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$.$

What is the thiele modulus using the dimensionless parameters: w$=$CA$/$CAs and l$=$z$/$L