To design a distillation column for the separation of a 50% ethanol and 50% water mixture, we will follow these steps:1. Determine the operating conditions2. Calculate the number of theoretical trays3. Determine the feed tray location4. Calculate the column diameterStep 1: Determine the operating conditionsThe boiling points of ethanol and water are 78.37C and 100C, respectively. We will operate the column at 1 atm pressure. Step 2: Calculate the number of theoretical traysWe will use the Fenske equation to determine the minimum number of theoretical trays Nmin required for the separation:Nmin = log xD 1 - xB / xB 1 - xD / log where xD is the mole fraction of ethanol in the distillate 0.95 , xB is the mole fraction of ethanol in the bottoms 0.05 , and is the relative volatility of ethanol to water. Assuming a relative volatility of 2.3 for ethanol to water at 1 atm:Nmin = log 0.95 1 - 0.05 / 0.05 1 - 0.95 / log 2.3 11.9We will round up to 12 theoretical trays as the minimum number required for the separation.To account for the actual column efficiency, we will use a Murphree tray efficiency of 70%. Therefore, the actual number of trays required is:Nactual = Nmin / tray efficiency = 12 / 0.7 17.1We will round up to 18 actual trays for the column.Step 3: Determine the feed tray locationWe will use the feed condition as a basis for determining the feed tray location. Assuming the feed is a saturated liquid q = 1 , we can use the following equation:q = L1/V * xF - xD / xB - xD where L1 and V are the liquid and vapor flow rates on the rectifying section, and xF is the mole fraction of ethanol in the feed 0.5 . Rearranging the equation to solve for L1/V:L1/V = 0.5 - 0.95 / 0.05 - 0.95 = 0.45 / -0.9 = 0.5Assuming a reflux ratio L1/D of 1.5, we can calculate the feed tray location:Feed tray location = Nmin * L1/V / 1 + L1/V = 12 * 0.5 / 1 + 0.5 8We will place the feed tray at the 8th tray from the top.Step 4: Calculate the column diameterThe column diameter can be calculated using the following equation:D = 4 * F / * L * vL where F is the feed rate 1000 kg/h , L is the liquid density assumed to be 900 kg/m for the ethanol-water mixture , and vL is the liquid velocity assumed to be 0.01 m/s .D = 4 * 1000 / * 900 * 0.01 1.41 mWe will use a column diameter of 1.41 meters.In summary, the distillation column design for the separation of a 50% ethanol and 50% water mixture is as follows:- Number of theoretical trays: 12 18 actual trays - Feed tray location: 8th tray from the top- Column diameter: 1.41 meters- Reflux ratio: 1.5