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K223 / K225 / 2027
Chemical Calculations

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Chemical Calculations

Write formulae and equations, then calculate moles, mass and molar mass.

SEC G2 Science K223 / K225 (2027)

01

Read and construct formulae

Subscripts count atoms; ion charges determine ratios.

An element symbol begins with a capital letter; a second letter is lower-case. Co is cobalt, while CO is carbon monoxide. In H2SO4, one formula unit contains 2 H, 1 S and 4 O atoms. Brackets multiply everything inside: Ca(OH)2 contains 1 Ca, 2 O and 2 H. A coefficient multiplies the entire formula: 3H2O represents six H atoms and three O atoms.

Worked exampleFrom atom counts to a formula

A model molecule contains two nitrogen atoms and four oxygen atoms. What is its formula, and how many oxygen atoms are in three molecules?

Try it first. Then show the worked stepsHide the worked steps
  1. Write N and O with the atom counts as subscripts: N2O4.
  2. Three molecules contain 3 x 4 = 12 oxygen atoms. Do not simplify N2O4 to NO2 when the actual atoms in one molecule are specified.
Answer

N2O4; 12 oxygen atoms in three molecules. A coefficient counts complete molecules; a subscript counts atoms within one.

A working symbol and formula bank
FamilySymbols or formulae
Common non-metalsH, C, N, O, F, P, S, Cl, Br, I; elemental gases H2, N2, O2, Cl2
Metals and other elementsLi, Na, K, Mg, Ca, Al, Zn, Fe, Cu, Ag, Pb; Si, He, Ne, Ar
Acids, alkalis and gasesHCl, HNO3, H2SO4, NaOH, Ca(OH)2, NH3, CO, CO2, SO2, NO, NO2, O3
Common salts and reagentsNaCl, MgCl2, CaCO3, CuSO4, AgNO3, Ba(NO3)2, KI, KMnO4
Oxides and organic examplesCaO, MgO, CuO, SiO2; CH4, C2H4, C2H5OH, CH3COOH

An ionic formula must have zero total charge. Al3+ and O2- balance at +6 and -6, giving Al2O3. Mg2+ and NO3- give Mg(NO3)2. Keep a polyatomic ion intact; use brackets only when more than one is needed.

Frequently used ion charges
Positive ionsNegative ions
Na+, K+, Ag+, NH4+Cl-, Br-, I-, OH-, NO3-
Mg2+, Ca2+, Zn2+, Cu2+, Fe2+, Pb2+O2-, CO32-, SO42-
Al3+, Fe3+A Roman numeral gives a metal ion oxidation state; distinguish iron(II) from iron(III).

Check your understanding

A compound has the formula XCl3, and each chloride ion is Cl-. What is the charge on X?

  1. 3+, because three Cl- ions give -3 and the compound is neutral
  2. 3-, because the subscript 3 is the charge on the X ion
  3. 1+, because a metal ion in a chloride is like Na+ in NaCl
Show the answer

3+, because three Cl- ions give -3 and the compound is neutral

Charges in an ionic compound add up to zero. Three Cl- ions contribute -3, so the one X ion must be X3+.

02

Balance atoms, then account for ions

A reaction changes arrangement, not the total number of atoms.

Write correct formulae first, then change coefficients until each element has the same atom count on both sides. Never alter a subscript to balance an equation. State symbols distinguish solid (s), liquid (l), gas (g) and aqueous solution (aq). Aqueous means dissolved in water, not simply liquid.

Worked exampleBalance combustion

Write the complete combustion of propane.

Try it first. Then show the worked stepsHide the worked steps
  1. Start C3H8(g) + O2(g) -> CO2(g) + H2O(l).
  2. Balance carbon: 3CO2. Balance hydrogen: 4H2O.
  3. Products contain ten O atoms, requiring 5O2.
Answer

C3H8(g) + 5O2(g) -> 3CO2(g) + 4H2O(l). Water is shown after cooling; in hot exhaust it is vapour.

An ionic equation removes spectator ions that remain unchanged in solution. Split dissolved ionic compounds into ions; keep solids, gases, water and undissociated molecular substances intact. Cancel identical ions on both sides and check both atoms and total charge.

