Question $3$

$[15]$

The irreversible homogeneous gas phase reaction:

$A0\mathrm{.}5B2C$

needs to occur in a PFR at $50C$ and $200$kPaa. The reaction is known to have the following kinetics:

$-r_A=10C_A\frac{\text{I}}{L*min}$

$r_C=25C_B\frac{\text{m}\text{o}\text{l}}{L*min}$

Pure A is fed to the reactor at $200mo\frac{l}{m}in.$

Write down the mole balances for $F_A,F_B$ and $F_C,$ and volumetric flowrate $(Q)$ as functions of $V($i$.$e$.\frac{d{F}_A}{dV},\frac{d{F}_n}{dV},\frac{d{F}_C}{dV},\frac{dQ}{dV}).$

Present a qualitative plot of $Q$ vs $V($i$.$e$.Q$ on $y-$axis and $V$ on the $x-$axis$)$ and explain the shape of the curve.

Determine the volume of a single reactor required to produce a maximum final outlet of concentration of B $($hint: this is NOT a Lievenspiel question$).$

$[6]$