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A countercurrent absorption tower is designed to remove $95\%$ of component $A$ from an incoming binary gas mixture using pure solvent $B$. The mole ratio of $A$ in the inlet gas is $0.02$. The carrier gas flow rate is $50$ $k$mol/$h$ The equilibrium relation is given by $Y= 2X$, where $Y$ and $X$ are the mole ratios of $A$ in the gas and liquid phases, respectively. If the tower is operated at twice the minimum solvent flow rate, the mole ratio of $A$ in the exit liquid stream is ____________ (rounded off to three decimal places).
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