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:

Avogadro's Number Example Problem

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

Solution:

Step 1 - Determine the mass of 1 mole of H₂O

The chemical formula for water is H₂O. To obtain the mass of 1 mole of water, look up the atomic masses for hydrogen and oxygen from the Periodic Table. Depending on the table you use, you may need to adjust the number of significant figures for each atomic mass. 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.

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.

For example, in the formula H₂O, there are two atoms of hydrogen (the subscript) and one atom of oxygen (no subscript is the same as "1"). In H₂SO₄, there are two atoms of hydrogen, one atom of sulfur, and four atoms of oxygen.

Another common problem is not watching your significant figures, which can throw off your answer in the last decimal place. Base the number of significant digits on the number given in the problem for the number of molecules.