QUESTION $2$

Answer ALL parts.

Reactant A decomposes by $3$ simultaneous reactions to form $3$ products, one that is desired $(B)$ and two that are undesired $(x$ and $Y).$ These gas phase reactions, along with the appropriate rate laws, are called Trambouze reactions:

$1$: $A{x}_i($zero order$),-r_{1}A=k_1,k_1=0\mathrm{.}0001mo\frac{l}{Ls}$

$2$: order$),-r_{2A}=k_2*C_A,k_2=0\mathrm{.}0015s^{-1}$

$3$: order$),-r_{3A}=k_3*C_A^2,k_3=0\mathrm{.}008L($mol$.$s$)$

a$)$ Write the net rate of reaction for each component.

$[15$ marks$]$

b$)$ Write the expression for overall selectivity.

$[10$ marks$]$

c$)$ Utilising material balances to define parameters in the overall selectivity expression, how would you achieve maximum selectivity in a CSTR$?$ Start by writing component material balances and assume the initial concentration of all products are zero.

$[45$ marks$]$

d$)$ What would be the optimum vessel volume if the reaction was to be carried out in a CSTR$?$ The entry stream has a concentration of $A$ of $0\mathrm{.}4M$ and a volumetric flow rate of $10\frac{L}{s}.$

$[30$ marks$]$