\(1.2 \mathrm{kmol}\) 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.