You are analyzing a process that revolves around the operation of a packed bed reactor.

The PBR contains $1\mathrm{.}5kg$ of catalyst, is operated isothermally at $500K,$ and runs the

elementary gas phase reaction $A+2B3C.$ The inlet stream consists of only A and $B$

with partial pressures of $10$atm for A and $20$atm for $B$ and a total volumetric flow rate of

$12\mathrm{.}5\frac{L}{m}in.$ The rate constant at the reactor's temperature is equal to $3**{10}^{-7}($Hint: the

units for rate constants for catalytic reactions can get complicated, consider this to be the

value when concentration, volumetric flow rate, and weight are expressed in $mol{m}^{-3},$

$m^{3}mi{n}^{-1},$ and $kg$ respectively$).$ Use $=0\mathrm{.}1k{g}^{-1}.$

a$.$ What is the outlet pressure?

b$.$ What is the outlet conversion of $A?$ What is the production rate of $C?$

c$.$ The plant manager tasks your operations team with finding a way to increase

production rate by only changing the operating conditions.

i$.$ Team member A suggests lowering the volumetric flowrate by half to

achieve a higher conversion.

ii$.$ Team member B suggests doubling the volumetric flowrate for more

throughput.

Which suggestion do you take and why? $[$Show quantitatively$]$