Answer:
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
