Evaluating the equation:

$A+BC$

In a non$-$isothermal batch reactor, the reaction is processed in the liquid phase. Find the

time required to reach $80\%$ conversion, assuming that the cooling system is adequate

enough to maintain the reactor wall at a temperature of $300K.$

Data:

$C_A^0=0\mathrm{.}5mo\frac{l}{1}$

$C_B^0=0\mathrm{.}6mo\frac{l}{1}$

$C_P^A=C_P^B=65\frac{J}{\text{m}\text{o}\text{l}\text{.}K},k={5\mathrm{.}10}^{-3}$exp$[\frac{20000(\frac{J}{\text{m}\text{o}\text{l}})}{R}(\frac{1}{300}-\frac{1}{T})]$

$C_P^C=150\frac{J}{\text{m}\text{o}\text{l}\text{.}K}$

$n_A^0=100$mol

$H_r=-15k\frac{J}{m}ol$

$U{A}_H=50\frac{J}{s.K}$

Knowing that the temperature of the cooling jacket is a function of time, given by:

$T_{\text{j}\text{a}\text{c}\text{k}\text{e}\text{t}}=T_0+0,2.t$

Based on this build:

$($a$)$ A figure for the conversion of reactant $A$ as a function of time.

$($b$)$ A figure for the change in reactor temperature as a function of time.

$($c$)$ A figure for the jacket temperature as a function of time.

$($d$)$ A figure for the kinetic constant $k$ as a function of time.

$($e$)$ Discuss the observed behaviors, and if the results obtained are expected.