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A student is asked to design a distillation column for the separation of a mixture consisting of ethanol and water. The student has to determine the number of theoretical plates required for the column to achieve a product concentration of 95% ethanol, given the feed mixture contains 25% ethanol and 75% water. The student also needs to calculate the amount of steam required for the reboiler to operate at a

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To determine the number of theoretical plates required for the distillation column, we can use the McCabe-Thiele method. First, we need to find the equilibrium data for the ethanol-water system. The equilibrium data can be found in the literature or by using the Antoine equation to estimate the vapor pressures of ethanol and water at the operating temperature.For simplicity, let's assume the following equilibrium data for the ethanol-water system at 1 atm:Mole Fraction of Ethanol in Liquid  x  | Mole Fraction of Ethanol in Vapor  y ----------------------------------------|--------------------------------------0.00                                    | 0.000.10                                    | 0.320.20                                    | 0.580.30                                    | 0.740.40                                    | 0.840.50                                    | 0.900.60                                    | 0.940.70                                    | 0.960.80                                    | 0.980.90                                    | 0.991.00                                    | 1.00Now, we can use the McCabe-Thiele method to determine the number of theoretical plates:1. Locate the feed point on the x-axis  x_F = 0.25  and draw a vertical line to the equilibrium curve.2. Draw a horizontal line from the intersection of the vertical line with the equilibrium curve to the 45-degree diagonal line  x=y .3. Draw a q-line from the intersection of the horizontal line with the diagonal line through the feed point  x_F, y_F  on the x-axis.4. Locate the desired product concentration on the x-axis  x_D = 0.95  and draw a horizontal line to the equilibrium curve.5. Draw a vertical line from the intersection of the horizontal line with the equilibrium curve to the diagonal line.6. Repeat steps 4 and 5 until the q-line is reached. Count the number of steps  vertical lines  to estimate the number of theoretical plates.By following these steps, we can estimate the number of theoretical plates required for the distillation column to achieve a product concentration of 95% ethanol.Next, we need to calculate the amount of steam required for the reboiler to operate at a reflux ratio of 3.5. The reflux ratio  L/D  is the ratio of the liquid returned to the column  L  to the distillate product  D . We can use the following equation to calculate the steam required:Steam required =  F - D  /  L/D Where F is the feed flow rate. Since we don't have the feed flow rate, we can only calculate the ratio of steam required to the feed flow rate:Steam required / F =  1 - D/F  /  L/D Assuming a reflux ratio of 3.5  L/D = 3.5 , we can calculate the ratio of steam required to the feed flow rate:Steam required / F =  1 - D/F  / 3.5To find the actual amount of steam required, we would need the feed flow rate  F  and the distillate flow rate  D .

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