In the production of chlorobenzenes by chlorination of benzene,

In the production of chlorobenzenes by chlorination of benzene, two close-boiling isomers, para-dichlorobenzene (P) and ortho-dichlorobenzene (O), are separated by distillation. The feed to the column consists of 62 mol% of the para isomer and 38 mol% of the ortho isomer. Assume that the pressures at the bottom and top of the column are 20 psia (137.9 kPa) and 15 psia (103.4 kPa), respectively. The distillate is a liquid containing 98 mol% para isomer. The bottoms product is to contain 96 mol% ortho isomer. At column pressure, the feed is slightly vaporized with q = 0.9. Calculate the number of theoretical stages required for a reflux ratio equal to 1.15 times the minimum-reflux ratio. Base your calculations on a constant relative volatility obtained as the arithmetic average between the column top and column bottom using appropriate vapor pressure data and the assumption of Raoult's and Dalton's laws. The McCabe-Thiele construction should be supplemented at the two ends by use of the Kremser equations as illustrated in Example 7.4.