Calculating the mass percent from a given volume % and density

[CynicusRex]

Homework Statement

A bottle of wine contains 12.5 % ethanol (volume%). The density of ethanol (C2H5OH) is 0.789 g/cm^3. Calculate the concentration of alcohol in wine in: a. mass percent, b. molarity.

Relevant Equations

mass solute a / solution * 100 = mass percent a
p = m/v

[I've solved b, but can't figure out a for the life of me. I have a couple of attempts, but it's just nonsense, it's like I've short circuited.]

 

[CynicusRex]

Okay, never mind. I didn't know the density of wine/water was 1g/ml.

 

[Borek]

Okay, never mind. I didn't know the density of wine/water was 1g/ml.

It wasn't

1 g/mL is a rather exact number for water and often a reasonably good approximation for not too concentrated water based solutions, but for better answer you need the density to be measured. 12.5% ethanol solution has a density of 0.9795 g/mL - that can be easily checked in tables. The density of wine is different, as it also contains many other substances, including substantial amount of sugars (which makes the density higher).

Plus, especially in the case of ethanol, calculations are quite difficult, as volumes are not additive - if you mix 50 mL of water with 50 mL of ethanol, you get 96.4 mL of solution.

You are probably expected to do only approximate calculations, but bear in mind they are a bit wrong by definition.