# 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:

### Key Takeaways: Molecules to Grams Conversion

• When you convert from number of molecules to grams, you use Avogadro's number as a conversion factor.
• But, the first step is finding the molar mass of the molecule. Do this by looking up the atomic mass of each element in the molecule from the periodic table and adding up the masses of all of the atoms.
• Then, multiply the number of molecules by the molar mass. Divide this value by Avogadro's number to get the mass in grams of the 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

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.

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.

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