Assume trays are plug flow, and repeat Problem 16.D21 parts a and \(b\). In addition, calculate \(\mathrm{E}_{\mathrm{pt}}\) for the three mole fractions \(\mathrm{x}_{\mathrm{W}}=0.48,0.36\), and 0.16. Compare your \(\mathrm{E}_{\mathrm{pt}}\) values and the \(\mathrm{E}_{\mathrm{MV}}\) value. Explain what is occurring.

Problem 16.D21

A small distillation column with a partial reboiler, a total condenser, and a liquid-liquid separator is separating \(100.0 \mathrm{kmol} / \mathrm{h}\) of saturated liquid feed that is \(19.0 \mathrm{~mol} \%\) water and \(81.0 \mathrm{~mol} \% \mathrm{n}\)-butanol. Operation is at \(1.0 \mathrm{~atm}\). Distillate product (from liquid-liquid separator) is \(97.5 \mathrm{~mol} \%\) water. Bottoms product is \(4.0 \mathrm{~mol} \%\) water. Boilup ratio \(=0.50\). Sieve trays in the column have approximately a 5 \(\mathrm{cm}\) height of liquid. Column diameter is \(1.0 \mathrm{~m}\). In the enriching section when \(\mathrm{x}_{\mathrm{W}}=0.48, \mathrm{E}_{\mathrm{MV}}\) was measured as 0.68 . In the stripping section when \(\mathrm{x}_{\mathrm{W}}=0.16, \mathrm{E}_{\mathrm{MV}}\) was 0.59 . Assume trays are well mixed.

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

b. Estimate \(\mathrm{E}_{\mathrm{MV}}\) when \(\mathrm{x}_{\mathrm{W}}=0.36\).

Suggestion: Plot equilibrium data on a \(y\) - \(x\) diagram, and find \(m\) by drawing tangent lines.