Derive the following equation to determine \(\mathrm{n}_{\mathrm{OG}}\) for distillation at total reflux for systems with constant relative volatility:

\[ \begin{equation*} \mathrm{n}_{\mathrm{OG}}=\frac{1}{1-\alpha} \ln \left[\frac{\left(\mathrm{y}_{\text {out }}-1\right)\left(\mathrm{y}_{\text {in }}\right)}{\left(\mathrm{y}_{\text {in }}-1\right)\left(\mathrm{y}_{\text {out }}\right)}\right]+\ln \left(\frac{\mathrm{y}_{\text {in }}-1}{\mathrm{y}_{\text {out }}-1}\right) \tag{16-113} \end{equation*} \]