In order to prepare \(2.0 \mathrm{~m}^{3}\) of alcohol-water solution, alcohol of mole fraction \(X_{1}=0.40\) 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 alcohol \(=38.3 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol}\)

Partial molar volume of water \(=17.2 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol}\)

Molar volume of alcohol \(=39.21 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol}\)

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