The feed to a distillation column (sketched below) is a 45.0 mole% n-pentane−55.0 mole% n hexane liquid mixture. The vapor stream leaving the top of the column, which contains 98.0 mole% pentane and the balance hexane, goes to a total condenser (which means all the vapor is condensed). Half of the liquid condensate is returned to the top of the column as re?ux and the rest is withdrawn as overhead product (distillate) at a rate of 85.0 kmol/h. The distillate contains 95.0% of the pentane fed to the column. The liquid stream leaving the bottom of the column goes to a reboiler. Part of the stream is vaporized; the vapor is returned to the bottom of the column as boilup, and the residual liquid is withdrawn as bottom: product.
(a) Calculate the molar ?ow rate of the feed stream and the molar ?ow rate and composition of the bottoms product stream.
(b) Estimate the temperature of the vapor entering the condenser, assuming that it is saturated (at its dew point) at an absolute pressure of 1 atm and that Raoult's law applies to both pentane and hexane. Then estimate the volumetric ?ow rates of the vapor stream leaving the column and of the liquid distillate product. State any assumptions you make.
(c) Estimate the temperature of the reboiler and the composition of the vapor boilup, again assuming operation at 1 atm.
(d) Calculate the minimum diameter of the pipe connecting the column and the condenser if the maximum allowable vapor velocity in the pipe is 10 m/s. Then list all the assumptions underlying the calculation of that number.
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