The effect of liquid maldistribution in packed columns can be explored with a McCabe-Thiele diagram. Assume that a packed distillation column is separating a saturated liquid binary feed that is \(40.0 \mathrm{~mol} \%\) MVC. A distillate product, \(\mathrm{D}=100.0 \mathrm{kmol} / \mathrm{h}\), that is \(90.0 \% \mathrm{MVC}\) is desired. Relative volatility \(=3.0\) and is constant. We operate at an L/D \(=2(\mathrm{~L} / \mathrm{D})_{\min }\). If there is liquid maldistribution, the actual L/V represents an average for the entire column. Assume that vapor is equally distributed throughout the column, but there is more liquid on one side than the other. The slope of the operating line on the low liquid side will be \(\mathrm{L}_{\text {low }} / \mathrm{V}\), not \((\mathrm{L} / \mathrm{V})_{\text {avg }}\). If the low liquid flow rate is small enough, the operating line on the low side will be pinched at the feed point, and the desired separation will not be obtained. What fraction of the average liquid flow rate must the low liquid flow rate beto just pinch at the feed concentration? Then generalize your result for \(\mathrm{L} / \mathrm{D}=\mathrm{M} \times(\mathrm{L} / \mathrm{D})_{\min }\), where \(\mathrm{M}>1\).