Question

I don't really understand why unit analysis works.

I found a simple example on a website (I can post the link in a comment if you want).

It says,
For example, convert 18 grams of water to moles. The molar mass of water is 18 g/mol; therefore :

18g H2O x 1 mol/18g H2O = 1 mol H2O

In 1 mol/18g H2O, I get that the denominator is molar mass, but how come the regular unit, g/mol, isn't used and just g is used? How come we're able to do that?

And what does this equation mean in words.. ?
There's 18g H2O for every 1mol of H2O (which weighs 18g)... So there's 1 mol of H2O...?

Answer 1

But I don't think division would mean "which" weighs 18g..

Answer 2

The molar mass is defined in simple terms as the mass of a mole plus the word "grams".

Answer 3

, but then would 1mol/18g H2O mean
1 mol per 18 grams per mol of H2O..? There's one mol for every 18g of H2O..? It's confusing

Answer 4

1 mol H2O is 18 grams. The factor used in dimensional analysis is 1 mol H2O/18 g H2O or 18g H2O/1 mol H2O.
1 mol/18 g H2O means 1 mol H2O/18 g H2O. I don't understand what's confusing about "There's one mol (of water) for every 18 g of H2O." Perhaps my (of water) addition helps clarify the statement.