# Mechanism of Catalytic Reaction

Develop the overall rate equation for the gas-phase heterogeneous reaction A à M + N, considering the following steps:

3. desorption of M and N

Assume step (ii) is controlling.

Calculations:

If s is taken as the active catalyst site,

The steps taking place are:

A + s à A.s

Rate of adsorption of A = raA = kaACAqV

Where qV is the fraction of unoccupied sites surface.

Rate of desorption of A is = rdA = kdAqA

At adsorption equilibrium, raA = rdA

i.e., kaACAqV = kdAqA

qA = KACAqV à 1

where KA = kaA / kdA

Where qA is the fraction of the surface covered by adsorbed species of A.

A.s + s à M.s + N.s

-rA = k qAqV à 2

Desorption of M and N:

M.s à M + s

N.s à N + s

Rate of desorption of M:

rdM = kdM qM

raM = kaM CMqV

at desorption equilibrium,

rdM = raM

i.e., kdM qM = kaM CMqV

qM = KM CMqV à 3

where KM = kaM/kdM

similarly,

qN = KN CNqV à 4

qV can be written in terms of known quantities by the definition of qV = 1 - (qA + qM + qN)

i.e., qV = 1 - qA - qM - qN = 1 - KACAqV - KMCMqV - KNCNqV

qV + qV(KACA + KMCM + KNCN) = 1

qV = 1 / (1 + KACA + KMCM + KNCN) à 5

substituting for qA and qV in equation 2, we get

-rA = k qAqV = k KACAqV2 = k KACA / (1 + KACA + KMCM + KNCN)2

The overall rate equation is

-rA = k KACA / (1 + KACA + KMCM + KNCN)2