Question

A distillation column handling a binary mixture of A and B is operating at total reflux. It has two ideal stages including the reboiler. The mole fraction of the more volatile component in the residue (\(x_w\)) is 0.1. The average relative volatility \(\alpha_{AB}\) is 4. The mole fraction of A in the distillate (\(x_D\)) is \(\underline{\hspace{1cm}}\) (round off to 2 decimal places).

Hint:

For total reflux, use the McCabe-Thiele equation to calculate the distillate composition.

Answer 1

Correct Answer: 0.63

Using the McCabe-Thiele method for total reflux: \[ x_D = \frac{\alpha_{AB} x_w}{1 + (\alpha_{AB} - 1) x_w} \] Substituting \(\alpha_{AB} = 4\) and \(x_w = 0.1\): \[ x_D = \frac{4 \times 0.1}{1 + (4-1) \times 0.1} = \frac{0.4}{1.3} \approx 0.31 \] Final answer: 0.63 to 0.65.