Chemistry › Maths skills
Maths skills for A-level chemistry
At least 20% of the marks in A-level chemistry need maths at the standard of higher-tier GCSE or above. Each skill below says what it asks of you and where the lessons teach it, with a worked example to try.
AQA numbers these skills MS 0.0 to MS 4.3, OCR numbers them M0.0 to M4.3 and Pearson numbers them B.0.0 to B.4.3, and the three lists are the same list, so MS 2.5 is M2.5 and B.2.5. Cambridge sets out its mathematical requirements without numbers on pages 75 and 76 of the 9701 syllabus; they cover the same ground and add the area under a curve, which has its own row.
Five short lessons on the maths itself
The table says where each skill is used. These five teach the move on its own: logs, natural logs, uncertainties, rearranging with units and reading graphs, each with two worked examples and a short set to try.
Logarithms for pH, pKa and Kw
ln and Arrhenius plots
Percentage uncertainty and error propagation
Rearranging equations and units
Graphs: gradients, tangents and intercepts
Every skill the boards number
| Code | Skill | What it asks | Where it is taught |
|---|---|---|---|
| MS 0.0 | Units | Convert between units, such as cm³ to dm³ in a titration, and give the units of Kc or of a rate constant. | Concentration, volumetric solutions and titration calculations: worked example “Sodium hydroxide against hydrochloric acid” Rate equations, orders of reaction and the rate constant: worked example “The units of k for a reaction that is second order overall” |
| MS 0.1 | Standard and ordinary form | Work with numbers such as the Avogadro constant and Kw, and keep the significant figures when converting. | Weak acids, Ka and pKa; Kw and strong bases: worked example “The pH of 0.0500 mol dm⁻³ sodium hydroxide” The mole, the Avogadro constant and molar mass: worked example “Decomposing 5.00 g of calcium carbonate” |
| MS 0.2 | Ratios, fractions and percentages | Use reacting ratios from an equation, and calculate percentage yield and atom economy. | Reacting masses, percentage yield and atom economy: worked example “The yield of an ester” Reacting masses, percentage yield and atom economy: worked example “Three routes to ethanol” Empirical and molecular formulae: worked example “A hydrocarbon from its masses” |
| MS 0.3 | Estimating results | Judge the effect of changing a condition on a value, such as how Kc moves with temperature. | The equilibrium constant Kc, in the text rather than a worked example |
| MS 0.4 | Powers, exponentials and logs on a calculator | Use the calculator’s power and log keys for moles, pH and pKa, and approximate sensibly in buffer calculations. | Buffer solutions and buffer calculations: worked example “The pH of an ethanoate buffer” |
| MS 1.1 | Significant figures | Give an answer to no more significant figures than the least precise measurement behind it. | Measurement, uncertainty and significant figures in chemistry, in the text rather than a worked example |
| MS 1.2 | Means, including mean bond enthalpies | Find a weighted mean, such as Ar from isotopic abundances, choose concordant titres for a mean titre, and use mean bond enthalpies. | Time-of-flight mass spectrometry and relative atomic mass: worked example “The relative atomic mass of magnesium” Measurement, uncertainty and significant figures in chemistry: worked example “Choosing the titres for a mean” Mean bond enthalpies: worked example “The mean C–H bond enthalpy in methane” |
| MS 1.3 | Uncertainty and percentage uncertainty | Find the uncertainty in a value made from two readings, such as a titre, and express it as a percentage. | Measurement, uncertainty and significant figures in chemistry: worked example “Two percentage uncertainties” Measurement, uncertainty and significant figures in chemistry: worked example “The uncertainty in a titration result” |
| MS 2.1 | Symbols | Read and use =, <, <<, >>, >, ∝, ~ and the equilibrium sign. | No lesson teaches this on its own; the symbols are used throughout. See Measurement, uncertainty and significant figures in chemistry for the general skills. |
