A ternary mixture of methanol, n-propanol, and n-butanol is flash distilled at a pressure of \(0.74 \mathrm{~atm}\). The feed is \(36 \mathrm{~mol} \%\) methanol, \(42 \mathrm{~mol} \% \mathrm{n}\)-propanol, and the remainder n-butanol. The relative volatility of methanol with respect to \(n-\) propanol is \(\alpha_{\mathrm{M}-\mathrm{P}}=3.58\), and the relative volatility of \(n\)-butanol with respect to \(n-\) propanol is \(\alpha_{\mathrm{B}-\mathrm{P}}=0.412\). Vapor pressure data for \(n\)-propanol are given in Problem 6.D4, and Antoine coefficients are in Table 2-3 (listed as 1-propanol). Use Raoult's law to find the K value of n-propanol.

a. Based on linear interpolation of data in Problem 6.D4, what is the lowest temperature at which a flash distillation can be done for this feed at \(\mathrm{p}_{\mathrm{drum}}=\) \(0.74 \mathrm{~atm} ?\)

b. If \(\mathrm{T}_{\text {drum }}=82.0^{\circ} \mathrm{C}\) and \(\mathrm{p}_{\text {drum }}=0.74 \mathrm{~atm}\), find \(\mathrm{V} / \mathrm{F}\), vapor and liquid mole fractions.