Methyl perchlorate is a violent explosive as such a batch reactor was used to

synthesize this product in a benzene solvent. A vessel was charged with $30d{m}^3$

of solution, with initial concentrations of $0\mathrm{.}5M$ methyl iodide $(C{H}_{3}I)$ and $0\mathrm{.}5M$

silver perchlorate $(AgCl{O}_4).$ The reaction between silver perchlorate and methyl

iodide is given below

$C{H}_{3}I+AgCl{O}_{4}C{H}_{3}Cl{O}_4+$AgI

$-r_{C{H}_3\text{I}}=k{C}_{C{H}_3\text{I}}{C}_{AgCl{O}_4}^2$

Additional Data: at $323K$ in benzene, $k=0\mathrm{.}2\frac{(d\frac{m^3}{m}ol{)}^2}{s}.$

a$.$ How long will it take to achieve $98\%$ conversion of the silver

perchlorate?

b$.$ If it takes $30$min to charge feed to the reactor, $30$min to heat the

reactor contents to the reaction temperature and $1\mathrm{.}5$ hours to empty

and clean the reactor, what is the time required to process one batch of

reactor.

c$.$ How many batches can be processed in one day $($note the plant

operates $16$ hours in a day$)?$