To determine the number of trays required in the distillation column, we can use the McCabe-Thiele method. First, we need to obtain the vapor-liquid equilibrium VLE data for the ethanol-methanol system at 1 atm. The VLE data can be represented by the following equations:y = x / 1 + - 1 x where y is the mole fraction of ethanol in the vapor phase, x is the mole fraction of ethanol in the liquid phase, and is the relative volatility of ethanol to methanol.For ethanol-methanol system at 1 atm, is approximately 2.3.Now, we can plot the equilibrium curve using the VLE data. Next, we need to determine the operating lines for the rectifying and stripping sections of the column.The rectifying section operating line equation is:y_R = R / R + 1 x + x_D / R + 1 where R is the reflux ratio, x_D is the mole fraction of ethanol in the distillate, and y_R is the mole fraction of ethanol in the vapor leaving the rectifying section.The stripping section operating line equation is:y_S = L / G x + x_W * G / L where L is the liquid flow rate in the stripping section, G is the vapor flow rate in the stripping section, x_W is the mole fraction of ethanol in the bottoms product, and y_S is the mole fraction of ethanol in the vapor leaving the stripping section.Given the desired product compositions, x_D = 0.8 and x_W = 0.01. To determine the number of trays, we need to choose an appropriate reflux ratio R . A higher reflux ratio will result in fewer trays but higher energy consumption, while a lower reflux ratio will require more trays but less energy consumption. For this problem, let's assume a reflux ratio of 1.5.Now, we can plot the operating lines on the same graph as the equilibrium curve. The intersection of the rectifying and stripping operating lines is the feed point. The number of trays can be determined by stepping off the stages between the feed point and the distillate and bottoms product compositions. Start at x_D and draw a horizontal line to the equilibrium curve, then draw a vertical line down to the rectifying operating line. Repeat this process until you reach the feed point. Do the same for the stripping section, starting at the feed point and moving towards x_W.After stepping off the stages, count the number of horizontal lines trays in both the rectifying and stripping sections. The total number of trays required for the desired separation is the sum of the trays in both sections.Please note that the actual number of trays will depend on the chosen reflux ratio and the efficiency of the distillation column. The McCabe-Thiele method provides an estimate of the number of trays required for a given separation, but the actual number of trays may be different due to factors such as tray efficiency, column design, and operating conditions.