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Question $3$

$[20$ Marks$]$

The following liquid$-$phase reaction is carried out in a semi$-$batch reactor:

$A+2BC$

The reaction is assumed to be zero order with respect to species A and B$,$ and the specific rate constant is $0\mathrm{.}2mo\frac{l}{d}{m}^3-$min.

Initially, the reactor volume is $60$ litres and there are $80$ moles of species $A$ in the reactor. Thereafter, a concentration of $12$ moles per litre of species B is gradually added to the reactor at a volumetric flow rate of $2$ litres per minutes. How much time does it take to reach a $50\%$ conversion of species $A?$

$($NB: Start from the general mole balance$)$