Skip to notes
wise otter.Chemistry
Contents
K223 / K225 / 2027
Chemical Calculations

Topic 3 of 3

The mole is a counting unit

Connect microscopic particles to measurable mass.

SEC G2 Science K223 / K225 (2027)

The mole is a counting unit

Connect microscopic particles to measurable mass.

Relative atomic mass, Ar, compares the average mass of an atom with one twelfth of the mass of a carbon-12 atom. Relative molecular mass, Mr, makes the same comparison for a molecule. Add the Ar values in its formula. For an ionic compound, call this relative formula mass instead. These relative masses have no units.

A mole is a fixed number of particles, so chemists can count particles by weighing them. The mass of one mole of a substance is its molar mass, M, in g mol-1. It has the same number as the relative atomic, molecular or formula mass: Ar(C) = 12, so one mole of carbon atoms has a mass of 12 g; Mr(H2O) = 18, so one mole of water molecules has a mass of 18 g. Always say which particles you are counting: atoms, molecules or formula units.

One relationship, three arrangements
  1. Find the amount

    n = m / M. Mass in g divided by molar mass in g mol-1 gives moles.

  2. Find the mass

    m = n x M. Moles multiplied by molar mass gives grams.

  3. Find the molar mass

    M = m / n. Compare the answer with Mr values to suggest what the substance is.

Worked example

Account for brackets in a formula

Find the relative formula mass of Ca(OH)2 and the amount in 3.70 g. Use Ca = 40, O = 16, H = 1.

  1. Mr = 40 + 2(16 + 1) = 74.
  2. Molar mass = 74 g mol-1.
  3. n = 3.70/74 = 0.0500 mol.
Answer

0.0500 mol of Ca(OH)2 formula units; if fully dissolved, this produces 0.100 mol of OH- ions.

Worked example

From moles to mass

What is the mass of 0.25 mol of carbon dioxide, CO2? Use C = 12, O = 16.

  1. Mr(CO2) = 12 + 2(16) = 44, so M = 44 g mol-1.
  2. m = n x M = 0.25 x 44 = 11 g.
Answer

11 g. Check the size: a quarter of a mole should have a quarter of the mass of one mole, and 44 / 4 = 11.

Check your understandingHow many moles of oxygen atoms are present in 0.25 mol of O2 molecules?Think it through, then reveal the answer
0.50 mol of oxygen atoms: each molecule contains two atoms. The amount of molecules remains 0.25 mol; always identify the entity being counted.

Worked example

Identify a substance from its molar mass

A 9.0 g sample of a pure substance contains 0.50 mol. Is it water (Mr = 18) or glucose (Mr = 180)?

  1. M = m / n = 9.0 / 0.50 = 18 g mol-1.
  2. Compare with the Mr values: 18 matches water, not glucose.
Answer

Water. The units check too: grams divided by moles gives g mol-1.

Check your understandingHow many moles of sodium hydroxide, NaOH, are in 4.0 g? Use Na = 23, O = 16, H = 1.Think it through, then reveal the answer
Mr = 23 + 16 + 1 = 40, so M = 40 g mol-1 and n = 4.0 / 40 = 0.10 mol of NaOH formula units.