Q$.$ II: The goal is to develop an expression for the Thiele modulus and concentration

profile of species A for the following reversible $1^{st}$ order reaction that takes place in a

porous planar $($slab$)$ catalyst: $Alongleftrightarro{w}_{k_{-1}}^{k_1}B,K=\frac{k_1}{k_{-1}}($Equilibrium constant$)$

with boundary conditions:

$C_A=C_{Ai}$

$\frac{d{C}_A}{dx}=0$

@$x=L($external surface of slab$)$

@ $x=0($centerline of slab$)$

a$)$ Write down the mass balance equation for $A$ in the catalyst. Express it in terms of

species A only. Further information is given below.$*$

b$)$ Let $=C_A-\frac{C}{K+1}$ and $=\frac{x}{L},$ and rewrite the mass balance equation in terms of

the new variables. Define the Thiele modulus, accordingly.

c$)$ Determine the concentration profile of $A,C_A(x).$

The unit of the rate is $($mole $\frac{A}{s}\frac{?}{m{g}_g^3}).$ Assume constant physical properties, and a

binary mixture $A-B$ with a total concentration $C=C_A+C_B.$