pts$)$ The gas$-$phase reaction $A+2B2D$ is to be carried out in an isothermal plug$-$flow reactor at

$5\mathrm{.}0$atm. The mole fractions of the feed streams are $y_{A0}=0\mathrm{.}20,y_{B0}=0\mathrm{.}50,$ and $y_{\text{i}\text{n}\text{e}\text{r}\text{t}}=0\mathrm{.}30.$

$($a$)(6$ pts$)$ Write the volumetric flow rate $(v=v(x)),$ concentrations of $A,B,D(C_A,C_B,C_D)$ as

functions of conversion $x($the initial volumetric flow rate and the initial concentration of $A_0$ are $v_0$

and $C_{A0},$ respectively.$).$

$($b$)(5$ pts$)$ What is the initial concentration of $A$ if the feed temperature is $55C?$

$($c$)(8$ pts$)$ Using Polymath, determine the volume of an isothermal ideal PFR operating at $55C$ that

achieves a conversion of $A$ of $70\%$ if the volumetric feed rate is $50L*min-1,$ and the rate law at

$55C$ is:

$-r_A=k{C}_A^{0\mathrm{.}5}{C}_B,(k=2\mathrm{.}5L^{0\mathrm{.}5}*mo{l}^{-0\mathrm{.}5}*mi{n}^{-1})$

$($d$)(6$ pts$)$ Using Polymath, plot the concentrations of A$,$ B$,$ D$,$ and inert, the volumetric flow rate, and

the conversion as a function of PFR volume $V.$