To design a distillation column for the separation of a binary mixture of ethanol and water, we need to follow these steps:1. Determine the feed composition and desired product purity.2. Calculate the number of theoretical plates required for the desired separation.3. Determine the height and diameter of the column based on the number of theoretical plates.Step 1: Feed composition and desired product purityFeed mixture: 40 mol% ethanol and 60 mol% waterDesired product purity: 95 mol% ethanolStep 2: Calculate the number of theoretical platesWe can use the Fenske equation to estimate the number of theoretical plates N required for the desired separation:N = [ log xD* 1-xB / xB* 1-xD / log ] - 1where xD is the desired distillate composition 0.95 , xB is the desired bottoms composition, and is the relative volatility of the two components.For ethanol and water, the relative volatility is approximately 2.3 at atmospheric pressure. To find xB, we can use the mass balance equation:xF*F = xD*D + xB*Bwhere xF is the feed composition 0.4 , F is the feed rate 1000 kg/hr , D is the distillate rate, and B is the bottoms rate.Assuming a recovery of 99% of ethanol in the distillate, we can calculate D and B:D = 0.99 * 0.4 * 1000 / 0.95 415.79 kg/hrB = 1000 - 415.79 584.21 kg/hrNow we can find xB:0.4 * 1000 = 0.95 * 415.79 + xB * 584.21xB 0.086Now we can calculate the number of theoretical plates using the Fenske equation:N [ log 0.95* 1-0.086 / 0.086* 1-0.95 / log 2.3 ] - 1N 15.5Since we cannot have a fraction of a theoretical plate, we round up to 16 theoretical plates.Step 3: Determine the height and diameter of the columnThe height of the column depends on the type of column internals trays or packing and the efficiency of the internals. For simplicity, let's assume we are using sieve trays with an average tray efficiency of 70%. The actual number of trays required will be:Actual trays = N / Tray efficiency = 16 / 0.7 23 traysAssuming a tray spacing of 0.6 m, the height of the column will be:Height = Actual trays * Tray spacing = 23 * 0.6 = 13.8 mThe diameter of the column depends on the vapor and liquid flow rates, tray design, and allowable pressure drop. This calculation requires detailed hydraulic analysis and is beyond the scope of this answer. However, a rough estimate for the diameter can be obtained using empirical correlations or by referring to similar industrial distillation columns.In conclusion, the distillation column should have approximately 16 theoretical plates 23 actual trays and a height of 13.8 meters. The diameter of the column needs to be determined through detailed hydraulic analysis or by referring to similar industrial distillation columns.