The following reaction in gas phase will take place in a perfectly mixed continuous reactor of $5,000$ L volume:

A $->2$B $+$ C

The rate law is $1$st order, with a rate constant equal to $0\mathrm{.}017$ min$-1$ at $150$oC$.$ The reactor will be fed with pure A at a pressure of $20$ bar and $100$oC $($or lower$).$

The reactor is designed to give a conversion of $80\%$ at $150$oC$.$

a$)$ Write the mass balances for the reactor to obtain the flow rate of the feed.$[40$ marks$]$

b$)$ Determine the temperature of the inlet feed that would be required to avoid the need for cooling or heating $($the reactor would be able to work adiabatically, in principle$).$ Is the adiabatic operation of the reactor feasible? Comment on the results.$[60$ marks$]$

DATA:

Ideal gas constant: $8\mathrm{.}314$ J$/($mol$.$K$)$

The specific heats $($average$,$ around $150$ oC$)$ and heats of formation of the various components at $25$ oC are $($note that the enthalpies of formation are in kJ$/$mol$)$:

A: cp $($J$/$mol$.$K$)1\mathrm{.}4,$hf $($kJ$/$mol$)10\mathrm{.}1$; B: cp $($J$/$mol$.$K$)2\mathrm{.}9,$ hf $($kJ$/$mol$)7\mathrm{.}5$; C: cp $($J$/$mol$.$K$)1\mathrm{.}1,$ hf $($kJ$/$mol$)-35\mathrm{.}2.$