Ok, so a very inquisitive tech asked me a question about a liquid calculation and while I know the right answer, I can't seem to figure out what's wrong with her calculation.

Here is the way I always calculate it. We need 1 L 0.5 N HCl from 12 N (37%) HCl.

ml= __(0.5 N)*(1L) __ = 41.67 ml + water up to 1 L

12N

Easy right? Ok, so here is the way she looked at it instead using the density of 37% HCl, which is 1.17 g/ml. She did this because the density is written on the bottle, but not the normality.

ml = (1 L)*(0.5 mol/1L)*(36.46 g/1 mol)*(1 ml/1.17 g) = 15.58 ml + water up to 1 L

I've realized that if I invert the density such that it is 1.17 ml/g then it gives me essentially the right answer, but I can't figure out why I would do that. Help me so that I can stop thinking about this stupid equation and get back to wasting time some other way!