Using the Wilson and NRTL equations, estimate the activity coefficients of the components of a binary system consisting of iso-butanol (1) and iso-propanol (2) at \(50^{\circ} \mathrm{C}\) and \(x_{1}=0.3\). At this temperature, the molar volumes of the components are \(V_{1}=65.2\) \(\mathrm{cm}^{3} / \mathrm{mol}\) and \(V_{2}=15.34 \mathrm{~cm}^{3} / \mathrm{mol}\).

Data given:

for Wilson equation

\[ \begin{aligned} & a_{12}=300.55 \mathrm{cal} / \mathrm{mol} \\ & a_{21}=1520.32 \mathrm{cal} / \mathrm{mol} \end{aligned} \]

for NRTL equation

\[ \begin{aligned} b_{12} & =685.21 \mathrm{cal} / \mathrm{mol} \\ b_{21} & =1210.21 \mathrm{cal} / \mathrm{mol} \\ \alpha & =0.552 \end{aligned} \]