Worked exampleFind the reacting ions

Aqueous silver nitrate reacts with aqueous sodium chloride.

Try it first. Then show the worked stepsHide the worked steps
  1. AgNO3(aq) + NaCl(aq) -> AgCl(s) + NaNO3(aq).
  2. Dissolved reactants provide Ag+, NO3-, Na+ and Cl-.
  3. Na+ and NO3- remain dissolved: cancel them.
Answer

Ag+(aq) + Cl-(aq) -> AgCl(s). Total charge is zero on both sides.

Check your understanding

To balance the formation of magnesium oxide, a student writes Mg + O2 -> MgO2. Is this acceptable?

  1. Yes. Both sides now have one magnesium atom and two oxygen atoms.
  2. No. It changes the formula of the product; write 2Mg + O2 -> 2MgO.
  3. No. Oxygen should be written as O, so the equation is Mg + O -> MgO.
Show the answer

No. It changes the formula of the product; write 2Mg + O2 -> 2MgO.

Balance by changing the numbers in front of formulae, never the subscripts. Magnesium oxide is MgO (Mg2+ and O2-), so the equation is 2Mg(s) + O2(g) -> 2MgO(s).

Check your understanding

Aqueous barium chloride is added to aqueous sodium sulfate, and a white precipitate forms. Which is the ionic equation?

  1. Na+(aq) + Cl-(aq) -> NaCl(s)
  2. Ba2+(aq) + SO42-(aq) -> BaSO4(s)
  3. BaCl2(aq) + Na2SO4(aq) -> BaSO4(s)
Show the answer

Ba2+(aq) + SO42-(aq) -> BaSO4(s)

Write only the ions that form the precipitate. Na+ and Cl- stay in solution unchanged, so they are spectator ions. The charges balance (2+ and 2- give 0).

03

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.

Quick revision

Revisit the essentials, then return to an explanation when you need it.

Exam definitions: learn these in mark-scheme words
TermDefinition to write
Relative atomic mass, ArThe average mass of one atom of an element (taking its isotopes into account), compared with 1/12 of the mass of one atom of carbon-12.
Relative molecular mass, MrThe average mass of one molecule of a substance, compared with 1/12 of the mass of one atom of carbon-12. It is the sum of the relative atomic masses of the atoms in the formula.
Calculation route
  1. Formula

    Write the correct formula, using ion charges for ionic compounds.

  2. Equation

    Balance atoms with coefficients, never by changing subscripts, and add state symbols.

  3. Relative mass

    Add the Ar values, counting every atom inside brackets.

  4. Moles

    n = m / M, m = n x M or M = m / n, with mass in g and M in g mol-1.

Scope

Learning outcomes

4. Chemical Calculations (K223 / K225). Use the outcome map to find the explanation for a particular syllabus requirement.

See the learning outcome map

  1. 4.1(a) Use chemical symbols and formulae

    • Element symbols
    • Formulae of named syllabus compounds

    Read and construct formulae

  2. 4.1(b) Translate atom counts and formulae

    • Subscripts, brackets and coefficients
    • Reverse interpretation

    Read and construct formulae

  3. 4.1(c) Balance ion charges to obtain formulae

    • Simple and polyatomic ions
    • Deduce ion charge from formula

    Read and construct formulae

  4. 4.1(d) Interpret equations and states

    • s, l, g and aq
    • Coefficients as mole ratios

    Balance atoms, then account for ions

  5. 4.1(e) Construct balanced equations

    • Full equations with states
    • Ionic equations and spectators
    • Conserve atoms and charge

    Balance atoms, then account for ions

  6. 4.2(a) Define relative atomic mass

    • Carbon-12 comparison
    • Average atomic mass

    The mole is a counting unit

  7. 4.2(b) Define and calculate relative molecular/formula mass

    • Sum relative atomic masses
    • Molecular versus ionic terminology

    The mole is a counting unit

  8. 4.2(c) Calculate amount, mass and molar mass

    • n = m / M, rearranged as needed
    • Molar mass equals the relative mass in g/mol
    • Reacting masses and gas volumes not required

    The mole is a counting unit