How to Calculate Moles: 3 Formulas Every Student Needs (with Worked Examples)

Q: What is a mole in Chemistry?

A mole is a unit of measurement used in Chemistry. One mole contains exactly 6.022 x 10^23 particles (atoms, molecules, or ions). It is the link between the mass of a substance you can weigh and the number of particles it contains.

Q: How do you calculate moles from mass?

Use the formula: moles = mass / Mr. Divide the mass of the substance (in grams) by its relative formula mass (Mr). For example, 10 g of NaOH (Mr = 40): moles = 10 / 40 = 0.25 mol.

Q: How do you calculate moles from concentration and volume?

Use the formula: moles = concentration x volume. The concentration must be in mol/dm3 and the volume must be in dm3. If the volume is in cm3, divide by 1000 first. For example, 25 cm3 of 0.1 mol/dm3 HCl: moles = 0.1 x 0.025 = 0.0025 mol.

Q: What is the molar gas volume?

At room temperature and pressure (RTP, 25 degrees C and 1 atm), one mole of any gas occupies 24 dm3 (24,000 cm3). This is the molar gas volume. Use the formula: moles = volume of gas / 24 (if volume is in dm3) or moles = volume of gas / 24000 (if volume is in cm3).

Key Takeaways

There are three mole formulas to learn. Moles from mass, moles from concentration and volume, and moles from gas volume.
Always check your units before substituting. Mass in grams, volume in dm³ (not cm³), concentration in mol/dm³.
The triangle method works. Cover the value you want to find. What remains tells you whether to multiply or divide.
Show every step in exams. Write the formula, substitute, and calculate. Examiners give method marks even if the final answer is wrong.

What is a mole?

A mole is the chemist's counting unit. Just like a "dozen" means 12, a "mole" means 6.022 × 10²³. This number is called Avogadro's constant.

Why such a strange number? Because atoms are incredibly small. If you weighed out exactly 12 g of carbon-12 atoms and counted them, you would have 6.022 × 10²³ atoms. That mass (12 g) is its relative atomic mass in grams, which equals one mole.

The mole is the bridge between the atomic scale (too small to see) and the lab scale (grams you can weigh). Every quantitative Chemistry calculation at GCSE and IB uses moles as the central unit.

Formula 1: Moles from mass

moles = mass (g) ÷ M_r

This is the most common mole formula. You use it whenever you are given a mass in grams and need to convert it to moles.

mass must be in grams (g)
M_r is the relative formula mass. Add up the A_r values of every atom in the formula.

You can rearrange this to find mass or M_r:

mass = moles × M_r
M_r = mass ÷ moles

Example: Moles from mass

Question: Calculate the number of moles in 5.85 g of sodium chloride (NaCl). A_r: Na = 23, Cl = 35.5

Step 1:Calculate M_r of NaCl: 23 + 35.5 = 58.5

Step 2:moles = mass ÷ M_r

Step 3:moles = 5.85 ÷ 58.5

moles = 0.100 mol

Formula 2: Moles from concentration and volume

moles = concentration (mol/dm³) × volume (dm³)

This formula is used whenever you are working with solutions. It connects the concentration of a solution to the number of moles dissolved in it.

Unit Trap

The volume must be in dm³, not cm³. To convert: divide cm³ by 1000. For example, 25.0 cm³ = 0.0250 dm³. This is the single most common mistake students make in titration and concentration questions.

Example: Moles from concentration

Question: Calculate the moles of HCl in 25.0 cm³ of 0.100 mol/dm³ hydrochloric acid.

Step 1:Convert volume: 25.0 cm³ ÷ 1000 = 0.0250 dm³

Step 2:moles = concentration × volume

Step 3:moles = 0.100 × 0.0250

moles = 0.00250 mol (2.50 × 10^-3 mol)

For multi-step titration problems, our Titration Calculator handles the full calculation with step-by-step working.

Formula 3: Moles from gas volume (at RTP)

moles = volume of gas (dm³) ÷ 24

At room temperature and pressure (RTP, approximately 25 °C and 1 atm), one mole of any gas occupies 24 dm³ (or 24,000 cm³). This is the molar gas volume.

