Assume the reaction is irreversible. Do the calculations for this one in Polymath.

The elementary, organic liquid$-$phase reaction

$A+BC$

Is to be carried out in a semibatch reactor. There are $500$ moles of A initially in the reactor at

$25C.$ Species B is fed to the reactor at $50C$ and a rate of $10mo\frac{l}{m}in.$ The feed to the

reactor is stopped after $500$mol of $B$ has been fed.

a$)$ Plot the temperature and conversion as a function of time when the reaction is carried out

adiabatically. Calculate to time $=2$ hours.

b$)$ Plot the conversion as a function of time when a heat exchanger $($UA $=100ca\frac{l}{m}i\frac{n}{K}$ is

placed in the reactor and the ambient temperature is constant at $50C.$ Calculate to time

$=3$ hours.

Parameter values:

$k=0\mathrm{.}01(d\frac{m^3}{m}o\frac{l}{m}in)$ at $300K$ with $E=10$kca$\frac{l}{m}ol$

$V_0=50d{m}^3,v0=1d\frac{m^3}{m}in,C_{A0}=C_{B0}=10mo\frac{l}{d}{m}^3$

For the reverse reaction, $k_r=10s^{-1}$ at $300K$ with $E_r=16$kca$\frac{l}{m}ol$

$H_A(273)=-20$kca$\frac{l}{m}o{l}_2{H}_B(273)=-15$kca$\frac{l}{m}ol,HC(273)=-41$kca$\frac{l}{m}ol$

$CP{A}_{PA}=CP{B}_{PB}=15ca\frac{l}{m}o\frac{l}{K},C_{PC}=30ca\frac{l}{m}o\frac{l}{K}$