The gas $-$phase reaction A$+2$B $->2$D a$-$ is to be carried out in an isothermal plug$-$flow reactor at $5$ atm. The mole fractions of the feed streams are, dm$/$min and the rate law at $55\backslash$deg C is: $-=$k C$\text{'}2$ C in kmol$/$m$3.$ Min $($or in gmol$/$dm$\text{'}.$min$)$ K$=2\mathrm{.}5$ dm$\text{'}/$gmol$.$ min' A$=0\mathrm{.}2,$ B$=0\mathrm{.}5,$ and inerts$($I$)=0\mathrm{.}3.$ b$-$ What are the expressions for the concentrations of A$,$ B$,$ and I $($inerts$)$ as a function of conversion at any point along the reactor c$-$ How large must the plug$-$flow reactor be to achieve a conversion of $0\mathrm{.}7,$ if the temperature in the reactor is uniform $(55\backslash$deg C$),$ the volumetric flow rate is $50$