$(20$ Points$)$ Often in reactions where A and B are diffusing

to and from a catalytic surface the relation between the

fluxes $N_A$ and $N_B$ at steady state is controlled by the

stoichiometry of the reaction at the boundary. An example

is the diffusion of gas A from the bulk phase to the catalyst

surface where it reacts instantaneously and irreversibly in

the heterogeneous reaction:

$A2B$

Gas B then diffuses back.

Gas A diffuses from Point $1$ at a partial pressure of

$101\mathrm{.}32$kPa to Point $2$ at a distance $2\mathrm{.}00mm$ away. At Point

$2,$ gas A undergoes a chemical reaction at the catalyst

surface

$A2B$

Gas B diffuses away from the catalytic surface at steady

state. The total pressure is $P=101\mathrm{.}32$kPa. The temperature

is $300K$ and $D_{AB}=0\mathrm{.}15**{10}^{-4}\frac{m^2}{s}.$

For the instantaneous rate of reaction determine $y_{A2}$ at the

catalytic surface and $N_A.$