Plant Trouble-Shooting. A distillation column is separating \(127.6 \mathrm{~kg} / \mathrm{min}\) of a feed at \(30^{\circ} \mathrm{C}\) and \(130 \mathrm{kPa}\) that is \(37.6 \mathrm{wt} \% \mathrm{n}\)-pentane and \(64.2 \mathrm{wt} \% \mathrm{n}\)-heptane. The distillation column has a total condenser and a partial reboiler. Pressure of the column at the top registers \(110 \mathrm{kPa}\) and at the bottom \(120 \mathrm{kPa}\). At an external reflux ratio of 2.2 the distillate flow rate is measured as \(48.5 \mathrm{~kg} / \mathrm{min}\) of \(99.8 \mathrm{wt} \%\) n-pentane at \(39^{\circ} \mathrm{C}\) and the bottoms is \(99.92 \mathrm{wt} \% \mathrm{n}\)-heptane at \(128^{\circ} \mathrm{C}\). The flow meter for the bottoms is broken. You have complained to the shift supervisor that the mole fractions of the feed cannot be correct and at least one of the flow rates must be wrong, but he is adamant that "That's what the instruments read." The next shift supervisor, who is a lot more helpful, corrects the feed weight fraction nheptane as \(62.4 \mathrm{wt} \% \mathrm{n}\)-heptane, and notes that the bottom temperature reading has been erratic and that the pressure gauges all read correctly when the column was opened for cleaning 2 months ago, but she does not change the readings of the flow rates. She does give you the following cooling water information for the total condenser: Cooling water from an underground source at a flow rate of 235 gallons per minute enters at an average temperature of \(16.1^{\circ} \mathrm{C}\) and leaves at \(31.1^{\circ} \mathrm{C}\). The condensed distillate liquid and reflux liquid are both at \(37.5^{\circ} \mathrm{C}\). The water meter was recalibrated last month, and she swears it is accurate within \(1 \%\) or better of the actual water flow rate. Your job is to reconcile these results and come up with your best prediction of the bottoms flow rate. Note: For plant data, these numbers are not bad.

a. What is your best guess of the feed mole fraction? Briefly explain your rationale for this value.

b. Why is one (or more) of the flow rates probably incorrect? What else could be wrong?

c. What distillate, feed, and bottoms flow rates do you report to your boss, and what error bars do you use?

d. Should the pressure at the bottom of the column be greater than at the top of the column?

e. Is the temperature gauge at the top of the column probably correct or incorrect? What is your evidence?

f. Is the temperature gauge at the bottom of the column probably correct or incorrect? What is your evidence?