To design a distillation column for the separation of a mixture containing 35% Ethanol and 65% Water, we need to determine the number of theoretical plates required for the separation. We will use the McCabe-Thiele method to calculate the number of theoretical plates.1. Determine the feed composition and desired product compositions:Feed: 35% Ethanol, 65% WaterTop product distillate : xD Ethanol composition, typically 90-95% Bottom product: xB Water composition, typically 5-10% 2. Obtain the vapor-liquid equilibrium VLE data for the Ethanol-Water system at 1 atm. This can be found in literature or by using software like Aspen Plus or ChemCAD. For simplicity, we will use the following simplified VLE data:x Ethanol liquid phase - y Ethanol vapor phase 0.00 - 0.000.10 - 0.310.20 - 0.520.30 - 0.660.40 - 0.760.50 - 0.840.60 - 0.900.70 - 0.940.80 - 0.970.90 - 0.991.00 - 1.003. Choose the desired product compositions:xD = 0.90 90% Ethanol in the distillate xB = 0.10 10% Ethanol in the bottoms 4. Determine the feed quality q based on the feed condition. Since the feed is a liquid mixture, we will assume q = 1.5. Calculate the operating lines for the rectifying and stripping sections using the reflux ratio R of 1.5:Rectifying section: y = R / R + 1 * xD + x / R + 1 Stripping section: y = L'/V' * x + q / q - 1 * xF - L'/V' * xB 6. Plot the VLE data, q-line, and operating lines on the x-y diagram. Then, perform a graphical McCabe-Thiele analysis by stepping off the number of theoretical plates trays between the operating lines.7. Count the number of steps theoretical plates required to achieve the desired separation. This will be the number of theoretical plates required for the distillation column.Note that the actual number of trays required in the distillation column will be higher than the number of theoretical plates, as the trays' efficiency is typically less than 100%. Tray efficiency can be estimated using methods like the O'Connell correlation or the Van Winkle-Moshfeghian method.In summary, the McCabe-Thiele method is a graphical method to determine the number of theoretical plates required for a distillation column. The actual design of the column, including tray type, column diameter, and height, will require further calculations and considerations based on the desired separation and process conditions.