For the binary system \(n\)-pentanol (1)- \(n\)-hexane (2), determine the activity coefficients at \(31 \mathrm{~K}\) in an equimolar mixture. The Wilson parameters are as follows:

\[ \begin{aligned} V_{1} & =109.2 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol} \\ V_{2} & =132.5 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol} \\ a_{12} & =7194.18 \mathrm{~J} / \mathrm{mol} \\ a_{21} & =697.52 \mathrm{~J} / \mathrm{mol} \end{aligned} \]