In Problem 9.D23, fractions were collected from ethanol mole fractions \(\mathrm{x}_{\mathrm{F}}=0.10\) to \(\mathrm{x}_{\mathrm{W} 1}=0.07\), from \(\mathrm{x}_{\mathrm{W} 1}\) to \(\mathrm{x}_{\mathrm{W} 2}=0.04\), and from \(\mathrm{x}_{\mathrm{W} 2}\) to \(\mathrm{x}_{\mathrm{W} 3}=\) \(\mathrm{x}_{\mathrm{W}, \text { final }}=0.01\). The solution is given under Answers to Selected Problems. Now collect a first product fraction (A) from \(\mathrm{x}_{\mathrm{F}}=0.10\) to \(\mathrm{x}_{\mathrm{WA}}\) \(=0.085\), a second product fraction \((\mathrm{B})\) from \(\mathrm{x}_{\mathrm{WOC} 1}=0.07\) to \(\mathrm{x}_{\mathrm{WB}}=0.05\), and a third product fraction (C), which is collected from \(\mathrm{x}_{\mathrm{W}}=0.04\) to \(\mathrm{x}_{\mathrm{W}, \text { final }}=0.01\). To obtain these product fractions, we need two offcuts: \(\mathrm{OC} 1\) from \(\mathrm{x}_{\mathrm{WA}}=0.085\) to \(\mathrm{x}_{\mathrm{WOC} 1}=0.07\), and \(\mathrm{OC} 2\) from \(\mathrm{x}_{\mathrm{WB}}=0.05\) to \(\mathrm{x}_{\mathrm{WOC} 2}=0.04\).

a. Find \(\mathrm{W}\) and \(\mathrm{D}\) (in kmol) and the mole fractions of ethanol \(\mathrm{x}_{\mathrm{D}, \text { avg }}\) for each fraction.

b. How would you reprocess the offcuts in the next batch?

Data From Problem 9.D23

\(1.2 \mathrm{kmol}\) of a \(10.0 \mathrm{~mol} \%\) ethanol and \(90.0 \mathrm{~mol} \%\) water feed is processed in a simple batch distillation system that consists of a still pot, a total condenser, and a fraction collector. We collect three fractions with \(\mathrm{x}_{\mathrm{W} 1}=7.0 \mathrm{~mol} \%\) ethanol, \(\mathrm{x}_{\mathrm{W} 2}=4.0 \mathrm{~mol} \%\) ethanol, and \(\mathrm{x}_{\mathrm{W} 3}=\mathrm{x}_{\mathrm{W}, \text { fin }}=1.0\) \(\mathrm{mol} \%\) ethanol. Find \(\mathrm{W}_{1}, \mathrm{~W}_{2}\), and \(\mathrm{W}_{\text {fin }} ; \mathrm{D}_{1}, \mathrm{D}_{2}\), and \(\mathrm{D}_{3}\) in kmole; and find mole fractions of ethanol \(\mathrm{x}_{\mathrm{D} 1 \text {,avg}}, \mathrm{x}_{\mathrm{D} 2 \text { avg }}\), and \(\mathrm{x}_{\mathrm{D} 3 \text {,avg. }} \cdot \mathrm{p}=1.0\) atm.