Q$2$

$[30$ Marks$]$

A rough scheme of the reaction of degradation of ascorbic acid in aqueous solution is:

$A{k}_{3}D{k}_{1}C$

where $A$ is ascorbic acid and $B$ is dehydroascorbic acid. $C$ and $D$ are undesired components, products of the degradation reactions. We wish to determine the conditions that maximise the concentration of dehydroascorbic acid in a CSTR $($perfectly mixed continuous reactor$).$ All reactions are $1^{st}$ order and the system is in liquid phase.

The activation energies of the $3$ steps are $E_{a1}=30,000$;$E_{a2}=20,000$; and $E_{a3}=27,500ca\frac{l}{m}ol.$ The specific reaction rates at $50C$ are $k_{50,1}=0\mathrm{.}0451s^{-1}$;$k_{50,2}=0\mathrm{.}00954s^{-1}$; and $k_{50,3}=0\mathrm{.}00452s^{-1}.$

The reaction can only take place at temperatures between $5$ and $95C.$ The reactor can be loaded with pure $A($concentration $25mo\frac{l}{L}),$ at a flow rate of $20\frac{L}{s}.$

a$)$ Determine the net rates of reaction of the reagent A and all products $B,C$ and $D.[8$ marks$]$

b$)$ Write the expression that defines the overall selectivity of $B($ratio of the flow rate of the desired product $B$ to that of the sum of the two undesired products $C$ and $D).$

$[10$ marks$]$

c$)$ From the general expression obtained in b$),$ can you advise regarding size of reactor, dilution of reagent and temperature of operation? What would you suggest doing to answer this question?

$[12$ marks$]$

Note:

$R=1\mathrm{.}987ca\frac{l}{\text{m}\text{o}\text{l}\text{.}K}$