It is desired to prepare \(2000 \mathrm{~cm}^{3}\) of an antifreeze solution consisting of \(30 \mathrm{~mol}\) per cent methanol in water. What volumes of pure methanol and pure water at \(25^{\circ} \mathrm{C}\) must be mixed to form the required volume of antifreeze, also at \(25^{\circ} \mathrm{C}\) ? The partial molar volumes of methanol and water in a \(30 \mathrm{~mol}\) per cent methanol solution and their pure species molar volumes, both at \(25^{\circ} \mathrm{C}\), are:

Methanol (1): \(\bar{V}_{1}=38.632 \mathrm{~cm}^{3} / \mathrm{mol} \quad V_{1}=40.727 \mathrm{~cm}^{3} / \mathrm{mol}\)

Water (2): \(\bar{V}_{2}=17.765 \mathrm{~cm}^{3} / \mathrm{mol} \quad V_{2}=18.068 \mathrm{~cm}^{3} / \mathrm{mol}\)