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Avogadro's number is the number of units per mole. A mole is 6.022x1023 (602,200,000,000,000,000,000,000) units. Because every element has a unique mass, it is primarily useful in chemistry for stoichiometric calculations. Hydrogen for example has a mass of ~1.01 grams per mole, so one gram of atomic hydrogen contains approximately 1 mole of hydrogen atoms, or 6.022x1023 hydrogen atoms. It seems arbitrary until you examine it's applications in practical use.

To create a molecule of water you need to combine 2 hydrogen atoms with one oxygen atom, along with a little bit of energy:

2H + O --> H2O

If you want to do this efficiently, you can't just throw 2 grams of hydrogen atoms together with 1 gram of oxygen atoms to create 3 grams of water because hydrogen and oxygen have different molecular masses. One oxygen atom is about 16 times heavier than 1 hydrogen atom, so with the above approach you'll only end up with about 1.125 grams of water with about 1.875 grams of hydrogen still floating about. This is where Avogadro's number comes into play.

Hydrogen is ~1 gram per mole (1 gram per 6.022x1023 atoms) and Oxygen is ~16 grams mer mole (16 grams per 6.022x1023 atoms). So to create 1 mole of water you need to combine approximately 2x6.022x1023 hydrogen atoms with approximately 6.022x1023 oxygen atoms, light a match, and prepare to get burned.

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