To determine the number of trays required to achieve the desired purity for both products, we can use the Fenske-Underwood-Gilliland FUG method. This method involves three main steps: Fenske equation for minimum number of trays, Underwood equation for minimum reflux ratio, and Gilliland correlation for actual number of trays.1. Fenske Equation:Nmin = log[ xD 1 - xB / xB 1 - xD ] / log where Nmin is the minimum number of trays, xD is the mole fraction of ethanol in the distillate, xB is the mole fraction of ethanol in the bottoms, and is the relative volatility of ethanol to water.Assuming the desired purity for both products is 99%, xD = 0.99 and xB = 0.01. The relative volatility of ethanol to water is approximately 2.3 at atmospheric pressure.Nmin = log[ 0.99 1 - 0.01 / 0.01 1 - 0.99 ] / log 2.3 Nmin 10.32. Underwood Equation:q = L/V min = - 1 / - where q is the minimum reflux ratio, L is the liquid flow rate, V is the vapor flow rate, is the equilibrium constant for the light key component ethanol , and is the equilibrium constant for the heavy key component water .Assuming an average value of = 2.3 and = 1 since water is the heavy key component , we can calculate the minimum reflux ratio:q = 2.3 - 1 / 2.3 - 1 q = 13. Gilliland Correlation:Nactual/Nmin = 1 + R/Rmin - 1 / 1 + R/Rmin ^0.567 where Nactual is the actual number of trays and R is the actual reflux ratio.Given the reflux ratio R = 2.5, we can calculate the actual number of trays:Nactual/10.3 = 1 + 2.5/1 - 1 / 1 + 2.5/1 ^0.567 Nactual 15.4Since the distillation column has 20 theoretical trays, it should be sufficient to achieve the desired purity for both products with the given reflux ratio of 2.5.