Q$3.$ The liquid phase isothermal reaction,

$A+B=P+Q$

follows a $2^{nd}$ order kinetics,

$-r_A=k{C}_A{C}_B$

The reaction is carried out in two CSTRs in series. The reactors operate at a

temperature of $50C$ and a pressure of $2$atm. The rate constant at the operating

condition is $36\mathrm{.}36m^3*kmo{l}^{-1}*hr-$ The feed flowrate is $1\mathrm{.}8m^3*h^{-1}$ and the

concentrations of A and $B$ are the same and equal to $0\mathrm{.}07$kmol.$m^{-3}.$ The desired

conversion is $75\%.$

$($a$)$ Determine the conversion in the $1^{st}$ reactor when the total volume of the reactor

cascade is minimum.

$[22$ marks$]$

$($b$)$ Use the conversion determined in section $($a$)$ or assume a conversion of $54\%$ in

$1^{st}$ reactor and determine the volume of the individual reactors and their

sequence.The liquid phase isothermal reaction, A$+$B$=$C$+$D follows a $2$ nd order reaction $(1$st order in A and $1$st order in B$).$ The feed volumetric flowrate is $3\mathrm{.}0\backslash$times $10^(-4)$m$^(3)$s$^(-1).$ The feed is equimolar and the initial concentration of A is $0\mathrm{.}12$kmolm$^(-3).$ The rate constant is $1\mathrm{.}0\backslash$times $10^(-2)$m$^(3)$kmol$^(-1)$s$^(-1).$ The reactor conversion is $70\%.$ Apply the graphical method, $($a$)$ to determine the volume of a CSTR$.($a$)$ to determine the total volume of a cascade of three identical CSTRs in series.