Answer Happy

Consider a spherical catalyst particle of radius R in a
catalytic reactor, where it is submerged in a gas stream containing
the reactant A and the product B. In the neighborhood of the
surface of the catalyst particle, we presume that the concentration
is CAs moles of A per unit volume. Reactant A diffuses through
the passages in the catalyst and is converted to B through a first
order reaction on the catalytic surfaces inside the particle
(rA = -kaCA where a is the available catalytic surface
per unit volume). The effective diffusivity for reactant A in the
porous medium is known as DA.
Derive a differential equation governing the concentration
profile of A in the particle (i.e. in the radial direction).
(You should be obtaining a second-order differential equation
with variable coefficients.) Write the appropriate boundary
conditions and Use the change of
variable CA/CAs = (1/ r) f(r) to
obtain the following differential equation:
dạf 11 ka D f dr2 A