Sometimes tested C4.3

Moles and Mass Conversions

This topic covers the fundamental chemical concept of the mole, which relates the measurable mass of a substance to the amount of it present. Mastering the conversion between mass (in g, kg, or tonnes) and moles is essential for almost all quantitative chemistry problems.

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

  • The 'amount' of a substance in chemistry is measured in moles (mol).
  • One mole of an element has a mass in grams that is numerically equal to its relative atomic mass (Ar).
  • One mole of a compound has a mass in grams that is numerically equal to its relative formula mass (Mr).
  • This mass of one mole is called the Molar Mass (M) and has units of grams per mole (g/mol).
  • Before any calculation, you must convert all masses into grams to match the units of molar mass.
  • Remember the key conversions: 1 tonne = 1000 kg, and 1 kg = 1000 g.

Formulae

Amount (mol) = Mass (g) / Molar Mass (g/mol)

Use this to calculate the number of moles when you know the mass of a substance and its chemical formula (to find Mr).

Mass (g) = Amount (mol) × Molar Mass (g/mol)

Use this rearranged version to find the mass of a substance required to provide a specific number of moles.

Definitions

Mole (mol)
The standard unit for the amount of a substance. It represents a specific number of particles (approx. 6.022 x 1023), and its mass in grams corresponds to the Ar or Mr of the substance.
Molar Mass (M)
The mass of exactly one mole of a substance, expressed in grams per mole (g/mol). Its value is numerically the same as the substance's Ar or Mr.

Worked example

What is the mass, in kilograms, of 500 mol of sulfur dioxide (SO2)? [Ar values: S = 32; O = 16]

  1. 1

    Step 1:

    Calculate the relative molecular mass (Mr) of SO2.

  2. 2
    Mr(SO2) = Ar(S) + 2 × Ar(O) = 32 + 2 × 16 = 32 + 32 = 64
  3. 3

    Step 2:

    State the molar mass (M).

  4. 4

    The Molar Mass of SO2 is 64 g/mol.

  5. 5

    Step 3:

    Use the formula to calculate the mass in grams.

  6. 6
    Mass (g) = Amount (mol) × Molar Mass (g/mol) = 500 × 64
  7. 7

    Step 4:

    Perform the multiplication.

  8. 8
    5 × 64 = 320

    So, 500 × 64 = 32000 g.

  9. 9

    Step 5:

    Convert the mass from grams to the required unit, kilograms.

  10. 10

    There are 1000 g in 1 kg, so divide by 1000.

    32000 g / 1000 = 32 kg.

Answer: 32 kg

Common mistakes

  • ×The most common mistake is failing to convert units. The molar mass formula requires mass in grams (g), so you must convert from kilograms (kg) or tonnes (t) before calculating moles.
  • ×Forgetting that common elemental gases are diatomic (e.g., O2, N2, H2). For oxygen gas, you must use the Mr of O2 (32), not the Ar of a single O atom (16).

No-calculator tips

  • ✓To manage large numbers from unit conversions (e.g., tonnes to grams), use standard form. For example, 2.7 tonnes is 2.7 x 103 kg, which is 2.7 x 106 g.
  • ✓When multiplying, handle the non-zero digits first, then add the zeros back. For 500 × 64, calculate 5 × 64 = 320, then add the two zeros from 500 to get 32000.
  • ✓When dividing, look for common factors to simplify the fraction. For example, to calculate moles in 880 g of CO2 (Mr=44), the calculation is 880/44. This simplifies to 88/4.4, or just (88/44) × 10 = 2 × 10 = 20 mol.

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

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