We are separating methanol and water in a staged distillation column at total reflux to determine Murphree efficiency. Pressure is \(101.3 \mathrm{kPa}\). The column has a 2.0 -in. head of liquid on each plug-flow stage. Molar vapor flux is \(30.0 \mathrm{lbmol} /\left(\mathrm{h}-\mathrm{ft}^{2}\right)\). At the top tray, with \(\mathrm{x}=0.8\), we measure \(\mathrm{E}_{\mathrm{MV}}=0.77\). At the bottom tray, with \(\mathrm{x}=0.16, \mathrm{E}_{\mathrm{MV}}=0.69\). Equilibrium data are given in Table 2-8.

a. Calculate \(\mathrm{k}_{\mathrm{x}} \mathrm{a}\) and \(\mathrm{k}_{\mathrm{y}} \mathrm{a}\).

b. Estimate \(\mathrm{E}_{\mathrm{MV}}\) when \(\mathrm{x}=\mathrm{x}_{\text {avg }}=0.48\).

c. Estimate the value of \(\mathrm{E}_{\mathrm{O}}\) for the column at total reflux.