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1.2.2Physical Chemistry

The Mole and The Avogadro Constant

5 min read 5 parts Lesson 8 of 63

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Section 1 of 5The Mole

1.2.2 The Mole and The Avogadro Constant

The mole lets chemists count huge numbers of particles by weighing.

Definition
  • One mole is the amount of substance containing as many particles as there are atoms in exactly 12 g of carbon-12.
Avogadro constant
  • The number of particles in one mole, 6.02 × 10²³ mol⁻¹.
Particles
  • Moles can refer to atoms, molecules, ions or electrons, so the particle type must always be stated.
Molar mass
  • The mass of one mole of a substance in g mol⁻¹, numerically equal to its Ar or Mr.

Section 2 of 5Key Relationships

Key Relationships
Mass
  • n = m / M links moles, mass in grams and molar mass in g mol⁻¹.
Number of particles
  • N = n × 6.02 × 10²³ gives the number of particles from moles.
Concentration
  • n = c × V with V in dm³ links moles, concentration in mol dm⁻³ and volume.
Volume conversion
  • Divide a volume in cm³ by 1000 to convert to dm³ before using concentration.

Section 3 of 5Method for Calculations

1
Identify what is given and what is asked for, noting the substance involved.
2
Convert the quantity given into moles using the appropriate relationship.
3
Rearrange to find the unknown quantity, keeping track of the particle type.
4
Check that units are consistent, particularly cm³ and dm³.
5
Give the answer to the same number of significant figures as the least precise data.

Section 4 of 5Worked Example

Question

  • 5.30 g of sodium carbonate, Na₂CO₃, is dissolved to make 250 cm³ of solution.
  • Calculate the amount in moles, the concentration, and the number of sodium ions present (Mr = 106.0).

  1. n = m / M = 5.30 / 106.0 = 0.0500 mol.
    What the symbols mean: n = amount of substance (mol) · m = mass (g) · M or Mr = molar mass (g mol−1, numerically equal to Mr)
  2. V = 250 / 1000 = 0.250 dm³, so c = 0.0500 / 0.250 = 0.200 mol dm⁻³.
  3. Each formula unit gives 2 Na⁺, so n(Na⁺) = 0.100 mol.
  4. Number of Na⁺ ions = 0.100 × 6.02 × 10²³ = 6.02 × 10²².

Answer

  • 0.0500 mol;
    • 0.200 mol dm⁻³;
    • 6.02 × 10²² sodium ions.

Section 5 of 5Exam Checklist & Tips

1.2.2 – Key Points for the Exam

  • Mole The amount of substance containing 6.02 × 10²³ particles.
  • Avogadro constant 6.02 × 10²³ particles per mole.
  • Molar mass The mass of one mole of a substance, in g mol⁻¹.
  • Concentration The amount of solute per unit volume, usually in mol dm⁻³.

Common Mistakes

  • Using the mass in kilograms rather than grams with molar mass in g mol⁻¹.
  • Not converting cm³ to dm³ when using concentration.
  • Forgetting to multiply by the number of ions per formula unit when counting ions.
  • Confusing moles of atoms with moles of molecules, such as Cl versus Cl₂.
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