# Use Avogadro's Number to Convert Molecules to Grams

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 1023.

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:

Question: Calculate the mass in grams of 2.5 x 109 H2O molecules.

Solution:

Step 1 - Determine the mass of 1 mole of H2O

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 H2O molecule, so the mass of H2O is:

mass of H2O = 2 (mass of H) + mass of O
mass of H2O = 2 ( 1.01 g ) + 16.00 g
mass of H2O = 2.02 g + 16.00 g
mass of H2O = 18.02 g

Step 2 - Determine the mass of 2.5 x 109 H2O molecules

One mole of H2O is 6.022 x 1023 molecules of H2O (Avogadro's number). This relation is then used to 'convert' a number of H2O molecules to grams by the ratio:

mass of X molecules of H2O / X molecules = mass of a mole of H2O molecules / 6.022 x 1023 molecules

Solve for the mass of X molecules of H2O

mass of X molecules of H2O = ( mass of a mole H2O · X molecules of H2O ) / 6.022 x 1023 H2O molecules

mass of 2.5 x 109 molecules of H2O = ( 18.02 g · 2.5 x 109) / 6.022 x 1023 H2O molecules
mass of 2.5 x 109 molecules of H2O = ( 4.5 x 1010) / 6.022 x 1023 H2O molecules
mass of 2.5 x 109 molecules of H2O = 7.5 x 10-14 g.