Problem $5(\frac{25}{100})$ : A first order reaction $AP$ is taking place isothermally within a catalytic

micro$-$channel schematically depicted below. The channel is symmetric and has two openings. The

channel walls are coated with platinum along the entire length of the channel. Neglect radial gradients.

It is known that the reactant A concentration at $z=L$ is one$-$tenth the concentration of $A$ at $z=0.$ The

concentration of $A$ at $z=0$ is $0\mathrm{.}001mo\frac{l}{L}.$ The micro$-$channel length $(2L)$ is $2{10}^{-3}cm,$ and the

diffusion coefficient is $0\mathrm{.}1c\frac{m^2}{s}.$