Question

Two compounds have boiling point of 130 and 150°C. Estimate the number of theoretical plates needed to separate these substances in a fractional distillation.

Answer 1

If we assume the vapor pressures are the ratios of the temperature ratios (150/130) and then plug it into the Fenske equation.

N = log [(X_d /(1 - X_d) x (1 - X_b) / X_b} / log _avg

where:
N = minimum number of theoretical plates required at total reflux (of which the reboiler is one)
X_d = mole fraction of more volatile component in the overhead distillate 0.99
X_b = mole fraction of more volatile component in the bottoms assume 0.50
_avg = average relative volatility of more volatile component to less volatile component (150/130)

N = log { 0.99 / (1 - 0.99) x (1 -.0.50) / 0.50) } / log (1.15)

N = log { 0.99 / (0.01) x (0.50) / 0.50) } / log (1.15)

N = log (99 x 1) / log 1.15

N = 1.99/0.061

N = 32.6 theoretical plates.