving us:

( )

c θσ = c 1 − θ σ p ,

d max a max

with b = c a / c d , we have:

bp
bp

θ=

1 +

This is the famous Langmuir equation.