# The mole and molar mass

Canonical: https://duckyhelper.com/learn/chemistry/mole-and-molar-mass/
Updated: 2026-10-01

A mole is a counting unit for tiny particles: 1 mole is \(6.022 \times 10^{23}\) atoms, molecules or ions. That number is Avogadro's number. Molar mass is the mass of 1 mole of a substance in grams per mole (g/mol). You find it by adding up atomic masses from the periodic table. Divide grams by molar mass to get moles, and multiply moles by Avogadro's number to get particles.

## Key ideas

Atoms are far too small to count one by one, so chemists count them in moles, the way you count eggs in dozens. A dozen is 12. A mole is \(6.022 \times 10^{23}\).

$$
n = \frac{m}{M} \qquad N = n \times N_A
$$

- \(n\) is the amount of substance, in moles (mol).
- \(m\) is the mass of the sample, in grams (g).
- \(M\) is the molar mass, in grams per mole (g/mol).
- \(N\) is the number of particles (atoms, molecules or formula units). It has no unit.
- \(N_A = 6.022 \times 10^{23}\ \text{mol}^{-1}\) is Avogadro's number, the number of particles in 1 mole.

**Molar mass** is the sum of the atomic masses of every atom in the formula. For water, \(\mathrm{H_2O}\):

$$
M_{\mathrm{H_2O}} = 2(1.008) + 16.00 = 18.02\ \text{g/mol}
$$

The atomic mass on the periodic table means two things at once: the mass of one atom in atomic mass units (u), and the mass of one mole of atoms in grams. Carbon is 12.01 u per atom and 12.01 g per mole.

**The conversion map: moles are always in the middle**

| From | To | Do this |
| --- | --- | --- |
| grams | moles | divide by molar mass (g/mol) |
| moles | grams | multiply by molar mass (g/mol) |
| moles | particles | multiply by \(6.022 \times 10^{23}\) |
| particles | moles | divide by \(6.022 \times 10^{23}\) |
| grams | particles | grams to moles first, then moles to particles |

> **Note: Atomic masses used on this page**
>
> H 1.008, C 12.01, N 14.01, O 16.00, Na 22.99, Cl 35.45, Cu 63.55 (g/mol), from the IUPAC standard atomic weights rounded the way most school periodic tables print them. Your table may differ in the last digit, which can change the last digit of an answer.

## Worked examples

**Example 1: molar mass of glucose**

Problem: Find the molar mass of glucose, \(\mathrm{C_6H_{12}O_6}\).

1. List each element and how many atoms of it are in one molecule: 6 C, 12 H, 6 O.
2. Multiply each count by its atomic mass.

   $$
   6(12.01) = 72.06 \qquad 12(1.008) = 12.096 \qquad 6(16.00) = 96.00
   $$
3. Add them up.

   $$
   M = 72.06 + 12.096 + 96.00 = 180.16\ \text{g/mol}
   $$

Answer: 180.16 g/mol

**Example 2: grams to moles**

Problem: How many moles of water are in 25.0 g of water?

1. Molar mass of water.

   $$
   M = 2(1.008) + 16.00 = 18.02\ \text{g/mol}
   $$
2. Divide the mass by the molar mass. Grams cancel, leaving moles.

   $$
   n = \frac{25.0\ \text{g}}{18.02\ \text{g/mol}} = 1.387\ \text{mol}
   $$
3. 25.0 g has 3 significant figures, so round to 3.

Answer: 1.39 mol of water

**Example 3: moles to molecules and atoms**

Problem: How many molecules are in 0.250 mol of \(\mathrm{CO_2}\)? How many oxygen atoms is that?

1. Multiply moles by Avogadro's number.

   $$
   N = 0.250\ \text{mol} \times 6.022 \times 10^{23}\ \text{mol}^{-1} = 1.5055 \times 10^{23}
   $$
2. Round to 3 significant figures: \(1.51 \times 10^{23}\) molecules.
3. Each \(\mathrm{CO_2}\) molecule has 2 oxygen atoms.

   $$
   2 \times 1.5055 \times 10^{23} = 3.011 \times 10^{23}
   $$

Answer: \(1.51 \times 10^{23}\) molecules of \(\mathrm{CO_2}\), containing \(3.01 \times 10^{23}\) oxygen atoms

**Example 4: grams to atoms in two steps**

Problem: How many copper atoms are in a 10.0 g copper wire?

1. Grams to moles, using Cu = 63.55 g/mol.

   $$
   n = \frac{10.0\ \text{g}}{63.55\ \text{g/mol}} = 0.15736\ \text{mol}
   $$
2. Moles to atoms. Keep the unrounded moles so the last digit stays right.

   $$
   N = 0.15736\ \text{mol} \times 6.022 \times 10^{23}\ \text{mol}^{-1} = 9.476 \times 10^{22}
   $$
3. Round to 3 significant figures.

