Chapter 7 Problems:

Chapter 7 Problems
These exercises provide excellent practice for graphical (McCabeThiele) design of distillation columns. This method is particularly wellsuited if you know how the column is supposed to perform but need to know how many equilibrium stages are required and which is the optimum feed tray.
For a fixed number of stages and the feed stage identified, only two specifications were required in addition to the feed, for instance, R and x_{D}. There is one additional unknown in this case; the number of stages. That means one more piece of information is needed in order to solve a problem. This could be a flow rate, composition, reflux ratio, or boilup.
You will need a starting and end point on the xy graph – x_{D} and x_{B}. These can usually be determined using the overall process total and species mole balances. Then the operating lines are drawn using a specified reflux or boilup ratio. Finally, it is just a matter of stepping off the stages. Remember that VLE graphs for all these mixtures can be printed from Excel “VLE”.
If you want to be awesome  and I know you do  compare your results to a process simulator like ChemCAD or Aspen. Make plots of the L, x, V, y, and T profiles. Vary parameters such as the reflux ratio and predict how it will change your results.
7.1 100 mol/s of an saturated liquid mixture of benzene (50 mol%) and toluene (50 mol%) is fed to the optimum tray of a distillation column operating at 1 atm. The distillate flow rate is 45 mol/s, the bottoms flow rate is 55 mol/s, and the reflux ratio is 2. That is three specifications, but ... make a convincing argument why this problem does not have a unique solution.
7.2 100 kmol/h of a saturated liquid mixture of benzene (60 mol%) and chlorobenzene (40 mol%) is fed to the optimum tray of a distillation column operating at 1 atm. The distillate has a flow rate of 50 kmol/s and a composition of 0.95 mol B/mol. The reflux ratio is twice the minimum. Determine the number of stages and identify the feed stage.
7.3 100 mol/s of a saturated liquid mixture of acetone (30 mol%) and isopropanol (70 mol%) is fed to the optimum tray of a distillation column operating at 1 atm. The bottoms composition is 0.1 mol A/mol, the distillate flow rate is 25 mol/s, and the reflux ratio is 2.0. Determine the number of stages and identify the feed stage.
7.4 100 mol/s of a saturated vapor mixture of ethylbenzene (60 mol%) and styrene (40 mol%) is fed to the optimum tray of a distillation column operating at 100 mm Hg. The distillate flow rate is 60 mol/s with composition 0.85 mol E/mol. The reflux ratio is 8. Determine the number of stages and identify the feed stage.
7.5 50 mol/s of a mixed feed (½ vapor – ½ liquid) with overall composition 40 mol% ethanol and 60 mol% water is fed to the optimum tray of a distillation column operating at 1 atm. The bottoms flow rate is 30 mol/s, the distillate composition is 0.8 mol E/mol, and the reflux ratio is twice the minimum. Determine the number of stages and identify the feed stage.
7.6 100 mol/s of a saturated liquid consisting of 40 mol% isopropanol and 60 mol% water is fed to the optimum tray of a distillation column operating at 1 atm. The distillate flow rate is 40 mol/s and its composition is 0.68 mol I/mol. The reflux ratio is 4.23. Determine the number of stages and identify the feed stage.
7.7 100 kmol/h of a saturated liquid containing 40 mol% hexane and 60 mol% octane is fed to the optimum tray of a distillation column operating at 1 atm. The distillate flow rate is 35 mol/s and its composition is 0.97 mol H/mol. The reflux ratio is twice the minimum. Determine the number of stages and identify the feed stage.
7.8 500 mol/h of a mixture with equal amounts of liquid and vapor is fed to the optimum tray of a distillation column operating at 1 atm. The overall composition of the feed is 50 mol% methanol and 50 mol% water. The bottoms flow rate is 300 mol/s, the reflux ratio is 1.0, and the distillate composition is 0.95. Determine the number of stages and identify the feed stage.
7.9 100 mol of a saturated vapor containing 60 mol% hexane and 40 mol% heptane is fed to the optimum tray of a distillation column operating at 2 atm. The bottoms flow rate is 40 mol/s, the reflux ratio is 1.0, and the distillate composition is 0.80 mol Hex/mol. Determine the number of stages and identify the feed stage.
7.10 100 mol of a saturated liquid containing 30 mol% butane and 70 mol% hexane is fed to the optimum tray of a distillation column operating at 1 atm. The bottoms composition is 0.05 mol B/mol, the reflux ratio is 1.0, and the distillate composition is 0.99 mol B/mol. Determine the number of stages and identify the feed stage.