A distillation column at \(101.3 \mathrm{kPa}\) is separating a two-phase feed that is \(60.0 \%\) liquid, \(40.0 \mathrm{~mol} \%\) methanol, and \(60.0 \mathrm{~mol} \%\) water. Distillate product is \(92.0 \mathrm{~mol} \%\) methanol, and bottoms is \(4.0 \mathrm{~mol} \%\) methanol. A total reboiler and a total condenser are used. Reflux is a saturated liquid. Assume CMO and use L/D \(=0.9\). Under these conditions \(\mathrm{H}_{\mathrm{G}}=\) \(1.3 \mathrm{ft}\) and \(\mathrm{H}_{\mathrm{L}}=0.8 \mathrm{ft}\) in both the enriching and stripping sections. Determine the required heights of both the enriching and stripping sections. Equilibrium data are given in Table 2-8.

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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