A vinegar sample was analyzed and found to be 5.88 acetic acid by volume. The density of pure acetic acid is 1.049g/mL. What volume of 0.500M of NaOH would be required to titrate 10mL aliquot of this vinegar?

This is the most stupid question I have seen lately.

Volume concentration is one of the worst ways of describing solution composition. Check volume-volume percentage discussion and what is wrong with percentages.

But that's not all. Density of the solution rarely changes linearly with concentration, but sometimes dependence is close to linear. In case of acetic acid is not only non-linear, it has a maximum. Pure water has in 20 deg C temperature density of 0.9982 g/mL, pure acetic acid has density of 1.0497 g/mL, 78% w/w acetic acid has density of 1.0700 g/mL.

All that makes calculation of the concentration very difficult - and ambiguous.

If you mix 5.88 mL of acetic acid with 94.12 mL of water you will get 99.4123 mL of solution of 1.0339 M concentration. (Note that mixing 5.88+94.12 you may expect final volume to be 100 mL - it is not due to contraction).

If you mix 5.88 mL of acetic acid with 94.71 mL of water you will get 100 mL of solution of 1.0278 M concentration.

I wonder which result (1.0339 or 1.0278) will be considered correct.

I also wonder where you are supposed to use pure acetic acid density - IMHO it is of no use here.

To check these results please download CASC - trial version has built in density table for acetic acid. Solution mixer is a tool I used when calculating above results. It doesn't support volume/volume concentrations due to their ambiguity, but it can be used with some skill to do such calculations too. Contact me off forum if you need further details.

Oh, and next time don't post such questions in inorganic chemistry forum

This is the most stupid question I have seen lately.  

Wow, not a very science-like thing to say Borek. I thought there were no "stupid" questions in science.

I think statements like this may be a little off putting to science students.

Ok that's cool, you're right it is not the student but the teacher.

Do you think that maybe you are making this answer unnecessarily confusing. At what level of chemistry would you expect a student to go into as much detail as you have, solving simple problems with software. Seems like a bit of over-kill to me.

Can you give an answer with your method? and how different is it from my method?

Mike

Yes this is true, the student will have made an assumption, although this is very common in science education.

So basically if the teacher had reworded the question (ie w/w rather than v/v) there would be no problem.

Well, thankyou very much for your knowledge (this is a great forum for sharing this type of information).

Cheers mate,

Mike