A solution is prepared by mixing 769 mL of ethanol with 507 mL of water. The molarity of ethanol in the resulting solution is 10.8 M. The density of ethanol at this temperature is 0.7893 g/mL. Calculate the difference in volume between the total volume of water and ethanol that were mixed to prepare the solution and the actual volume of the solution.

To make things clear, when 769 mL of ethanol were mixed with 507 mL of water, the resulting volume was not (769+507) 1276 mL, but a lower value. This is because of the interactions between liquid molecules.

First we calculate how many grams of ethanol are there in 769 mL, using the given density:

mass = density * volume

0.7893 g/mL * 769 mL = 606.97 g ethanol

Then we convert 606.97 g of ethanol into moles, using its molar mass:

606.97 g ÷ 46.07 g/mol = 13.17 mol

Now we calculate the actual volume of the solution, using the definition of molarity:

Volume = Moles / Molarity

13.17 mol / 10.8 M = 1.219 L

Finally we convert 1.219 L to mL, and calculate the difference in volume:

1.219 L * 1000 = 1219 mL

1276 mL - 1219 mL = 57 mL