I need to make a solution of 50% ethanol in water (by mass). The partial molar volume of water is 17.0mL/mol and the partial molar volume of ethanol is 52.0mL/mol. What is the density of this solution/

To find the density of the solution, you need to know the mass and volume of the solution.

To begin, we can assume that the total mass of the solution is 100 grams (since we are aiming for a 50% ethanol solution by mass). This means that the mass of ethanol is 50 grams and the mass of water is also 50 grams.

Next, we need to calculate the volumes of ethanol and water in the solution.

The volume of ethanol can be calculated using the formula:

Volume of ethanol = (mass of ethanol) / (density of ethanol)

The density of ethanol is approximately 0.789 g/mL, so substituting the values:

Volume of ethanol = 50 g / (0.789 g/mL) = 63.46 mL

Similarly, the volume of water can be calculated using the formula:

Volume of water = (mass of water) / (density of water)

The density of water is approximately 1 g/mL, so substituting the values:

Volume of water = 50 g / (1 g/mL) = 50 mL

Now, we can calculate the total volume of the solution:

Total volume = volume of ethanol + volume of water = 63.46 mL + 50 mL = 113.46 mL

Finally, we can calculate the density of the solution using the formula:

Density = (mass of the solution) / (total volume of the solution)

Substituting the values:

Density = 100 g / 113.46 mL

Before calculating the density, we need to be consistent with the units. In this case, we want the answer in grams per milliliter (g/mL), so it is essential to ensure that both the mass and volume are in grams and milliliters, respectively.

Converting 100 grams to milliliters using the density of water (1 g/mL):

100 g = 100 mL

Density = 100 mL / 113.46 mL = 0.881 g/mL

Therefore, the density of the 50% ethanol solution is approximately 0.881 g/mL.