To design a distillation column for the separation of a 75% ethanol and 25% water mixture, we will use the McCabe-Thiele method, which is based on the equilibrium stages concept. The following steps will be taken to design the column:1. Determine the boiling points of ethanol and water at atmospheric pressure:Ethanol: 78.37CWater: 100C2. Choose an operating pressure for the column:We will operate the column at atmospheric pressure 1 atm since the boiling points of ethanol and water are significantly different at this pressure.3. Determine the feed mixture boiling point at the chosen pressure:Using the lever rule, the boiling point of the feed mixture 75% ethanol and 25% water at 1 atm is approximately 83.5C.4. Construct the equilibrium curve for the ethanol-water system:Using the vapor-liquid equilibrium data for ethanol and water, plot the equilibrium curve on an x-y diagram x: liquid phase mole fraction, y: vapor phase mole fraction .5. Determine the number of equilibrium stages required:Using the McCabe-Thiele method, draw the operating lines for the rectifying and stripping sections of the column on the x-y diagram. The intersection of these lines is the feed stage. Count the number of equilibrium stages required to achieve the desired separation 95% ethanol in the distillate and no more than 5% ethanol in the bottom product .6. Design the column internals:Based on the number of equilibrium stages, choose an appropriate type of column internals trays or packing and design the column height and diameter. For this case, we will use sieve trays. The tray spacing should be around 0.6 m to ensure good vapor-liquid contact and minimize pressure drop.7. Determine the reflux ratio:Using the Fenske equation, calculate the minimum reflux ratio Lmin/D and choose an operating reflux ratio L/D that is 1.2-1.5 times the minimum reflux ratio to ensure good separation.8. Calculate the flow rates of the distillate D and bottom product B :Using the mass balance equations and the given feed rate 1000 kg/hr , calculate the flow rates of the distillate and bottom product.9. Design the condenser and reboiler:Design a condenser that can cool the vapor leaving the top of the column to the desired distillate temperature using the available cooling water supply at 20C. Design a reboiler that can provide the necessary heat to vaporize the bottom product and maintain the desired temperature in the stripping section.In conclusion, the distillation column should be designed with the following operating conditions:- Operating pressure: 1 atm- Feed temperature: 83.5C- Number of equilibrium stages: Determined using the McCabe-Thiele method- Column internals: Sieve trays with 0.6 m spacing- Reflux ratio: 1.2-1.5 times the minimum reflux ratio- Distillate flow rate D and bottom product flow rate B : Calculated using mass balance equations- Condenser and reboiler design: Based on the required heat transfer rates and available cooling water supplyThis design should effectively separate the ethanol-water mixture into a distillate with at least 95% ethanol and a bottom product with no more than 5% ethanol.