Kilogram prototypes have all changed to different weights and no-one knows why

Unless they have changed the definition, back when I studied it the mole was defined as the number of particles found in 12 grams of C (C-12), 6.022*10^23.

So the mole depended on the gram.

As it turns out, a mole of carbon doesn't mass exactly 12/16 of a mole of oxygen or 12× a mole of hydrogen. (Carbon's average atomic mass is 12, not 14.) So you'd have to pick an atom.

At present, the definition runs the other direction: a dalton is defined as 1/(Avogadro's number) of a gram. But Avogadro's number is a little difficult to measure directly; what you end up doing is picking an element and measuring its atomic mass. They picked carbon.

It seems to me that the definition you describe would indeed be a reasonable one, since Avogadro's number is known to seven significant figures at this point, which seems comparable to the mass stability of the international prototype kilogram.

That was the idea, but they immediately made a prototype kilogram mass in 1799 when they came up with that definition, and it turns out that it was off by about 25 ppm, and we've been working from that prototype ever since — so water only has that density to four significant figures.

No, this has been an issue for years. http://en.wikipedia.org/wiki/Kilogram#Stability_of_the_inter...