Q$3(35$ p$)$: The liquid phase reaction $AP$ will be carried out in a $4m^3$ volume BR operated at a constant temperature of $300K$ with the aim of achieving a $85\%$ conversion of $A$ to $P.$ Based on the provided information below, determine:

a$)$ Required reaction time

b$)$ Conversion profile $)=(f(t)$

c$)$ Jacket temperature profile $)=(f(t)$

d$)$ Discuss all your results

Data

Reaction rate constant at $300K=0\mathrm{.}385mi{n}^{-1}$

Enthalpy of the reaction at $300K$:$-H=-1742ca\frac{l}{m}ol$

The initial concentration of $A=2\mathrm{.}3mo\frac{l}{m^3}$

Mean molar heat capacity of the reaction mixture $=25ca\frac{l}{m}olC$

Overall heat transfer coefficient $=700ca\frac{l}{m^2}hC$