Two components have boiling points of 130°c and 150°c. estimate the number of theoretical plates needed to separate these substances in a fractional distillation.

The number of theoretical plates need to separate these substance = 32.6

Explanation:

Step 1: Data given

Component 1: boiling point = 130 °C

Component 2: Boiling point = 150 °C

Step 2:  Fenske Equation

We will use the fenske equation: it's an equation used for calculating the minimum number of theoretical plates required for the separation of a binary feed stream by a fractionation column. In continuous fractional distillation

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 [(Xd/(1-Xd) x (1-Xb)/Xb}  /  log αavg

⇒ with N = minimum number of theoretical plates required at total reflux (of which the reboiler is one)

⇒ with Xd = the mole fraction of more volatile component in the overhead distillate 0.99

⇒ with  Xb = the mole fraction of more volatile component in the bottoms assume 0.50

⇒ wth  αavg = the average relative volatility of more volatile component to less volatile component (150/130)

In this situation

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

N = log (99 * 1) / log 1.15 = 1.99/0.061 = 32.6 theoretical plates

The number of theoretical plates need to separate these substance = 32.6