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K223 / K225 / 2027
Chemical Calculations

Lesson 3 of 3

The mole is a counting unit

Connect microscopic particles to measurable mass.

SEC G2 Science K223 / K225 (2027)

  • I can define relative atomic mass.Syllabus

    Syllabus K223 / K225, 4.2(a). Define relative atomic mass

  • I can define and calculate relative molecular/formula mass.Syllabus

    Syllabus K223 / K225, 4.2(b). Define and calculate relative molecular/formula mass

  • I can calculate amount, mass and molar mass.Syllabus

    Syllabus K223 / K225, 4.2(c). Calculate amount, mass and molar mass

The mole is a counting unit

Connect microscopic particles to measurable mass.

Make a guess. You are not marked.

You weigh out 12 g of carbon and 12 g of magnesium. Use C = 12 and Mg = 24. Which sample contains more atoms?

  1. Both contain the same number of atoms
  2. The 12 g of magnesium, as its atoms are bigger
  3. The 12 g of carbon, as its atoms are lighter
Show the answer

The 12 g of carbon, as its atoms are lighter

Carbon atoms are half as heavy, so 12 g holds 1 mol of carbon atoms but only 0.5 mol of magnesium atoms.

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 exampleAccount 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.

Try it first. Then show the worked stepsHide the worked steps
  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.

Try it step by step

Work it out in steps: Molar mass, then Amount in moles.

  1. Problem 1. Find the amount of sodium carbonate, Na2CO3, in 5.30 g. Use Na = 23, C = 12, O = 16. Give the amount in mol to 3 significant figures.
  2. Problem 2. Find the amount of magnesium sulfate, MgSO4, in 6.00 g. Use Mg = 24, S = 32, O = 16. Give the amount in mol to 3 significant figures.
  3. Problem 3. Find the amount of calcium nitrate, Ca(NO3)2, in 4.10 g. Use Ca = 40, N = 14, O = 16. Give the molar mass in g mol-1 and the amount in mol to 3 significant figures.
Show the answer

Problem 1.

Molar mass: M(Na2CO3) = 2(23) + 12 + 3(16) = 106 g mol-1. Count every atom in the formula: two Na, one C and three O.

Amount in moles: n = m / M = 5.30 / 106 = 0.0500 mol of Na2CO3 formula units.

Problem 2.

Molar mass: M(MgSO4) = 24 + 32 + 4(16) = 120 g mol-1.

Amount in moles: n = m / M = 6.00 / 120 = 0.0500 mol. Write 0.0500, not 0.05, to show 3 significant figures.

Problem 3.

Molar mass: M(Ca(NO3)2) = 40 + 2(14 + 3 x 16) = 40 + 2(62) = 164 g mol-1. The 2 outside the bracket doubles everything inside it.

Amount in moles: n = m / M = 4.10 / 164 = 0.0250 mol of Ca(NO3)2.

Worked exampleFrom moles to mass

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

Try it first. Then show the worked stepsHide the worked steps
  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 understanding

How many moles of oxygen atoms are in 0.25 mol of O2 molecules?

  1. 0.50 mol of oxygen atoms, since each molecule has two
  2. 0.125 mol of oxygen atoms, half the molecules
  3. 0.25 mol of oxygen atoms, the same as the molecules
Show the answer

0.50 mol of oxygen atoms, since each molecule has two

Each O2 molecule holds two O atoms, so 0.25 x 2 = 0.50 mol of atoms. The amount of molecules is still 0.25 mol; always say which particle you are counting.

Worked exampleIdentify 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)?

Try it first. Then show the worked stepsHide the worked steps
  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 understanding

How many moles of sodium hydroxide, NaOH, are in 4.0 g? Use Na = 23, O = 16, H = 1.

  1. 0.17 mol, since Mr = 23 and 4.0 / 23 = 0.17
  2. 0.10 mol, since Mr = 40 and 4.0 / 40 = 0.10
  3. 10 mol, since 40 / 4.0 = 10
Show the answer

0.10 mol, since Mr = 40 and 4.0 / 40 = 0.10

Mr = 23 + 16 + 1 = 40, so the molar mass is 40 g mol-1. Moles = mass / molar mass = 4.0 / 40 = 0.10 mol.