$($GATE $1997$ modified$)$ It is desired to absorb $90\%$ acetone from a dilute

mixture of acetone$/$air containing $1$mol$\%$ acetone by contacting it counter

currently with pure water in an absorber$.$ The total inlet gas flow rate is $30$

$k.mo\frac{l}{h}r$ and that of water is $90k.mo\frac{l}{h}r.$ Under the operating conditions,

the equilibrium relationship for acetone in gas$-$liquid is $y=2x.$ Estimate the

mol fraction of acetone in the water stream leaving the absorber$.$ Also

determine the number of theoretical $($ideal$)$ stages to which the absorber is

equivalent.