The series reactions

$2AB{?}_{(2)}^{longrightarro{w}^4}3C$

are catalyzed by $H_{2}S{O}_4.$ All reactions are first order in the reactant concentration.

The reaction is to be carried out in a semibatch reactor that has a heat exchanger

inside with $UA=35,000ca\frac{l}{h}*K$ and an exchanger temperature, $T_v$ of $298K.$

Pure A enters at a concentration of $4mo\frac{l}{d}{m}^3,$ a volumetric flow rate of $240d\frac{m^3}{h}.$

and a temperature of $305K.$ Initially there is a total of $100d{m}^3$ in the reactor, which

contains $1\mathrm{.}0mo\frac{l}{d}{m}^3$ of A and $1\mathrm{.}0mo\frac{l}{d}{m}^3$ of the catalyst $H_{2}S{O}_4.$ The reaction

rate is independent of the catalyst concentration. The initial temperature of the reac$-$

tor is $290K.$ Plot the species concentrations and temperature as a function of time.

Additional information:

$k_{1A}=1\mathrm{.}25h^{-1}at320K$ with $E_{1A}=9500ca\frac{l}{m}ol$

$k_{2a}=0\mathrm{.}08h^{-1}at300K$ with $E_{2B}=7000ca\frac{l}{m}ol$

$H_{\text{k}\text{a}\text{l}\text{A}}=-6500ca\frac{l}{m}$olA

$H_{\text{k}\text{a}\text{s}}=+8000ca\frac{l}{m}$olB

$C_{P_A}=30ca\frac{l}{m}ol*K$

$C_{r_b}=60ca\frac{l}{m}ol*K$

$C_{P_C}=20ca\frac{l}{m}ol*K$

$C_{r_{N_{2}s{o}_4}}=35ca\frac{l}{m}ol*K$

$C_{P_A}=30ca\frac{l}{m}ol*K$

$C_{P_B}=60ca\frac{l}{m}ol*K$

$C_{P_C}=20ca\frac{l}{m}ol*K$

$C_{V_{C_{2}s{O}_4}}=35ca\frac{l}{m}ol*K$

a$.-$ Write all the relevant equations for solving the question according

to the relevant steps

b$.-$ Write the solution in Polymath

c$.-$ Plot the temperature and concentration as a function of time.