A first$-$order, heterogeneous, irreversible reaction

is taking place within a catalyst pore which is plated with platinum entirely along the length of

the pore. The reactant concentration at the plane of symmetry $($i$.$e$.,$ equal distance from the pore

mouths$)$ of the pore is equal to one$-$tenth the concentration at the pore mouth. The

concentration at the pore mouth is $0\mathrm{.}001$ mol$/$L$,$ the pore length $(2$L$)$ is $2$ x $103$ cm$,$ and the

diffusion coefficient is $0\mathrm{.}1$ cm $2$

$/$s$.$

Write a differential molar balance for the pore, assuming

that you have no gradients of concentration in the radial

or angular directions. State the boundary conditions.

What

is the expression for the Thiele modulus,

$,$ in this case?

HINT: For part $($a$)$ assume that the reaction is happening in the $$bulk$$ of the pore. For part $($b$),$

write the differential equation you obtained in part $($a$)$ in terms of the dimensionless parameters

$($C A $/$C AS$)$ and

$($z$/$L$).$ The term multiplying the dimensionless concentration y will be equal to the

Thiele modulus squared.