Exercise $7\mathrm{.}6$: Thiele modulus and first$-$order kinetics

A catalytic reaction that is first order in the concentration of A

$AB$

is carried out in a spherical pellet with a $0\mathrm{.}20-cm$ radius. The effective diffusivity of A

in the pellet is $0\mathrm{.}015c\frac{m^2}{s}.$ The rate of reaction at $398K$ is $2\mathrm{.}63{10}^{-5}mo\frac{l}{c}{m}^3*s$

when the concentration of $A$ is $3\mathrm{.}25{10}^{-5}mo\frac{l}{c}{m}^3.$ The intrinsic activation energy

is $20$kca$\frac{l}{m}ol.$

Assuming $D_A$ is independent of temperature, what is the rate at $448K$ for the same

concentration of $A?$