$($a$)$ A reversible exothermic reaction is carried out in a Plug flow reactor under adiabatic condition. Explain how can you find the size of the reactor?

$($b$)$ The elementary second order irreversible liquid$-$phase reaction: $A+BC$ is carried out adiabatically in a CSTR$.$ An equal molar feed in A and B enters at $27C,$ and the volumetric flow rate is $2d\frac{m^3}{s}$ and $C_{A0}($in mixture$)=0\mathrm{.}1mo\frac{l}{d}{m}^3.$ Conversion achieved is $85\%.$

$($i$)$ Determine the temperature of the reaction mixture in the reactor.

$($ii$)$ Calculate the rate constant $\text{'}k\text{'}$ at the reactor temperature.

$($iii$)$ Calculate the volume of the CSTR$.$

$(3)$

Data given:

$H_A^0=-20$kca$\frac{l}{m}ol$;$H_B^0=-41$kca$\frac{l}{m}ol$;$H_C^0=-41$kca$\frac{l}{m}ol$

$C_{PA}=C_{PB}=15Ca\frac{l}{m}ol-K$;$C_{PC}=30Ca\frac{l}{m}ol-k$

$k=0\mathrm{.}01\frac{d{m}^3}{(mol)-s}at300K$;$E=10,000ca\frac{l}{m}ol$

Dentigh

$($c$)$ How will you select the appropriate temperature for favourable product distribution for the reaction

$A1R2S,if$

$($i$)E_1>E_2,$

$($ii$)E_1{E}_2{E}_1?$

$(E_1$ and $E_2$ are the activation energies $of$ paths $1$ and $2$ respectively$)$

$(2)$