The isothermal, first-order reaction of gaseous A occurs within the pores of a spherical catalyst pellet. The reactant concentration halfway between the external surface and the center of the pellet is equal to one-fourth the concentration at the external surface.
(a) What is the relative concentration of A near the center of the pellet?
(b) By what fraction should the pellet diameter be reduced to give an effectiveness factor of 0.7?