In order to prepare \(3.0 \mathrm{~m}^{3}\) of an alcohol-water solution, alcohol of mole fraction \(X_{1}=\) 0.60 is required to be mixed with water at \(25^{\circ} \mathrm{C}\). Determine the volumes of alcohol and water needed to prepare the mixture, given that Partial molar volume of methanol \(=57.11 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol}\)

Partial molar volume of water \(=17.5 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol}\)

Molar volume of alcohol \(=56.21 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol}\)

Molar volume of water \(=18 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol}\).