Derive the expression of Langmuir absorption isotherm
Answers
Answer:
PLZ MARK ME BRAINLLEST PLZ
Explanation:
Thermodynamic Derivation
The adsorption process between gas phase molecules, A, vacant surface sites, S, and occupied surface sites, SA, can be represented by the equation,
assuming that there are a fixed number of surface sites present on the surface.
An equilibrium constant, K, can be written:
q = Fraction of surface sites occupied (0 <q< 1)
Note that
[SA] is proportional to the surface coverage of adsorbed molecules, or proportional to q
[S] is proportional to the number of vacant sites, (1 - q)
[A] is proportional to the pressure of gas, P
Thus it is possible to define the equilibrium constant, b:
Rearranging gives the expression for surface coverage:
Kinetic Derivation
The rate of adsorption will be proportional to the pressure of the gas and the number of vacant sites for adsorption. If the total number of sites on the surface is N, then the rate of change of the surface coverage due to adsorption is:
eq_3
The rate of change of the coverage due to the adsorbate leaving the surface (desorption) is proportional to the number of adsorbed species:
eq_4
In these equations, ka and kd are the rate constants for adsorption and desorption repectively, and p is the pressure of the adsorbate gas. At equilibrium, the coverage is independent of time and thus the adorption and desorption rates are equal. The solution to this condition gives us a relation for q:
where b = ka/kd.