Avogadro's number is the number of items in one mole. The number is experimentally determined based on measuring the number of atoms in precisely 12 grams of the carbon-12 isotope, giving a value of approximately 6.022 x 10^{23}.

You can use Avogadro's number in conjunction with atomic mass to convert a number of atoms or molecules into the number of grams. For molecules, you add together the atomic masses of all the atoms in the compound to get the number of grams per mole. Then you use Avogadro's number to set up a relationship between the number of molecules and mass. Here's an example problem that shows the steps:

## Avogadro's Number Example Problem

**Question:** Calculate the mass in grams of 2.5 x 10^{9} H_{2}O molecules.

**Solution:**

To obtain the mass of 1 mole of water, look up the atomic masses for hydrogen and oxygen from the Periodic Table. There are two hydrogen atoms and one oxygen for every H_{2}O molecule, so the mass of H_{2}O is:

mass of H_{2}O = 2 (mass of H) + mass of O

mass of H_{2}O = 2 ( 1.01 g ) + 16.00 g

mass of H_{2}O = 2.02 g + 16.00 g

mass of H_{2}O = 18.02 g

**Step 2** - Determine the mass of 2.5 x 10^{9} H_{2}O molecules

One mole of H_{2}O is 6.022 x 10^{23} molecules of H_{2}O (Avogadro's number). This relation is then used to 'convert' a number of H_{2}O molecules to grams by the ratio:

mass of X molecules of H_{2}O / X molecules = mass of a mole of H_{2}O molecules / 6.022 x 10^{23} molecules

Solve for the mass of X molecules of H_{2}O

mass of X molecules of H_{2}O = ( mass of a mole H_{2}O · X molecules of H_{2}O ) / 6.022 x 10^{23} H_{2}O molecules

mass of 2.5 x 10^{9} molecules of H_{2}O = ( 18.02 g · 2.5 x 10^{9}) / 6.022 x 10^{23} H_{2}O molecules

mass of 2.5 x 10^{9} molecules of H_{2}O = ( 4.5 x 10^{10}) / 6.022 x 10^{23} H_{2}O molecules

mass of 2.5 x 10^{9} molecules of H_{2}O = 7.5 x 10^{-14} g.

**Answer**

The mass of 2.5 x 10^{9} molecules of H_{2}O is 7.5 x 10^{-14} g.

## Helpful Tips for Converting Molecules to Grams

The key to success for this type of problem is paying attention to the subscripts in a chemical formula. For example, in this problem, there were two atoms of hydrogen and one atom of oxygen. If you're getting the incorrect answer for this type of problem, the usual cause is having the number of atoms wrong. Another common problem is not watching your significant figures, which can throw off your answer in the last decimal place.