The 
is called Thiele modulus for spherical pellet . Equation (10) gives the concentration profile of A in the pellet.
This concentration profile is used to evaluate the rate of reaction rp for the whole pellet. Calculating the diffusion rate of reactant into pellet at position Rs per unit mass of catalyst pellet
  |
(12) |
Substituting the value of mp in equation (12)
or
 |
 |
(13) |
Differentiating 
and evaluating the derivative at 
and substituting in equation (13), following relation for 
can be obtained for isothermal conditions.
Then substituting the in the rate for whole pellet in terms of concentration at outer surface 
, can be written as
