The system at 200C consists of a flask that holds a mixture of ethantol in water (20 % m/m) with a total density ρ = 968.7 kg/m3. The partial molar volume of ethanol in the solution is 52.3 cm3/mol. The objective is to calculate the partial molar volume of water in the mixture.
What I would like to do is to choose the total volume freely so that I can calculate the total mass of the solution and then the number of moles of each component in interest.
The total volume can be written as Vtot = VEtOHnEtOH + Vwaternwater, and Vwater is easily isolated from the other quantities.
What I am uncertain about is the background for the free choise of the total volume, is it not because both the density and the partial molar volume will have the same values regardless of the magnitude of this volume Vtot, i.e. they are intensive properties?