A distillation column, as shown in the figure to the right, is a device used to separate components with different volatilities. In a specific process, a distillation column is used to separate a feed stream containing 0.4500 mol ethanol/mol and 0.5500 mol water/mol into two product streams: an overhead stream that is ethanol-rich and a bottoms stream that is water-rich. Vapor containing 0.8500 mol ethanol/mol (and 0.1500 mol water/mol) leaves the top of the distillation column and enters a condenser, where the stream condenses completely into a liquid. This stream is then split; the reflux returns to the column and the overhead product leaves the process. The ratio of the flow rates of reflux to overhead product is given by the reflux ratio:
R= flow rate of reflux / flow rate of overhead product and for this particular process, R = 1.64. Liquid leaving the bottom of the distillation column enters a reboiler, where a fraction of the stream is vaporized and returns to the distillation column as boil up, while the liquid fraction leaves the process as bottoms product. The composition of the boil up and the bottoms product streams are governed by the relative volatility of ethanol and water:
where yE is the mole fraction of ethanol in the vapor stream, yW is the mole fraction of water in the vapor stream, xE is the mole fraction of ethanol in the liquid stream, and xW is the mole fraction of water in the liquid stream. For this particular process? = 8.197, and the ratio of ethanol leaving the reboiler in the boilup to ethanol leaving the reboiler in the bottoms product is 0.710. For a basis of 100 mol of feed, 48.58 mols of overhead product is produced. Given this basis answer the following questions Label the process flow diagram below. Label any quantities as \"unknown\" if they are not given or implied above. Do not leave any blank spaces. Variables names are given for reference later.
Given the basis, what is n6, the moles of bottoms product?
What is the mole fraction of ethanol in the bottoms product?
What is n2, the moles of vapor leaving the distillation column (before the condenser)?
What is y7, the mole fraction of ethanol in the boil up stream?
What is n7, the moles of boil up?