Question $3$:

Considered the sequence of consecutive first$-$order gas$-$phase reactions:

$A{k}_{1}B{k}_{2}C$

$k_1=5\mathrm{.}3{10}^{10}x{e}^{-Ea\frac{1}{R}T}$

$k_2=4\mathrm{.}6{10}^{17}x{e}^{-Ea\frac{2}{R}T}$

$($fork in min$-1$ and $T$ in $K).$

The initial concentrations $($mol$/$L$)$ of species $A,B,$ and $C$ were $x,y,$ and $z,$

respectively.

a$.$ At $T=300C,$ plot the concentration of $A{B}_{?},$ and $C$ with time upte $95\%$ of $A$

reacted.

b$.$ Determine the temperature at which the reactor should be operated

isothermally to maximize the concentration of species $B$ at $30$ minutes. What

is the composition of the reaction mixture at this time? What is the maximum

concentration of species $B$ at this time?

c$.$ What is the maximum concentration of species $B$ that could be obtained

when operating at the optimum temperature if the time constraint of $30$min

is not applicable? How much time would be required to achieve this

maximum?