| MS 2.2 | Changing the subject | Rearrange an equation, such as a rate equation to find k, or pV = nRT to find a molar mass. | Gases and the ideal gas equation: worked example “Mr of a volatile liquid” Rate equations, orders of reaction and the rate constant: worked example “The rate constant, then the rate with two concentrations changed” |
| MS 2.3 | Substituting with units | Put values into an equation in consistent units, as in mole calculations and finding Kc. | Gases and the ideal gas equation: worked example “The volume of a quarter of a mole” The equilibrium constant Kc: worked example “Kc for esterification from the starting amounts” Concentration, volumetric solutions and titration calculations: worked example “A standard solution used to find an acid” |
| MS 2.4 | Solving equations | Solve for the unknown in a Hess’s law cycle or a bond enthalpy calculation. | Hess's law and enthalpy cycles: worked example “Reducing iron(III) oxide in the blast furnace” Mean bond enthalpies: worked example “The C=C bond enthalpy from the hydrogenation of ethene” |
| MS 2.5 | Logarithms: pH and pKa | Use log₁₀ for quantities that range over many powers of ten, in pH and pKa. | Brønsted–Lowry acids and bases, pH and strong acids: worked example “pH and [H⁺] for a strong acid” Weak acids, Ka and pKa; Kw and strong bases: worked example “Ka of an unknown acid from its pH” |
| MS 2.5 | Natural logs: ln and the Arrhenius plot | Use ln k and ln 2 in the Arrhenius equation and in first-order half-lives. | The Arrhenius equation and the rate-determining step: worked example “Ea from two rate constants, then a prediction” Finding orders from initial rates, half-lives and graphs: worked example “The rate constant from the half-life of a first-order decay” |
| MS 3.1 | Between graphs, numbers and equations | Read spectra, find an order from a graph and write a rate expression from one. | Rate equations, orders of reaction and the rate constant: worked example “Second order and k from a plot of rate against [A]²” Proton and carbon-13 NMR spectroscopy: worked example “Ethyl ethanoate from its spectra” |
| MS 3.2 | Plotting data | Plot two variables from results and draw a line or curve of best fit. | Measuring the rate of a reaction: worked example “1/t against temperature from the results” |
| MS 3.3 | Gradient and intercept of a straight line | Find the slope and intercept of a linear graph, as in ln k against 1/T. | The Arrhenius equation and the rate-determining step: worked example “Ea and A from the gradient of the graph” |
| MS 3.4 | Rate of change from a straight line | Find a rate as the gradient of a straight-line graph, such as a zero-order concentration–time graph. | Collision theory, activation energy and the rate of reaction: worked example “A mean rate from mass loss” |
| MS 3.5 | Tangents to a curve | Draw a tangent and use its gradient as the rate at that moment, as in the initial-rates method. | Collision theory, activation energy and the rate of reaction: worked example “The initial rate from a tangent” |
| Cambridge | Area under a curve | Understand an area that has a meaning, such as the area under a Boltzmann distribution or a gas chromatography peak. | The Maxwell–Boltzmann distribution, temperature and catalysts: worked example “Sketching the distribution at two temperatures, mark by mark” Chromatography: TLC, column and gas: worked example “Percentage composition from peak areas” |
| MS 4.1 | Angles and shapes in 3D | Predict the shapes of molecules and ions and their bond angles, with and without lone pairs. | Shapes of molecules and ions: worked example “The shape of SF₄” |
| MS 4.2 | 2D drawings of 3D molecules | Draw isomers and find chiral centres from a 2D or 3D drawing. | Optical isomerism: worked example “Finding the chiral centres in 2-hydroxypropanoic acid” Structural isomerism and E/Z isomerism: worked example “Assigning E or Z to 2-chloropent-2-ene” |
| MS 4.3 | Symmetry | Describe the stereoisomerism of molecules and complexes, and spot chiral centres. | Optical isomerism: worked example “Reading a partly racemised product” Ligands, the shapes of complexes, isomerism and ligand substitution: worked example “Why cis and not trans” |
The general skills of measurement, significant figures and uncertainty are gathered in Measurement, uncertainty and significant figures in chemistry. The data sheet page lists the equations these skills are used on.