$3)$ The exothermic, liquid$-$phase reaction A $->$ B $+$ C is carried out in a $50$ dm$3$ CSTR with accooling coil. The feed stream is equimolar in A and B $($CA$0=5$ mol$/$dm$3$ and u o $=2$ dm$3/$min$)$ and enters the reactor at $300$ K$.$ To avoid boiling of the liquid, the temperature in the reactor cannot exceed $350$ K$.$ Assume shaft work is negligible. Ethylene glycol enters the cooling coil at $270$ K with a very high flow rate. CPA $=$ CPB $=$ CPC $=50$ cal$/$mol$$K$,$ Ea $=15,000$ cal$/$mol$,\backslash$Delta Ho Rx $=-10,000$ cal$/$mol$,$ U $=50$ cal$/$ft$2$min$$K$,$ kA$(300$ K$)=0\mathrm{.}02$ dm$3/$mol$$min$.$

a$)$ What is the maximum conversion that you could obtain in this system?

b$)$ What surface area must your cooling coil have to maintain the conversion in part $($a$)?$