Derive the following expression for determining \(\mathrm{K}_{\mathrm{y}} \mathrm{a}\) from the measurement of \(\mathrm{E}_{\mathrm{MV}}\) in a distillation column if the flow pattern is plug flow.

\[ \begin{equation*} \mathrm{K}_{\mathrm{y}} \mathrm{a}=-\left[\mathrm{V} /\left(\mathrm{h} \mathrm{A}_{\text {active }}\right)\right] \ln \left\{1-[\mathrm{L} /(\mathrm{mV})] \ln \left[\mathrm{E}_{\mathrm{MV}}(\mathrm{mV} / \mathrm{L})+1\right]\right\} \tag{16-112} \end{equation*} \]