Mole to Mole Conversions

[Hannah Alltucker 3L]

While working on some practice problems and the homework problems, I continue to see a pattern in mole to mole conversions that is something along these lines:

If you are doing a conversion that requires converting H2O to H, you do (1 mole of H2O) x (2 mol H/1 mol H2O) in your stoichiometry, and this is applicable to other necessary conversions. However, i'm a little confused on to why its done this way, and how two moles of H are taken from H2O when a mole seems to be based on the fixed definition that a mole of a substance is 6.022 x 10^23 (Avogadro's Number) particles. Is there something i'm missing when it comes to figuring how many moles of an element are in a molecule when the definition of what a mole is seems to be pretty set in stone?

If someone has a good way to explain this kind of conversion it would be greatly appreciated, thanks!

[Sam Wentzel 1F 14B]

Finding moles H from moles H2O must be done by performing the 1 mol H2O x 2 mol H / 1 mol H2O as you mentioned because there are 2 atoms of Hydrogen per 1 molecule of H2O.

We can prove that the mole conversion applies using Avogadro's number as it relates to moles.

Suppose we have a single molecule of H2O. We can perform the following calculations based on this fact.

1 molecule H2O x 1 mol H2O / (6.022x10^23 molecules H2O) = 1.66x10^-24 mols H2O
1.66x10^-24 mols H2O x 2 mol H / 1 mol H2O = 3.32x10^-24 mols H
3.32x10^-24 mols H x 6.022 x 10^23 atoms H / 1 mol H = 2 atoms H.

Therefore for every molecule of H2O, we have two atoms of H. Additionally, as you can see, at one point in the equation, I first divided by 6.022x10^23 "somethings" and then multiplied by 6.022x10^23 "somethings". Because of this, we can essentially cancel out the 6.022x10^23's altogether. This is why the molar ratios between a molecule (H2O) and its component atoms (in this case, H and O) apply mathematically.
Hope this helps :D

[OwenSumter_2F]

This was also confusing to me, but I was able to rationalize by thinking of Avogadro's number or moles not as just used for elements or molecules but as a number that can be used for any purpose. Therefore, you can look at it in simpler terms, such that if I had a ten pencil boxes with 3 pencils in each, I would have 10 pencil boxes but 30 pencils, which is more than the combined totals. This reasoning can be applied to moles, where 1 mole of a molecule, such as H₂O, can be made up of 2 moles of Hydrogen and 1 mole of Oxygen.