Question

derive langmuir adsorption isotherm equation from BET equation​

Answer 1

For molecules in contact with a solid surface at a fixed temperature, the Langmuir Isotherm, developed by Irving Langmuir in 1916, describes the partitioning between gas phase and adsorbed species as a function of applied pressure.  Image of surface

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:        please mark me brain mark list