Calculate the partial molar volume of water in a \(50 \mathrm{~mol}\) per cent ethanol-water solution in which the partial molar volume of ethanol is \(52.37 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol}\). Given that the density of the mixture is \(800.21 \mathrm{~kg} / \mathrm{m}^{3}\).