The elementary liquid$-$phase reaction A $+$ B $->$C takes place in a $1000$L CSTR$.$ A and B are fed equimolarly

at $300$K and a volumetric flow rate of $500$L$/$min$.$ The concentration of A in the feed is $1$M$.$ When the reaction

was carried out isothermally at $300$K$,$ the conversion was found to be $0\mathrm{.}18.$ When the reaction was carried out

adiabatically at a temperature in the reactor of $350$K$,$ the conversion was found to be $0\mathrm{.}4.$

The heat capacities of A$,$ B and C are $25,35$ and $60$ J$/$mol$\backslash$times K$,$ respectively.

a$)$ What is Q for the isothermal operation? Is this energy supplied or removed from the system?

b$)$ We add a heat exchanger to the reactor with a UA of $6\mathrm{.}0$kJ$/$min$\backslash$times K$.$ The temperature of the fluid is the same at

the inlet and outlet of the heat exchanger. What is this temperature?

c$)$ What is the conversion if the reactor is operated at $345$K$?$

d$)$ What is in Q this case $($c$)?$ What will be the temperature of the fluid in the heat exchanger to maintain the

temperature at $345$K in the reactor? How do Q and the temperature of the coolant compare to those in

isothermal operation at $300$K $($see a and b$)$