To design a distillation column for the given mixture of benzene and toluene, we need to follow these steps:1. Determine the relative volatility of benzene and toluene:The relative volatility is the ratio of the vapor pressures of the two components. For benzene and toluene, the relative volatility is approximately 2.5 at typical distillation conditions.2. Calculate the minimum reflux ratio Rmin :Using the Fenske equation, we can determine the minimum number of theoretical trays Nmin required for the desired separation:Nmin = [ log 1 - xD * xB / log 1 - xB * xD ] / log where xD is the mole fraction of benzene in the distillate 0.99 and xB is the mole fraction of benzene in the bottoms 0.01 .Nmin 10.6Now, we can use the Underwood equation to find the minimum reflux ratio Rmin :Rmin = * Nmin / - 1 Rmin 5.33. Determine the actual number of trays N and the actual reflux ratio R :Since the given reflux ratio 2.5 is less than the minimum reflux ratio 5.3 , we need to increase the number of trays to achieve the desired separation. We can use the Gilliland correlation to find the actual number of trays:N = Nmin * [1 + R / R + 1 ^0.5]N 17.4Since we cannot have a fraction of a tray, we round up to 18 trays.4. Design the distillation column:Now that we have determined the number of trays and the reflux ratio, we can design the distillation column. The column will have 18 theoretical trays, including the reboiler and condenser. The column diameter, tray spacing, and other design parameters can be determined based on the flow rates and physical properties of the mixture.5. Verify the product purity:Using simulation software or rigorous calculations, verify that the designed column with 18 trays and a reflux ratio of 2.5 achieves the desired product purity of at least 99% for both benzene and toluene.In conclusion, to achieve a product purity of at least 99% for both benzene and toluene with a reflux ratio of 2.5, a distillation column with 18 theoretical trays should be designed.