Formula Mass, Molecular Mass, and Molar Mass

Formula mass is the sum of the atomic masses (in u) of all atoms in a formula unit, molecular mass is the sum for a molecule, and molar mass is the mass in grams of one mole of a substance, which has the same numerical value as the formula or molecular mass but the unit g/mol. In brief: the molecular mass of water, H₂O, is 2(1.008) + 15.999 = 18.015 u, so its molar mass is 18.015 g/mol; the formula mass of NaCl is 22.990 + 35.45 = 58.44 u, and its molar mass is 58.44 g/mol.

Chemists count atoms and molecules by weighing, and molar mass is the conversion factor between the two. Almost every calculation in quantitative chemistry starts with finding a molar mass. This article defines the three terms, explains how to calculate them from a formula including those with parentheses and hydrates, lists the molar masses of common substances in a table, works through examples, describes how atomic masses are determined and gives some history.

What are formula mass, molecular mass and molar mass?

• Atomic mass (relative atomic mass) is the average mass of the atoms of an element compared with one twelfth of the mass of a carbon-12 atom, given in atomic mass units (u). It is found on the periodic table.
• Molecular mass is the sum of the atomic masses of the atoms in a molecule. It applies to substances made of molecules, such as H₂O, CO₂ and glucose.
• Formula mass is the sum of the atomic masses in the formula of a substance. It is used for ionic compounds and network solids, which do not consist of discrete molecules, such as NaCl and SiO₂. For molecular compounds the terms formula mass and molecular mass are the same.
• Molar mass (M) is the mass of one mole of a substance, in grams per mole. A mole contains 6.022 × 10²³ particles. Numerically, the molar mass in g/mol equals the formula mass in u.

The reason for this equivalence is the definition of the atomic mass unit and the mole: 1 u = 1/12 of the mass of a carbon-12 atom, and 1 mol of carbon-12 has a mass of about 12 g. So the molar mass constant is about 1 g/mol per u.

How do you calculate a molar mass?

1. Write the correct chemical formula.
2. List each element and the number of its atoms in the formula. For parentheses, multiply everything inside by the subscript outside. For hydrates, add the water molecules.
3. Multiply the atomic mass of each element by its number of atoms.
4. Add the results and write the unit g/mol.

Molar masses of common substances

Worked examples

1. Sodium carbonate, Na₂CO₃. 2(22.990) + 12.011 + 3(15.999) = 45.980 + 12.011 + 47.997 = 105.988, so M = 105.99 g/mol.
2. Ammonium sulfate, (NH₄)₂SO₄. The parentheses contain NH₄, which is multiplied by 2: N 2 × 14.007 = 28.014; H 8 × 1.008 = 8.064; S 32.06; O 4 × 15.999 = 63.996. The sum is 132.134, so M = 132.13 g/mol.
3. Hydrate, MgSO₄·7H₂O. MgSO₄: 24.305 + 32.06 + 4(15.999) = 120.361. Seven waters: 7 × 18.015 = 126.105. The sum is 246.466, so M = 246.47 g/mol.
4. Comparing the number of particles per gram. 1.00 g of H₂O contains 1.00 ÷ 18.015 = 0.0555 mol. 1.00 g of NaCl contains 1.00 ÷ 58.44 = 0.0171 mol. Water has about 3.2 times as many formula units per gram.
5. Mass of a single molecule. One molecule of water has a mass of 18.015 u. In grams: 18.015 g ÷ 6.022 × 10²³ = 2.99 × 10⁻²³ g.
6. Mass of a mole of atoms and a mole of molecules. 1 mol of oxygen atoms (O) has a mass of 15.999 g. 1 mol of oxygen molecules (O₂) has a mass of 31.998 g, since each molecule has two atoms. State clearly which one is meant.
7. Percent difference from the nearest whole number. Use of rounded atomic masses (H = 1, C = 12, O = 16) gives glucose as 180 g/mol, within 0.1% of the more precise 180.16 g/mol.

Where do atomic masses come from?

Most elements have several isotopes, and the atomic mass on the periodic table is a weighted average of the masses of the naturally occurring isotopes. For chlorine, the average is 35.45 because chlorine is 75.76% chlorine-35 and 24.24% chlorine-37. The abundances of isotopes vary slightly with the source, so for some elements, such as hydrogen, carbon, oxygen and sulfur, IUPAC gives an interval of values (for example, carbon: 12.0096 to 12.0116), and a conventional value for use in calculations, such as 12.011. Isotope masses are measured with a mass spectrometer to high precision.

How many digits should you use?

Use atomic masses with at least one more significant figure than the least precise measurement in the calculation, and round at the end. For a sample weighed to 0.01 g, a molar mass given to two decimal places is adequate. Use the unrounded periodic table values within the calculation if possible. Do not round the molar mass to a whole number unless the problem allows it.

How did atomic masses develop?

John Dalton published the first table of relative atomic weights in 1805 to 1808, with hydrogen as 1. Jöns Jacob Berzelius determined atomic masses with remarkable accuracy in the 1810s and 1820s. Stanislao Cannizzaro’s work at the 1860 Karlsruhe Congress resolved the confusion between atomic and molecular masses by applying Avogadro’s hypothesis. The standard changed from oxygen to carbon-12 in 1961, and the mass of the carbon-12 atom defines the atomic mass unit. Since 2019 the mole is defined by fixing the Avogadro constant, and the molar mass of carbon-12 is therefore very close to, but no longer exactly, 12 g/mol.

Which mistakes are common?

Mistake 1: Forgetting to multiply the atoms inside parentheses

In Ca(OH)₂ there are two O and two H atoms. In Al₂(SO₄)₃ there are 3 S and 12 O atoms.

Mistake 2: Leaving out the water of hydrates

The molar mass of CuSO₄·5H₂O is 249.68 g/mol, not 159.61 g/mol.

Mistake 3: Using the atomic mass for a diatomic element

The molar mass of chlorine gas (Cl₂) is 70.90 g/mol, not 35.45 g/mol.

Mistake 4: Omitting the unit

Formula mass is in u, molar mass is in g/mol. Write the unit in every step.