SHOW POLYMATH CODE: The elementary gas$-$phase reaction

A $$ B $+2$C

is carried out isothermally in a tubular reactor. The specific reaction rate is $0\mathrm{.}044$ min$-1.$ A enters the reactor

at $10$ atm, $127$ degrees C$,$ CA$0=0\mathrm{.}3$ mol$/$L$,$ and FA$0=2\mathrm{.}5$ mol$/$min$.$

a$)$ Analytically calculate the reactor volume and space time to achieve $74\mathrm{.}81\%$ conversion in a PFR with no pressure drop.

b$)$ Plot X and y as functions of PFR volume when there is pressure drop with alpha $=0\mathrm{.}001$ L$-1.$ Calculate the conversion and the pressure at the exit of this reactor when the volume matches that found in part a