To calculate the number of theoretical trays required in the distillation column, we can use the McCabe-Thiele method. This method is based on the equilibrium stages concept and uses graphical representation to determine the number of theoretical trays.Step 1: Determine the equilibrium curveFor ethanol-water system, we can use the following equation for the equilibrium curve:y = x / 1 + - 1 x where y is the vapor phase mole fraction of ethanol, x is the liquid phase mole fraction of ethanol, and is the relative volatility of ethanol to water. For ethanol-water system, is approximately 2.3.Step 2: Determine the feed lineThe feed line equation is given by:y = q / q - 1 x - qF / q - 1 where q is the liquid fraction of the feed and F is the feed composition. Since the feed is a liquid, q = 1. The feed composition is 30 mol% ethanol, so F = 0.3.y = 1 / 1 - 1 x - 0.3 / 1 - 1 = xStep 3: Determine the rectifying and stripping linesThe rectifying line equation is given by:y = L / L + D x + D / L + D xDwhere L is the liquid flow rate in the rectifying section, D is the distillate flow rate, and xD is the distillate composition. The reflux ratio is given as L/D = 2, so L = 2D. The desired distillate composition is 95 mol% ethanol, so xD = 0.95.y = 2D / 2D + D x + D / 2D + D 0.95 = 2/3 x + 1/3 0.95The stripping line equation is given by:y = L' / L' - D x - D / L' - D xBwhere L' is the liquid flow rate in the stripping section and xB is the bottom composition. Since the feed rate is 100 kmol/hour and the distillate composition is 95 mol% ethanol, we can assume that the bottom composition is negligible xB 0 .y = L' / L' - D xStep 4: Determine the number of theoretical traysUsing the graphical method, we can plot the equilibrium curve, feed line, rectifying line, and stripping line on the same graph. The intersection points of these lines represent the theoretical trays. We can count the number of intersection points between the feed line and the rectifying line, and between the feed line and the stripping line, to determine the total number of theoretical trays required.Unfortunately, as an AI text-based model, I am unable to create or display graphical representations. However, you can follow the steps above and create the graph yourself, or use software like Aspen Plus, ChemCAD, or Excel to create the graph and determine the number of theoretical trays required to achieve the desired distillate composition.