How to Calculate the Number of Atoms Given the Grams and Atomic Mass Units

By Lauren Whitney; Updated April 24, 2017
Each element has a unique atomic weight.

If you look at the periodic table of elements, you'll see each element's atomic weight listed. Scientists call the unit of measure in which that atomic weight is expressed the atomic mass unit. Avogadro's constant -- 6.02 x 10^23 -- describes the number of atoms within a mole of an element. Weighing a sample gives you its mass in grams. Knowing all three pieces of information -- atomic weight, grams and Avogadro's number -- will tell you the number of atoms in the sample.

Express the relationship of the three pieces of information you need to calculate the number of atoms in the sample in the form of an equation. Scientists express atomic weights in terms of grams per mole, so the resulting equation looks like this: atomic weight expressed in atomic mass units = grams/mole. In scientific notation, it would appear like this: u = g/mole.

Look up the sample's atomic weight on a periodic table of the elements. For example, boron has an atomic weight of 10.811 atomic mass units which you could also express as 10.811 grams per mole of the element. Plugging that figure into the above equation would look like this: 10.811 = g/mole.

Solve the equation for the unknown quantity; if u = g/mole and you have a number for u and g, then the number of moles is your target. Multiply everything through by the divisor to isolate the unknown quantity and you will reach an equation that looks like this: mole = g/u, where g equals the sample's weight in grams and u equals the element's atomic weight in atomic mass units.

Divide the grams of your sample by its atomic weight to derive the number of moles the sample contains. If your sample of boron weighed 54.05 g, your equation would look like this: mole = 54.05/10.811. In this example, you would have 5 moles of boron.

Multiply the number of moles in the sample by Avogadro's number, 6.02 x 10^23, to derive the number of atoms in the sample. In the given example, multiply Avogadro's constant by 5 to discover that the sample contains 3.01 x 10^24 individual boron atoms.

Check your work to ensure that it makes sense. Negative numbers, small numbers and numbers that do not seem to fit with the sample size mean a mathematical error.

Tip

Check your units of measurement to see if you must make any conversions; if you've measured your sample in kilograms or pounds, convert those figures to grams before proceeding. Carrying decimal places out to more digits will result in a more precise answer. Scientists add the atomic weights of atoms that comprise molecules together and use this derived number, the formula unit, to calculate the number of molecules in a sample of a compound.

Warning

Keep an eye on your exponents when you convert your answer into scientific notation; note how the exponent in the example changed from 10^23 to 10^24.

About the Author

Lauren Whitney covers science, health, fitness, fashion, food and weight loss. She has been writing professionally since 2009 and teaches hatha yoga in a home studio. Whitney holds bachelor's degrees in English and biology from the University of New Orleans.