The partial molar volume of water (1) in its mixture with methanol (2) at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) can be approximated by:

where \(a=-3.2 \mathrm{~cm}^{3} / \mathrm{mol}\).

\[ \bar{V}_{1}=18.1+a x_{2}^{2} \]

Develop an expression for the partial molar volume of methanol at the same condition, given that \(V_{2}\) at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) is \(40.7 \mathrm{~cm}^{3} / \mathrm{mol}\). Determine also the partial molar volume of methanol at infinite dilution.