Q$2.$ Consider a reactor with the result of a tracer test give below:

$C_T(t)=0\frac{g}{L}$

$C_T(t)=-30+4t-0\mathrm{.}1t^2\frac{g}{L}$

$C_T(t)=10\frac{g}{L}$

$t10$min

$10=20$min

The flowrate though the reactor for the test, and in normal operation, is $300\frac{L}{m}in.$ There is a

large excess of $B$ and the reaction is effectively half order in $A$ :

$A(aq)+B(aq)2C(aq)r_A=-k{C}_A^{0\mathrm{.}5}$ where $k=0\mathrm{.}25mo\frac{l^{0\mathrm{.}5}}{L^{0\mathrm{.}5}}*min$

a$)$ What is the residence time distribution function, $E(t),$ for this reactor?

b$)$ What is the volume of the reactor $($in L$)?$ Integrations to be completed step by step by

hand $($i$.$e$.$ don't integrate numerically!$).$

c$)$ The reactor is fed with $9mo\frac{l}{L}$ of A$.$ Determine the conversion for this reactor.

Integrations to be completed numerically with code$/$spreadsheet attached.

for part B $->$ Using the dNa$/$dt $=$ r$\_$A $*$ V how would you integrate the formula for volume.