GATE 2023 CH – Question 34
A liquid $L$ containing a dissolved gas $S$ is stripped in a countercurrent operation using a pure carrier gas $V$. The liquid phase inlet and outlet mole fractions of $S$ are 0.1 and 0.01, respectively. The equilibrium distribution of $S$ between $V$ and $L$ is governed by $y_e = x_e$, where $y_e$ and $x_e$ are the mole fractions of $S$ in $V$ and $L$, respectively. The molar feed rate of the carrier gas stream is twice as that of the liquid stream. Under dilute solution conditions, the minimum number of ideal stages required is __________ (in integer).
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Correct answer: 3
Explanation
Number the stages from the liquid inlet. The balance from the top to stage $n$ gives $y_n = \frac{L}{V}(x_{n-1} - x_N) + 0$, with $\frac{L}{V} = 0.5$ and the pure gas entering at the bottom, and the equilibrium of the stage is $y_n = x_n$. So $x_n = 0.5(x_{n-1} - 0.01)$. Starting with $x_0 = 0.1$: $x_1 = 0.045$, $x_2 = 0.0175$, $x_3 = 0.00375$. The required exit composition 0.01 is passed between the second and the third stage, so 3 ideal stages are needed.