GATE 2023 CH – Question 57
Distillation of a non-reactive binary mixture with components $A$ and $B$ is carried out in a batch still as shown in the figure below. The initial charge of the mixture in the still is 1 kmol. The initial and final amounts of $A$ in the still are 0.1 kmol and 0.01 kmol, respectively. Use a constant relative volatility of 4.5. The mole fraction of $B$ remaining in the vessel is _______ (rounded off to three decimal places).
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Correct answer: 0.972 to 0.992
Explanation
The initial composition is $x_0 = 0.1$ and the final amount of A is 0.01 kmol in $W$ kmol, so $x_W = \frac{0.01}{W}$. The Rayleigh equation for a constant relative volatility $\alpha$ is $\ln\frac{W_0}{W} = \frac{1}{\alpha - 1}\left[\ln\frac{x_0}{x_W} + \alpha\ln\frac{1 - x_W}{1 - x_0}\right]$, with $\ln\frac{W_0}{W} = \ln(100x_W)$. Solving this by trial gives $x_W = 0.0182$. The mole fraction of $B$ is $1 - 0.0182 = 0.982$.