A petrochemical plant located in Seri Iskandar, Perak is to be commissioned to produce products $B$ and $C.$ The reaction is following exothermic reaction,

$AB+C$

The reaction was carried out adiabatically and the following data was recorded as shown in TABLE Q$3.$ The entering molar flowrate of reactant A was $250mo\frac{l}{m}in.$

TABLE Q$3$ reaction rate as function of conversion

$\backslash$table$[[x,0,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}45,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}8,0\mathrm{.}9],[-r_4,1\mathrm{.}0,1\mathrm{.}8,5\mathrm{.}0,5\mathrm{.}0,5\mathrm{.}0,5\mathrm{.}0,1\mathrm{.}55,0\mathrm{.}71],[(\frac{\text{m}\text{o}\text{l}}{d}{m}^3*min),,,,,,,,]]$

a$.$ Estimate the CSTR and PFR volume necessary to achieve $50\%$ conversion.

$[8$ marks$]$

b$.$ Determine the range of conversion when the CSTR and PFR reactor volumes are identical.

$[4$ marks$]$

c$.$ Calculate the conversion of A if a $70-$dm$^3{?}^3$ PFR is followed in series by a $24-$dm ${?}^3$ CSTR$.$

$[8$ marks$]$

d$.$ Using Levenspiel plot, propose the best reactor arrangement that can reduce the total volume of the rector$($s$)$ to achieve $0\mathrm{.}8$ conversion as compared to part $($c$)$ arrangement.

$[5$ marks$]$