If the volume is given in cm³, use: moles = volume ÷ 24,000

Example: Moles from gas volume

Question: A student collects 120 cm³ of hydrogen gas at RTP. Calculate the number of moles.

Step 1:moles = volume ÷ 24,000

Step 2:moles = 120 ÷ 24,000

moles = 0.00500 mol (5.00 × 10^-3 mol)

For IB students: the molar gas volume at STP (0 °C and 100 kPa) is 22.7 dm³. Use the value given in Section 2 of the IB Data Booklet.

Common mistakes

The 5 mistakes that cost marks

Forgetting to convert cm³ to dm³. Always divide by 1000. If your answer is 1000 times too big or small, this is probably why.
Using the wrong M_r. Double-check the formula. H₂SO₄ has an M_r of 98, not 97. Count every atom carefully.
Mixing up moles and mass. Moles is a count (like "dozen"). Mass is in grams. They are not the same thing.
Not showing the formula before substituting. "moles = mass / Mr" earns you a method mark even if you get the arithmetic wrong.
Using 24,000 when the volume is already in dm³. If the gas volume is 2.4 dm³, divide by 24 (not 24,000). Match the unit to the formula.

More worked examples

Example: Finding mass from moles

Question: What mass of calcium carbonate (CaCO₃) contains 0.35 mol? A_r: Ca = 40, C = 12, O = 16

Step 1:M_r of CaCO₃ = 40 + 12 + (3 × 16) = 100

Step 2:mass = moles × M_r

Step 3:mass = 0.35 × 100

mass = 35.0 g

Example: Finding concentration

Question: 0.040 mol of NaOH is dissolved in 500 cm³ of water. What is the concentration?

Step 1:Convert volume: 500 cm³ ÷ 1000 = 0.500 dm³

Step 2:concentration = moles ÷ volume

Step 3:concentration = 0.040 ÷ 0.500

concentration = 0.080 mol/dm³

Want to check your answers? Our Moles Calculator solves all three formulas with full working shown.

Exam tips for mole calculations

How to get full marks

Write the formula first. Even before you substitute numbers. This earns a method mark.
Show your unit conversion. Write "25.0 cm³ ÷ 1000 = 0.0250 dm³" on a separate line. Examiners want to see this.
Include units in your final answer. "0.25 mol" is better than "0.25".
Use appropriate significant figures. Give your answer to the same number of significant figures as the data in the question (usually 3 s.f.).
Sense-check your answer. If you calculate 500 moles from a 5 g sample, something has gone wrong. Moles are usually small decimal numbers at GCSE level.

For full Topic 3 coverage including moles, concentration, and yield, see our AQA Topic 3: Quantitative Chemistry notes.

Frequently Asked Questions

What is a mole in Chemistry?

A mole is a unit of measurement. One mole = 6.022 × 10²³ particles. It lets you convert between the mass of a substance (which you can weigh on a balance) and the number of atoms, molecules, or ions it contains. It is the central unit in all quantitative Chemistry.

How do you calculate moles from mass?

Divide the mass (in grams) by the relative formula mass (M_r): moles = mass ÷ M_r. For example, 4.0 g of NaOH (M_r = 40) = 4.0 ÷ 40 = 0.10 mol.

How do you calculate moles from concentration and volume?

Multiply the concentration (in mol/dm³) by the volume (in dm³): moles = C × V. If the volume is in cm³, divide by 1000 first. For example, 50.0 cm³ of 0.20 mol/dm³ HCl: moles = 0.20 × 0.050 = 0.010 mol.

What is the molar gas volume?

At room temperature and pressure (RTP), one mole of any gas occupies 24 dm³ (24,000 cm³). At STP (0 °C, 100 kPa), it is 22.7 dm³. You can use this to convert gas volumes to moles: moles = volume ÷ molar gas volume.

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How to Calculate Moles: The 3 Formulas Every Chemistry Student Needs