P$8-4$A Consider the following system of gas$-$phase reactions:

$Ax,x=k_1{C}_A^{\frac{B}{2}},k_1=0\mathrm{.}004(\frac{\text{m}\text{o}\text{l}}{d}{m}^3{)}^{\frac{1}{2}}*min-1$

ABri$=k_2{C}_A,k_2=0\mathrm{.}3mi{n}^{-1}$

AlongrightarrowY,$r=k_3{C}_A^3,k_3=0\mathrm{.}25d\frac{m^3}{m}ol*min$

$B$ is the desired product, and $x$ and $Y$ are foul pollutants that are expensive to pet rid of$.$ The specific reaction rates are at $27C.$ The reaction system is to be operated at $27C$ and $4$ atm. Pure A enters the system at a volumetric flow rate of $10d\frac{m^3}{m}in.$

a$.$ Skstoh tho inotantancous oclectivtico $|)$ as a function of tho concentration of $C_A.$

b$.$ Consider a series of reactors. What should be the valume of the lirst reactor?

c$.$ What are the effluent concentrations of $A,B,x$ and $Y$ from the first reactor?

d$.$ What is the corversion of $A$ in the first reactor?

$9.$ If $99\%$ conversion of $A$ is desired, what reaction schame and reactor sizes should you use to maximize $S_{\frac{B}{x}Y}?$

f$.$ Suppose that $E_1-20000ca\frac{l}{m}ol,E_2-10000ca\frac{l}{m}ol,$ anc $E_3-30000ca\frac{l}{m}ol.$ What tenperature would ycu recommend for a singla CST$7$ with a space time of $10$min and an enterino concentration of $A$ of $0\mathrm{.}1mo\frac{l}{d}{m}^3?$

$9.$ If you could vary the pressure between' and $100$atn, what pressure would you choose?