The liquid phase reaction $AB$ is run in a batch reactor. The following data are valid.

$r_A=-k{C}_A$

$k(298K)=1\mathrm{.}7{10}^{-4}{s}^{-1}$

$E_A=41\mathrm{.}87{10}^{3}k\frac{J}{k}$mole

$H(298K)=-167\mathrm{.}5{10}^{3}k\frac{J}{k}$mole

$=1050k\frac{g}{m^3}$

$C_p=4\mathrm{.}19k\frac{J}{k}gK$

$C_{A0}=2$kmol$\frac{e}{m^3}$

$V=0\mathrm{.}5m^3$

$C{P}_P$ and $$ can be assumed to be constant. The tank reactor is made of steel and weighs $800kg,C_{p-\text{s}\text{t}\text{e}\text{e}\text{l}}=502\mathrm{.}4k\frac{J}{k}gK.$

Calculate the conversion and the reactor temperature as a function of the reaction time if the initial temperature at time $t=0$ is $298K$ and under the condition that the reactor is well insulated that the temperature losses to the environment may be neglected. What reaction time is required for a conversion of $95\%?$