Consider an isothermal batch reactor for a given conversion of

the reactant aA $+$ bB $->$ cC $+$ 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 NA $=$

$0\mathrm{.}001$ gmol, NB $=0\mathrm{.}003$ gmol, NC $=0\mathrm{.}0$ gmol and ND $=0\mathrm{.}0$ gmol,

respectively. A mixture of A and B is charged into a $1-$liter

reactor. Determine the holding time $($in min$)$ required to achieve

$90\%$ fractional conversion of A$.$ The rate constant is k $=1\mathrm{.}0$x$105$

$[($liter$)2/$ gmol$2-$min$)]$ and the reaction is first order in A$,$

second order in B and third order overall.$$