Answer: \(9.48 \times 10^{22}\) copper atoms

## Common mistakes and how to fix them

- **Multiplying when you should divide.** Check the units: \(\text{g} \div \text{g/mol} = \text{mol}\). If the units do not cancel, flip the step.
- **Missing a subscript or parentheses.** \(\mathrm{Ca(OH)_2}\) has 2 O and 2 H, not 1 of each. Fix: write out the atom count before you add.
- **Using the atomic number instead of the atomic mass.** Oxygen's atomic number is 8, but its molar mass is 16.00 g/mol. Use the decimal number on the periodic table.
- **Mixing up molecules and atoms.** 1 mol of \(\mathrm{H_2O}\) is \(6.022 \times 10^{23}\) molecules but 3 times that many atoms. Fix: say what you are counting in the answer.
- **Rounding too early.** Rounding the moles before the next step can change the last digit. Keep one or two extra digits and round once at the end.

**Practice problems**

1. What is the molar mass of sodium chloride, NaCl?
   A. 35.45 g/mol
   B. 58.44 g/mol
   C. 116.88 g/mol
   D. 11.00 g/mol

   Answer: 58.44 g/mol. Add one sodium and one chlorine: \(22.99 + 35.45 = 58.44\) g/mol. 35.45 counts only the chlorine, 116.88 counts the formula twice, and 11.00 is sodium's atomic number, not a mass.

2. How many moles are in 88.0 g of carbon dioxide, \(\mathrm{CO_2}\)?

   Answer: 2.00 mol. \(M = 12.01 + 2(16.00) = 44.01\) g/mol. Then \(88.0 \div 44.01 = 1.9995\), which rounds to 2.00 mol (3 significant figures).

3. What is the mass of 3.00 mol of water?
   A. 6.01 g
   B. 18.0 g
   C. 54.0 g
   D. 162 g

   Answer: 54.0 g. Moles to grams means multiply: \(3.00\ \text{mol} \times 18.02\ \text{g/mol} = 54.06\) g, which is 54.0 g to 3 significant figures.

4. How many water molecules are in 9.01 g of water?

   Answer: \(3.01 \times 10^{23}\) molecules. Grams to moles: \(9.01 \div 18.02 = 0.500\) mol. Moles to molecules: \(0.500 \times 6.022 \times 10^{23} = 3.01 \times 10^{23}\).

5. Which sample contains more atoms in total: 1.0 mol of helium (He) or 0.50 mol of water (\(\mathrm{H_2O}\))?
   A. 1.0 mol of He
   B. 0.50 mol of H2O
   C. They contain the same number of atoms

   Answer: 0.50 mol of H2O. Helium is single atoms, so 1.0 mol of atoms. Each water molecule has 3 atoms, so 0.50 mol of water has \(0.50 \times 3 = 1.5\) mol of atoms.

## Frequently asked questions

### Why is a mole \(6.022 \times 10^{23}\) and not a round number?

The number was picked so that atomic masses and molar masses match. One atom of carbon-12 has a mass of exactly 12 u, and \(6.022 \times 10^{23}\) of them have a mass of 12 grams. Since 2019 the SI has fixed Avogadro's number at exactly \(6.02214076 \times 10^{23}\) per mole.

### Is molar mass the same as atomic mass?

They have the same number but different units. Atomic mass is the mass of one atom in atomic mass units (u). Molar mass is the mass of one mole of atoms in grams per mole. Sodium is 22.99 u per atom and 22.99 g/mol.

### How many decimal places should I use for molar mass?

Use the values on the periodic table your class uses, usually two decimal places, and keep at least one more significant figure than your data has. The final answer gets its significant figures from the measured data, like 25.0 g, not from the molar mass.

### Does the mole work for things that are not atoms?

Yes. A mole is just a number, like a dozen. You can have a mole of ions, a mole of electrons or a mole of formula units of an ionic compound such as NaCl. Always say which particle you are counting.

## Sources

- [OpenStax Chemistry 2e, 3.1 Formula Mass and the Mole Concept](https://openstax.org/books/chemistry-2e/pages/3-1-formula-mass-and-the-mole-concept), accessed 2026-10-01
- [CIAAW, Standard atomic weights](https://www.ciaaw.org/atomic-weights.htm), accessed 2026-10-01
- [NIST, Avogadro constant (CODATA exact value)](https://physics.nist.gov/cgi-bin/cuu/Value?na), accessed 2026-10-01

## Related

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