# Calculate the Mass in Grams of a Single Water Molecule

Learning how to calculate the mass in grams of a single molecule of water is a useful exercise because it reinforces concepts of atomic weight, molecular formulas, the mole, and Avogadro’s number. Here is how you find the mass of one molecule, along with a discussion of why this value is just an estimate.

1. Write the molecular formula. For example, the molecular formula of water is H2O.
2. Look up the atomic masses of the elements on the periodic table. For example, the atomic mass of hydrogen is 1.008 and the atomic mass of oxygen is 15.994.
3. Add up the masses of the atoms in the molecule. Multiply the mass of each element by its subscript (if it has one). For example, the molar mass of water is (1.008 x 2) + (15.994 x 1) = 18.01 grams per mole.
4. Divide the molar mass by Avogadro’s number for the mass of a single molecule in grams. For water, this is 18.01 ÷ 6.022 x 1023 = 2.99 x 10-23 grams.

### How to Calculate Mass of One Molecule

First, understand that there are two main ways of expressing the mass of one molecule.

Mass given in daltons (Da) or atomic mass units (amu) is approximately the same as the molar mass of an atom or compound. For example, the molar mass of hydrogen is 1.008 grams per mole, so the mass of a single hydrogen atom is about 1.008 Da or 1.008 amu. Similarly, the mass of a single carbon dioxide molecule is its molar mass expressed as Da or amu. For carbon dioxide, look up the atomic masses of carbon (12.011) and oxygen (15.994) on the periodic table. Add the masses of the elements in the compound for the molar mass (12.011 + 2×15.994 = 44.0). The mass of single molecule of carbon monoxide is 44.0 Da or 44.0 amu. This value also goes by the name of “molecular mass.”

Mass in grams is a bit different. Once again, start with the molecular formula for a compound. Look up the atomic masses of each element on the periodic table. Add up the masses of each element. If there is a subscript following an element symbol, multiply the atomic mass by that number. This gives the molar mass of the compound, which is grams per mole.

But, there are Avogadro’s number of molecules in one mole of a compound. In other words, each mole of a compound contains 6.022×1023 molecules. So, get the mass in grams of a compound by dividing the molar mass by Avogadro’s number. For carbon dioxide, the mass in grams of a single molecule is 44.0 g/mol ÷ 6.022×1023 molecules/mol = 7.3 x 10-23 grams.

### Find Mass in Grams of a Single Water Molecule

A classic homework problem is finding the mass in grams of a single water molecule.

The chemical formula of water is H2O. The subscript following the symbol for hydrogen (H) is 2, meaning each water molecule contains two atoms of hydrogen. There is no subscript after the symbol for oxygen (O), so you know each molecule only contains one atom of oxygen.

Now, find the mass of one mole of water in grams. This is the sum of the masses of the atoms in the molecule, which is the sum of the hydrogen masses plus the oxygen mass. From the periodic table, the mass of each hydrogen atom is 1.008 g/mol, while the mass of the oxygen atom is 15.994 g/mol. The molar mass of water is 2×1.008 + 15.994 = 18.01 g/mol.

Each mole of water contains 6.022×1023 water molecules. So, the mass of a single water molecule is the molar mass (18.01 g/mol) divided by Avogadro’s number (6.022×1023 molecules/mole).

mass of individual water molecule = 18.01 g/mol ÷ 6.022×1023 molecules/mol = 2.99 x 10-23 grams

### Why Is Mass of a Molecule Just an Estimate?

There are three reasons why the mass of a molecule is an approximation.

• There is error from rounding the numbers.
• Atomic weights of the elements are weighted averages based on the natural abundance of the elements. A single molecule may not contain the same isotope ratio.
• Even if you know the exact isotopes of each element, you can’t simply add up the mass of protons, neutrons, and electrons. When atoms bind together and form compounds, the bond formation either results in a (very) slight mass increase (endothermic reactions) or (very) slight mass decrease (exothermic reactions). Chemical bonds either absorb or else release energy, while the sum of mass plus energy is conserved.

### References

• Chang, Raymond (2005). Physical Chemistry for the Biosciences. ISBN 978-1-891389-33-7.
• International Union of Pure and Applied Chemistry (1980). “Atomic Weights of the Elements 1979”. Pure Appl. Chem. 52 (10): 2349–84. doi:10.1351/pac198052102349
• Lilley, J.S. (2006). Nuclear Physics: Principles and Applications. Chichester: J. Wiley. ISBN 0-471-97936-8.
• Neufeld, R.; Stalke, D. (2015). “Accurate Molecular Weight Determination of Small Molecules via DOSY-NMR by Using External Calibration Curves with Normalized Diffusion Coefficients”. Chem. Sci. 6 (6): 3354–3364. doi:10.1039/C5SC00670H