Analytical Solution in Determining the Number of Theoretical Stages In the Distillation of Ideal Binary MixturesSpecifications:1. Relative Volatility2. Feed ConditionsMole Fraction of the more volatile component Feed Quality

3. Product ConditionsBottoms Mole Fraction of the more volatile component Distillate Mole Fraction of the more volatile component Steps:1. Get the pinch point by determining the intersection of the Feed line and the equilibrium curve:Equilibrium Curve:

Feed Line:

Combining (1) and (2) to solve for the abscissa of the pinch point gives the quadratic equation:

Substituting the positive value for to (1) to solve for ordinate of the pinch point:

2. Solve for the Minimum Reflux Ratio

This expression is also the slope of the enriching operating line at minimum reflux.3. Select a reflux ratio. Usually, it is 1.5 times the minimum reflux.

4. Determine the intersection of the feed Line and the enriching operating line by equating (2) and (7):

The resulting expression for and are:

5. Start the iteration in determining the number of stages at Stage 1: (45DL EC EOL)

Stage 2: (EOL EC EOL)

Use equations (1) and (7), the y in the previous point in the operating line is equal to that of the equilibrium curve. The x value of that corresponding y can be determined by equation (1) and will be the same x in the next operating line. The y value in the next operating line is determined using equation (7)

When or the resulting x value from the equilibrium curve to the operating line becomes less than the value of the intersection of the feed and enriching operating line, (7) is replaced by (8):

Stage k: (EOL EC SOL)

Iteration stops when, or the resulting x value is less than the bottoms mole fraction.Stage N-1:

Stage N:

6. Solve for the theoretical number of stages: