Consider the following liquid phase reaction $($constant volume$)$ in an adiabatic

batch reactor.

$A+BC$

The initial concentrations for A and $B$ are $4\mathrm{.}55$kmo$\frac{l}{m^3}$ and $5\mathrm{.}34$kmo$\frac{l}{m^3}.$

The reaction is a first$-$order reaction for both A and $B(-r_A=k{C}_A{C}_B).$ The rate

constant $k=1\mathrm{.}37{10}^{12}$exp$(\frac{-12628}{T})\frac{m^3}{\text{k}\text{m}\text{o}\text{l}*s}$

The energy balance equation is

$T-T_0=\frac{n_{A0}(-H_r)}{\frac{m_{\text{t}\text{o}\text{t}}}{b}ar(C_{p,\text{t}\text{o}\text{t}})}{x}_A$

$H_r=-33\mathrm{.}5k\frac{J}{m}ol$

$T_0=326K$

$m_{\text{t}\text{o}\text{t}}$ is the total mass of the reaction mixture.

The volumetric heat capacity for the reaction mixture is $1980k\frac{J}{m^3*K}$

a$)$ Derive the relationship between $T$ and $x_A$

b$)$ Calculate the time needed for the system to reach $373K($you may use your

calculator for the integral$)$Consider the following liquid phase reaction $($constant volume$)$ in an adiabatic

batch reactor.

$+->$

The initial concentrations for A and B are $4\mathrm{.}55/*$ and $5\mathrm{.}34/*.$

The reaction is a first$-$order reaction for both A and B