Chemical calculations
Formulae, balanced and ionic equations, the mole, concentration, limiting reactants, and percentage yield and purity for G3 Pure and O-Level Chemistry.
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Before you begin
Chemical calculations turn a balanced equation into real amounts: how many grams to weigh, what volume of gas to expect, what concentration a solution has. The lessons start with formulae and equations, introduce the mole as the link between mass and number of particles, and then use it for formulae, gas volumes, solutions, limiting reactants, and yield and purity. Each calculation reuses the conversions before it.
Be comfortable with: elements, compounds and mixtures, atoms and the unit conversions in measurement and experimental techniques.
Learning goals
- State the symbols of the elements and the formulae of the compounds in the syllabus
- Deduce a compound's formula from the relative numbers of its atoms, and the reverse
- Deduce the formula of an ionic compound from the charges on its ions, and the reverse
- Interpret chemical equations that include state symbols
- Construct chemical and ionic equations with state symbols
- Define relative atomic mass, Aᵣ
- Define relative molecular mass, Mᵣ, and calculate Mᵣ and relative formula mass by adding relative atomic masses
- Define the mole using the Avogadro constant
- Calculate the percentage by mass of an element in a compound
- Calculate empirical and molecular formulae from data
- Calculate reacting masses and gas volumes, including with a limiting reactant, taking one mole of gas as 24 dm³ at room temperature and pressure
- Use solution concentrations in mol/dm³ or g/dm³ to process titration results and solve problems
- Calculate percentage yield and percentage purity
Syllabus statements covered
- state the symbols of the elements and formulae of the compounds mentioned in the syllabus
- deduce the formulae of simple compounds from the relative numbers of atoms present and vice versa
- deduce the formulae of ionic compounds from the charges on the ions present and vice versa
- interpret chemical equations with state symbols
- construct chemical equations, with state symbols, including ionic equations.
- define relative atomic mass, Ar
- define relative molecular mass, Mr, and calculate relative molecular mass (and relative formula mass) as the sum of relative atomic masses
- define the term mole in terms of the Avogadro constant
- calculate the percentage mass of an element in a compound when given appropriate information
- calculate empirical and molecular formulae from relevant data
- calculate stoichiometric reacting masses and volumes of gases (one mole of gas occupies 24 dm3 at room temperature and pressure); calculations involving the idea of limiting reactants may be set (knowledge of the gas laws and the calculations of gaseous volumes at different temperatures and pressures are not required)
- apply the concept of solution concentration (in mol/dm3 or g/dm3) to process the results of volumetric experiments (e.g. titration) and to solve simple problems (appropriate guidance will be provided where unfamiliar reactions are involved)
- calculate % yield and % purity.
Lessons
Work through them in order.
Symbols and equations
- Writing chemical symbols and formulaeWrite ionic formulae by balancing ion charges, and name compounds with Roman numerals.
- Writing and balancing chemical equationsBalance equations by changing coefficients, never subscripts, and add state symbols.
- Writing ionic equationsWrite ionic equations by cancelling spectator ions and checking atoms and charge.
Amounts and formulae
- Relative atomic, molecular and formula massDefine relative atomic and molecular mass, and calculate Mᵣ from a formula.
- Moles, molar mass and particle countsConvert between mass, moles and numbers of particles using molar mass and the Avogadro constant.
- Percentage composition by massCalculate the percentage by mass of an element in a compound, and work backwards from it.
- Finding empirical and molecular formulaeWork out empirical and molecular formulae from masses, percentages and Mᵣ.
Reaction calculations
- Gas volumes and reacting amountsConvert gas volumes at RTP to moles and calculate reacting masses and gas volumes.
- Solution concentration and titration calculationsCalculate concentrations, the effect of dilution and unknown concentrations from titrations.
- Limiting reactants and excess left overFind the limiting reactant, the most product it allows and the excess left over.
- Percentage yield: actual versus theoreticalCalculate percentage yield from the theoretical yield, and explain yields below or above 100%.
- Percentage purity: finding the pure partFind the pure part of a sample from titration or gas results and calculate percentage purity.
Practise and check
Or choose
Topic reference
Quick reference
| Quantity | Equation | Unit |
|---|---|---|
| amount from mass | n = m/M | mol |
| number of particles | N = nNA, with NA = 6.02 × 10²³ mol⁻¹ | (a count) |
| amount of gas at RTP | n = V/(24 dm³ mol⁻¹) | mol |
| concentration | c = n/V, so n = cV | mol dm⁻³ |
| concentration by mass | (mass of solute)/V | g dm⁻³ |
| percentage by mass | (number of atoms × Aᵣ)/Mᵣ × 100% | % |
| percentage yield | (actual yield)/(theoretical yield) × 100% | % |
| percentage purity | (mass of pure substance)/(mass of sample) × 100% | % |
1 dm³ = 1000 cm³, so the molar volume at RTP is also 24 000 cm³ mol⁻¹.
Core knowledge to remember
- Relative atomic mass, Aᵣ: the average mass of one atom of an element compared with 1/12 of the mass of one carbon-12 atom.
- Relative molecular mass, Mᵣ: the average mass of one molecule compared with 1/12 of the mass of one carbon-12 atom; the sum of the relative atomic masses in the formula. For ionic compounds the same sum is the relative formula mass.
- Mole: one mole of a substance contains the Avogadro constant, 6.02 × 10²³, of particles of that substance.
- Molar mass: the mass of one mole of a substance, numerically equal to its Aᵣ or Mᵣ, in g mol⁻¹.
- Empirical formula: the simplest whole-number ratio of atoms in a compound. Molecular formula: the actual number of atoms in one molecule.
- One mole of any gas occupies 24 dm³ at room temperature and pressure.
- A balanced equation gives the ratio of the amounts in moles that react, so every reacting-quantity calculation goes through moles.
- The limiting reactant is used up first and decides the theoretical yield; the other reactant is in excess.
Common mistakes
- Comparing masses or volumes of different substances directly instead of converting to moles.
- Leaving out the mole ratio from the balanced equation, or using an unbalanced equation.
- Using a volume in cm³ with 24 dm³ mol⁻¹ or with a concentration in mol dm⁻³.
- Using the gas molar volume for a solid or a solution.
- Deciding the limiting reactant from the smaller mass or amount without dividing by the coefficients.
- Confusing yield (product compared with the maximum) with purity (pure part compared with the whole sample).
- Rounding intermediate values; keep them unrounded until the final answer.