A reactor $($Tank $1)$ is set up with a fixed, small amount of

catalyst which catalyzes the reaction $A2B.$ The outlet of

Tank $1$ flows into a collection tank $($Tank $2),$ which has no

outflow. Tank I has an initial liquid volume of $V_1=500L$

and Tank $2$ has an initial volume $V_2=0.$ There is initially

no $A$ or $B$ in either of the tanks and you can assume that the

liquid density is not impacted by the concentration of A and

B$.$ At $t=0,$ component $A$ is introduced in the feed to Tank

$1$ at a concentration of $C_{A,r}=20$mol$\frac{A}{L}$ at a rate of $Q=10$

Lmin. This flowrate is equal to the outlet flowrate of Tank

The time dependent concentration of $A$ in tank $1$ is found

to be $C_{A1}=\frac{C_{A,Q}}{V_1}{}_0(1-e^{-\frac{1}{{}_0}}),$ where ${}_0=(\frac{Q}{V_1}+k_1{)}^{-1}$ and $k_1=0\mathrm{.}1mi{n}^{-1}.$

Rate of consumption of $A$ in Tank $1$: $r_1=k_1{C}_{A1}[mol\frac{A}{L}\frac{?}{\text{m}\text{i}\text{n}}]$

Rate of consumption of $A$ in Tank $2$:$0$

a$.$ Complete the following expressions: $)$

b$.$ What is the steady$-$state concentration of A in Tank $1,$ C AI$,$SS $[$mol A$/$L$].(5$ pts$)[$hint: how are time

and steady state connected?

c$.$ How would increasing the hydraulic retention time in Tank $1({}_1=\frac{V_1}{Q})$ impact the steady$-$state

value of $A,C_{AI,SS}($it increases, decreases, stays the same, or impossible to determine$).$ Why? $(5$

pts$)$

d$.$ Perform an unsteady$-$state material balance on moles of component A in Tank $2$ and derive an

expression for $d{C}_A/$dt using only symbolic terms from the problem statement. You don't need to