$(20$ pts$)$ A plug$-$flow reactor can be designed by reading the Levenspiel plot $(-\frac{1}{r_A}vs.x_A)$ of the reaction. $r_A$ is the

rate of disappearance of $A,$ and $x_A$ is the percent conversion of $A.$ The area from a Levenspiel plot is related to the

reactor volume via the following relation: $V=F_{A0}*A_{PFR}.$

$F_{AO}$ is the molar flowrate and APFR $($in $\frac{m^6}{k}$mol $)$ is the area under the Levenspiel plot's curve. If it is desired to design a

reactor that would convert $80\%$ of a fresh reactant to $x_A=0\mathrm{.}80).$ If $F_{AO}=0\mathrm{.}125$kmo$\frac{l}{m^3},$ find the volume of the

reactor in $m^3.$ Answer: A$=148\mathrm{.}42345$ ; V$=18\mathrm{.}5529375$