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K223 / K225 / 2027
Chemical Calculations

Full chapter

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 example

From 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?

  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 understandingThe compound is XCl3 and each chloride ion is Cl-. What is the charge on X?Think it through, then reveal the answer
X3+: three chloride ions contribute -3, so one X ion must contribute +3. This is charge balance, not a rule that every metal forms the same charge.
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 example

Balance combustion

Write the complete combustion of propane.

  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 example

Find the reacting ions

Aqueous silver nitrate reacts with aqueous sodium chloride.

  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 understandingCan Mg + O2 -> MgO2 be used to balance formation of magnesium oxide?Think it through, then reveal the answer
No: that changes the product formula. The correct equation is 2Mg(s) + O2(g) -> 2MgO(s).
03

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.

Quick revision

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

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