Consider a narrow cylindrical pore of length $L=1\mathrm{.}0cm.$ At the entrance to the pore, the concen$-$

tration of species A is $C_{A,0}=1\mathrm{.}0mo\frac{l}{L}.$ Species A diffuses into the pore and reacts according to

the following reaction:

$AB$ with $r=k{C}_A^2$ where $k=0\mathrm{.}01\frac{L}{m}$ols

Neglecting radial terms gives the following differential equation:

$D_A\frac{d^2{C}_A}{d{x}^2}=k{C}_A^2$

With $D_A=1\mathrm{.}0{10}^{-3}c\frac{m^2}{s}.$ Assume that the end of the pore $(x=L)$ is closed off.

i$)$ State appropriate boundary conditions for this problem.

ii$)$ Set up finite difference equations. Explain how the boundary conditions can be implemented.

iii$)$ Solve the system in python. How do you know your answer has converged? How many

significant digits are you confident of in your solution?

iv$)$ Plot the results. Determine the overall rate of reaction in the pore.