Less common C4.2

The Mole and Avogadros Number

Avogadro's number is a fundamental constant in chemistry that provides the exact number of particles in one mole of any substance, acting as a bridge between the atomic scale and the macroscopic quantities used in calculations.

Part of the ESAT Chemistry syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.

Key points

  • One mole (mol) of any substance contains exactly the same number of particles.
  • This specific number is called Avogadro's number (or Avogadro's constant, NA).
  • The value of Avogadro's number is approximately 6.02 x 1023 particles per mole.
  • The term 'particles' can refer to atoms, molecules, ions, or electrons, depending on the substance.
  • The amount of substance, measured in moles, is different from the mass of the substance, measured in grams.

Formulae

Number of particles = moles × NA

Use this to convert between the amount of substance in moles and the actual number of individual particles (atoms, molecules, etc.).

Definitions

Mole (mol)
The SI unit for the amount of a substance. It represents a specific quantity of 6.02 x 1023 elementary entities (e.g., atoms or molecules).
Avogadro's Number (N_A)
The number of constituent particles (usually atoms or molecules) that are contained in one mole of a substance. It is a constant with a value of approximately 6.02 x 1023 mol-1.

Worked example

A sample of methane (CH4) gas contains 1.204 x 1024 molecules. How many moles of methane are in the sample? (Use Avogadro's number, NA = 6.02 x 1023 mol-1)

  1. 1

    Identify the formula relating moles, particles, and Avogadro's number:

    Number of particles = moles × NA.

  2. 2

    Rearrange the formula to find the number of moles:

    moles = Number of particles / NA
  3. 3

    Substitute the given values into the rearranged formula:

    moles = (1.204 x 1024) / (6.02 x 1023)
  4. 4

    Separate the calculation into two parts:

    the numbers and the powers of ten.

  5. 5

    Calculate the powers of ten:

    1024 / 1023 = 10^(24-23) = 101 = 10.

  6. 6

    Calculate the numbers.

    Notice that 1.204 is exactly double 0.602.

    So, 1.204 / 6.02 is equivalent to 12.04 / 60.2, which simplifies to 1/5 or 0.2.

  7. 7

    Combine the two parts:

    moles = 0.2 × 10 = 2

Answer: 2 mol

Common mistakes

  • ×Confusing the number of moles with the number of particles. Remember a mole is a unit for an amount, like a 'dozen', not the final particle count.
  • ×Making errors with standard form arithmetic, particularly when dividing powers of ten. Always subtract the exponent of the denominator from the numerator.
  • ×Forgetting to consider the number of atoms within a molecule. For example, 1 mole of H2O contains 1 mole of oxygen atoms but 2 moles of hydrogen atoms.

No-calculator tips

  • ✓Exam questions will use numbers that simplify easily. Look for simple ratios like 3.01/6.02 (which is 1/2) or 1.204/6.02 (which is 1/5 or 0.2).
  • ✓Handle the powers of 10 separately from the leading numbers to avoid confusion. Combine them only at the final step.
  • ✓Do a quick sense-check of your answer. If the number of particles is greater than Avogadro's number, you must have more than one mole.

Read this topic in the official UAT-UK ESAT guide →

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