What is the mole fraction of ethanol when 10.00 ml of pure ethanol is combined with 2.00 ml of water? the volume of 10 ml of the solution must be measured?

The mole fraction is calculated using the formula:

mole fraction of component A = # of moles of component A / # of total moles of the solution.

A) number of moles of ethanol

To calculate the number of moles of ethanol, you need its density, which will permit you to determine the mass of the 10.00 ml, and then convert into moles using the molar mass of ethanol.

The normal density of ethanol is 0.789 g/ml

density = mass / volume => mass = density  * volume = 0.789 g/ml * 10.00 ml = 7.890 g

Molar mass of ethanol = 46.07 g/mol

number of moles = mass / molar mass = 7.890g / 46.07 g/mol = 0.1713 mol

B) number of moles of water

density of water = 1.00 g/mol

mass of water = density * volume = 1.00 g/mol * 2.00 ml = 2.00 g

number of moles of water = mass / molar mass = 2.00 g / 18.0 g/mol = 0.111  mol

C) mole fraction

mole fraction of ethanol = number of moles of ethanol / number of moles of solution

number of moles of ethanol = 0.1713 / (0.1713 + 0.111) = 0.1713 / 0.2824 = 0.607

0.607

The volume of the final solution may  be calculated by adding the volume of the two components. This is 10.00 ml of ethanol + 2.00 ml of water makes 12.00 ml of solution.

It is not clear what the second question is meant for. Some context is missing. If you know density and you know maqss (or can calculate the mass from other data) you do not need to measure the volume.