Reaction rate in presence of significant external mass transfer limitation

Consider a gaseous irreversible reaction A → B that is occurring on a solid catalyst. Assume the reaction to be of first order with respect to A. Since the reaction is irreversible, the concentration of B at the catalyst surface does not influence the rate. Also assume desorption of B to be very fast (path -3).

Hence the reaction is controlled by the following two steps

1. (1) transportation of A from bulk to catalyst surface (path -1)

..........(2) reaction of A to B at catalyst surface (path -2)

Diffusion rate of A from bulk gas to surface is ------------ (1)

Surface reaction rate is ----------------------- ----------- ----------- ---- (2)

Here rate is mol /s. g catalyst.

Where,

At steady state, rate of diffusion and surface reaction rate will be equal. Hence

And overall reaction rate can be expressed by either of two

--------------------------------------------------- (3)

Here, is the steady state rate per unit mass of catalyst pellets.

From (1) , (2) and (3)

Or, -------------------------- Or ,

(4)

Substituting the value of C_s in

Or

(5)

Where . The k_o is called the overall rate constant