$($a$)$ A waste stream contains $0\mathrm{.}5\%$ toluene and it is moving at $0\mathrm{.}5m^3{s}^{-1}$ at $40C$ and $1$ atm. We wish to recover $99\%$ of the toluene by absorption in a suitable solvent. Assume $H_{\text{t}\text{o}\text{l}\text{u}\text{m}\text{e}}=0\mathrm{.}07$atm in this solution. What is the minimum scrubbing liquid flow rate required? Hint: $Y_i^{**}=0\mathrm{.}8Y_i$ and See Figure below.

$(10$ marks$)$

Typical operating line diagram