GATE 2022 CH – Question 56
An equimolar binary mixture is to be separated in a simple tray-distillation column. The feed rate is 50 kmol min$^{-1}$. The mole fractions of the more volatile component in the top and bottom products are 0.90 and 0.01, respectively. The feed as well as the reflux stream are saturated liquids. On application of the McCabe-Thiele method, the operating line for the stripping section is obtained as $y = 1.5x - 0.005$ where $y$ and $x$ are the mole fractions of the more volatile component in the vapor and liquid phases, respectively. The reflux ratio is _______ (rounded off to two decimal places).
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Correct answer: 0.62 to 0.64
Explanation
The stripping line is $y = \frac{\bar{L}}{\bar{V}}x - \frac{B}{\bar{V}}x_B$. The intercept gives $\frac{B}{\bar{V}} \times 0.01 = 0.005$, so $\frac{B}{\bar{V}} = 0.5$ (the slope $1.5 = 1 + 0.5$ agrees). The product rates are $D = 50 \times \frac{0.5 - 0.01}{0.9 - 0.01} = 27.53$ and $B = 22.47$ kmol/min. Then $\bar{V} = \frac{22.47}{0.5} = 44.94$ and $\bar{L} = 67.42$. For a saturated liquid feed, $\bar{L} = L + F$, so $L = 17.42$ and $R = \frac{L}{D} = \frac{17.42}{27.53} = 0.63$.