The mole, the Avogadro constant and concentration
Chemists count particles in moles, because individual atoms are far too small and numerous to count. Three short equations link moles to mass, to the number of particles, and to concentration.
Part 1 of 3: Learn it
In short
- n = m ÷ Mr (mass in g).
- Number of particles = n × L, with L = 6.022 × 10²³ mol⁻¹.
- c = n ÷ V, with V in dm³; divide cm³ by 1000 first.
Where this is in your specification
Spec points: AQA 7405 3.1.2.1 and 3.1.2.2, OCR A H432 2.1.3, Edexcel 9CH0 Topic 5
| Board | Topic: Atomic structure and amount of substance |
|---|---|
| AQA 7405 | 3.1.1 and 3.1.2 |
| Edexcel 9CH0 | Topics 1 and 5 |
| OCR H432 | 2.1.1 to 2.1.3, 2.2.1 and 3.1.1 |
| Higher C813 76 | 1(a) Periodicity; 3(a) Getting the most from reactants |
The mole
One mole of a substance contains 6.022 × 10²³ particles (the Avogadro constant, L or Nₐ). The mass of one mole in grams equals the substance's Mᵣ, which is why n = m ÷ Mᵣ works. Always say which particle you mean: one mole of O₂ molecules contains two moles of O atoms.
Concentration
Concentration is in mol dm⁻³ when V is in dm³ (1 dm³ = 1000 cm³). To change to g dm⁻³, multiply by Mᵣ.
Significant figures
Give answers to the same number of significant figures as the least precise data in the question, and keep full values on your calculator until the final step.
What is the mass of 0.200 mol of CaCO₃ (Mᵣ = 100.1)?
Show the answer
0.200 × 100.1 = 20.0 g.
Part 2 of 3: See it worked
Worked examples
Example 1
How many moles are in 4.90 g of sulfuric acid, H₂SO₄ (Mᵣ = 98.1)?
- n = 4.90 ÷ 98.1
- = 0.04995
Answer: 0.0500 mol (3 s.f.).
Example 2
How many moles of sodium hydroxide are in 25.0 cm³ of a 0.100 mol dm⁻³ solution?
- V = 25.0 ÷ 1000 = 0.0250 dm³
- n = c × V = 0.100 × 0.0250
Answer: 2.50 × 10⁻³ mol.
Example 3
How many water molecules are in 0.25 mol of water?
- N = n × L = 0.25 × 6.022 × 10²³
Answer: 1.5 × 10²³ molecules.
Common mistakes
- Using the volume in cm³ in c = n ÷ V.
- Using Aᵣ instead of Mᵣ for a molecule such as O₂.
- Confusing moles of molecules with moles of atoms.
- Rounding part way through a multi-step calculation.
Convert 0.150 mol dm⁻³ of NaCl (Mᵣ = 58.5) to g dm⁻³.
Show the answer
0.150 × 58.5 = 8.78 g dm⁻³.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
What is the mass of 0.200 mol of CaCO₃ (Mᵣ = 100.1)?
0.200 × 100.1 = 20.0 g.
Convert 0.150 mol dm⁻³ of NaCl (Mᵣ = 58.5) to g dm⁻³.
0.150 × 58.5 = 8.78 g dm⁻³.
How many atoms are in 1 mol of CO₂ molecules?
Each molecule has 3 atoms, so there are 3 mol of atoms: about 1.81 × 10²⁴ atoms in total.
Jobs that use this
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