Question $3[30$ Marks$]$

Gas $A$ in a solvent carrier gas diffuses through a membrane to a catalytic surface where an irreversible heterogeneous reaction occurs. Gas A reacts instantaneously at the surface.

$\frac{1}{2}AB,R_A=-k^{\text{'}\text{'}}{C}_A$

As soon as B is formed, it is swept away by the carrier gas.

Figure $2$: Diffusion of A to a catalytic surface

a$)$ Develop the concentration profile of A using shell mass balance.

$[20$marks$]$

b$)$ Make a sketch of the concentration profiles of A and B for the defined system.

$[5$ marks$]$

c$)$ Find the concentration of $A$ at a distance of $z=\frac{1}{3}$ if $x_{AO}=0\mathrm{.}025$gmo$\frac{l}{c}{m}^3$

$[5$ marks$]$