The liquid phase reversible reaction,

$A+$BharrC$+D$

occurs in a batch reactor at $50C$ and atmospheric pressure. The forward and reverse reactions are pseudo $1^{st}$ fast order $($pseudo $1^{st}$ order in A and pseudo $1^{st}$ order in $C).$ The forward and reverse rate constants are $k_1=1\mathrm{.}65{10}^{-3}mi{n}^{-1}$ and $k_r=1\mathrm{.}7{10}^{-3}mi{n}^{-1}$ at $50C$ respectively.

$($i$)$ Calculate the equilibrium conversion at the reactor operating condition

Anssmer $($a$)x_a=492558$

$($ii$)$ Calculate the required time to reach $80\%$ of the equilibrium conversion

Ansner: $18)t=0\mathrm{.}452$ hours:

$($iii$)$ Calculate the reactor volume. $($Hints: take appropriate assumptions; e$.$g$.,$ Production of $C,$ downtime $1h$; initial concentration, density$)$