Example $4\mathrm{.}2.$ The Consider an isothermal batch reactor for a given conversion of the reactant

$aA+bBcC+dD$

where component $A$ is the limiting reactant. The stoichiometric coefficients are: $a=1,b=2,c=1,$ and $d=0.$ The initial moles of components $A,B,C,$ and $D$; are $N_A=0\mathrm{.}001$ gmol, $N_B=0\mathrm{.}003$gmol,$N_C=0\mathrm{.}0$gmol,$N_D=0\mathrm{.}0$gmol, respectively. The mixture of A and $B$ is charged into a $1-$liter reactor. Determine the holding time required to achieve $90\%$ fractional conversion of $)=(0\mathrm{.}9.$ The rate constant is $k=1\mathrm{.}0{10}^5[\frac{(\text{l}\text{i}\text{t}\text{e}\text{r}{)}^2}{gmo{l}^2*min}]$ and the reaction is first order in $A,$ second order in $B$ and third order overall.

the given data, the holding time required equals

$t_{\text{h}\text{o}\text{l}\text{d}\text{i}\text{n}\text{g}\text{t}\text{i}\text{m}\text{e}}=8\mathrm{.}86$min

it would take approximately $9$ minutes to convert $90\%$

iter reactor.

I need u to solve it so the holding time will be $8\mathrm{.}8$ mins $..$ for the intergation use trapizodial