In a certain chemical plant, a reversible fluid-phase isomerization A→←B is carried out over a solid catalyst in a tubular packed-bed reactor. If the reaction is so rapid that mass transfer between the catalyst surface and the bulk fluid is ratelimiting, show that the kinetics are described in terms of the bulk concentrations C_A and C_B by 

−rA″=kB[CA−(1/K)CB]1/K+kB/kA
where −rA′ = moles of A reacting per unit area catalyst per
k_A, k_B = transfer coefficients for A and B
K = equilibrium constant It is desired to double the capacity of the existing plant by processing twice the feed of reactant A while maintaining the same fractional conversion of A to B in the reactor. How much larger a reactor, in terms of catalyst weight, would be required if all other operating variables are held constant? You may use the Thoenes–Kramers correlation for mass transfer coefficients in a packed bed.