Avogadro's Number Example Chemistry Problem

Mass of a Known Number of Molecules

You can apply Avogadro's number to determine the mass of molecules.
You can apply Avogadro's number to determine the mass of molecules. Lawrence Lawry, Getty Images

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 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 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.

Answer

The mass of 2.5 x 109 molecules of H2O 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.