Avogadro's number is the quantity of items in one mole. You can use it in conjunction with atomic mass to convert a number or 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 number of molecules and mass. Here's an example problem that shows the steps:

### Avogadro's Number Example Problem - Mass of a Known Number of Molecules

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

**Solution**

**Step 1** - Determine the mass of 1 mole of H_{2}O

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 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.