A simple batch distillation separates \(0.6 \mathrm{kmol}\) of a binary feed that is 70.0 \(\mathrm{mol} \%\) methanol and \(30.0 \mathrm{~mol} \%\) water. The final still pot is \(10.0 \mathrm{~mol} \%\) methanol. Find \(\mathrm{W}_{\text {final }}\), distillate \(\mathrm{D}_{\text {total }}\), and \(\mathrm{x}_{\mathrm{D}, \text { avg. }}\). VLE data are in Table \(2-8 . \mathrm{p}=1.0 \mathrm{~atm}\).

a. Use Simpson's rule.

b. Use the Gaussian quadrature formula.

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TABLE 2-8. Vapor-liquid equilibrium data for methanol water (p = 1 atm) (mol %) Methanol Liquid Methanol Vapor Temp., C 0 0 100 2.0 13.4 96.4 4.0 23.0 93.5 6.0 30.4 91.2 8.0 36.5 89.3 10.0 41.8 87.7 15.0 51.7 84.4 20.0 57.9 81.7 30.0 66.5 78.0 40.0 72.9 75.3 50.0 77.9 73.1 60.0 82.5 71.2 70.0 87.0 69.3 80.0 91.5 67.6 90.0 95.8 66.0 95.0 97.9 65.0 100.0 100.0 64.5