A-Level Chemistry Formula Sheet — Every Equation You Need (AQA 7405)
This is the complete calculation toolkit for AQA A-Level Chemistry (7405), covering both AS and A2. Every formula and equation you need is organised by topic, with a short note on when to use each one — keep it open while you revise, and use it alongside our free A-Level practice tests to check you can actually apply each equation under exam conditions.
Amount of Substance
| Formula / Equation | What it is / When to use it |
|---|
| n = m / Mr | Moles = mass (g) ÷ molar mass. The starting point for almost every calculation. |
| PV = nRT, with R = 8.31 J K−1 mol−1 | Ideal gas equation: P in Pa, V in m3, T in K. Use it to find moles, volume or Mr of a gas. |
| Number of particles = n × 6.02 × 1023 | Convert moles into atoms, molecules or ions using the Avogadro constant. |
| Concentration (mol dm−3) = moles ÷ volume (dm3) | For solutions; remember cm3 ÷ 1000 = dm3. Rearrange to moles = concentration × volume for titrations. |
| Percentage yield = (actual amount ÷ theoretical amount) × 100 | Use moles or masses, as long as both amounts are in the same units. |
| Atom economy = (Mr of desired product ÷ sum of Mr of all reactants) × 100 | Measures how much of the reactants ends up in the useful product; addition reactions score 100%. |
| Empirical formula: divide each mass or % by Ar, then divide every result by the smallest; molecular formula = (Mr ÷ empirical mass) × empirical formula | The standard two-step method for finding a formula from composition data and a measured Mr. |
| Percentage uncertainty = (uncertainty ÷ reading) × 100 | For apparatus errors; if a reading is taken twice (e.g. start and end of a burette), add the two percentage uncertainties together. |
Energetics & Entropy
| Formula / Equation | What it is / When to use it |
|---|
| q = mcΔT | Heat change in calorimetry: m = mass of water/solution (g), c = 4.18 J g−1 K−1, ΔT = temperature change. |
| ΔH = q ÷ n | Enthalpy change per mole from a calorimetry experiment; the sign is negative if the temperature rose (exothermic). |
| Hess cycle (formation route): ΔH = ΣΔfH(products) − ΣΔfH(reactants) | Use when you are given enthalpies of formation; go elements → reactants and elements → products. |
| Hess cycle (combustion route): ΔH = ΣΔcH(reactants) − ΣΔcH(products) | Use with enthalpies of combustion; note this one is reactants minus products, the reverse of the formation route. |
| ΔH = (bonds broken) − (bonds formed) | Mean bond enthalpy route: breaking bonds takes energy in (+), forming bonds releases energy (−). |
| Born–Haber cycle: work around the cycle so ΔfH = atomisation enthalpies + ionisation energies + electron affinities + lattice enthalpy | Any one step (usually lattice enthalpy) can be found from all the others; watch the signs and multiply steps for ions formed per formula unit. |
| ΔS = ΣS(products) − ΣS(reactants) | Entropy change of the reaction from standard entropy values; result is in J K−1 mol−1. |
| ΔG = ΔH − TΔS | Gibbs free energy: a reaction is feasible when ΔG ≤ 0. Convert ΔS to kJ K−1 mol−1 and T to kelvin first. |
| T at the feasibility limit = ΔH ÷ ΔS | Set ΔG = 0 and rearrange; gives the temperature at which a reaction just becomes (or stops being) feasible. |
Kinetics
| Formula / Equation | What it is / When to use it |
|---|
| Rate = k[A]m[B]n | Rate equation: m and n are the orders with respect to each reactant, found only from experimental data. |
| Units of k: rearrange k = rate ÷ ([A]m[B]n) and cancel | Zero order: mol dm−3 s−1; first order: s−1; second order: mol−1 dm3 s−1. |
| First-order reactions have a constant half-life | If successive half-lives are equal, the reaction is first order in that reactant — a quick way to read orders off a graph. |
| k = A e(−Ea/RT) | Arrhenius equation: k rises sharply with temperature because more collisions exceed the activation energy. |
| ln k = ln A − Ea/RT | Straight-line form of the Arrhenius equation, used to plot ln k against 1/T. |
| Gradient of ln k vs 1/T graph = −Ea/R | So Ea = −gradient × R; remember temperatures must be in kelvin. |
| Rate-determining step (RDS) | The slowest step in a mechanism; only species involved in steps up to and including the RDS appear in the rate equation. |
Equilibrium: Kc and Kp
| Formula / Equation | What it is / When to use it |
|---|
| Kc = [products]coefficients ÷ [reactants]coefficients | Equilibrium constant in concentration terms; find its units by substituting mol dm−3 into the expression and cancelling. |
| Mole fraction xi = ni ÷ ntotal | Fraction of the total moles of gas mixture made up by gas i; all mole fractions add up to 1. |
| Partial pressure pi = xi × Ptotal | Each gas contributes a share of the total pressure in proportion to its mole fraction. |
| Kp = (partial pressures of products)coefficients ÷ (partial pressures of reactants)coefficients | Same pattern as Kc but for gas mixtures; find units by cancelling the pressure units (kPa or atm). |
| Temperature changes the value of K | Raising the temperature shifts equilibrium in the endothermic direction, so K increases for endothermic reactions and decreases for exothermic ones. |
| Pressure and catalysts do not change the value of Kp (or Kc) | Pressure can shift the position of equilibrium, and a catalyst speeds up both directions equally, but neither alters K itself. |
Acids, Bases & Buffers
| Formula / Equation | What it is / When to use it |
|---|
| Kw = [H+][OH−] = 1.00 × 10−14 mol2 dm−6 at 298 K | Ionic product of water; use it to find [H+] from [OH−] and to calculate the pH of strong bases. |
| pH = −log10[H+] | And the reverse: [H+] = 10−pH. |
| Strong acid: [H+] = acid concentration | Monoprotic strong acids dissociate completely, so the hydrogen ion concentration equals the acid concentration. |
| Ka = [H+][A−] ÷ [HA] | Acid dissociation constant for a weak acid; the larger Ka, the stronger the weak acid. |
| Weak acid: [H+] ≈ √(Ka × [HA]) | Quick weak-acid pH calculation, assuming [H+] = [A−] and that very little HA dissociates. |
| pKa = −log10 Ka | Converts very small Ka values into a handy scale; smaller pKa means a stronger acid. |
| Buffer pH = pKa + log([salt] ÷ [acid]) | Henderson–Hasselbalch equation for an acidic buffer; [salt] stands for the conjugate base (A−) provided by the salt. |
| Ksp: for AxBy(s) ⇌ xAy+(aq) + yBx−(aq), Ksp = [Ay+]x[Bx−]y | Solubility product of a sparingly soluble salt at saturation; solids never appear in the expression. |
| Precipitation rule: compare the ionic product with Ksp | Ionic product > Ksp: a precipitate forms. Ionic product < Ksp: no precipitate, everything stays dissolved. |
Electrochemistry
| Formula / Equation | What it is / When to use it |
|---|
| E°cell = E°(cathode, reduction) − E°(anode, oxidation) | Take the more positive electrode potential minus the more negative one; the result is the maximum voltage the cell can deliver. |
| Feasibility rule: E°cell > 0 | A positive cell potential means the reaction is thermodynamically feasible (though it may still be slow). |
| ΔG = −nFE, with F = 96,500 C mol−1 | Links cell potential to free energy: n = moles of electrons transferred, E = E°cell. A negative ΔG matches a positive Ecell. |
| Conventional cell representation: oxidation written on the left, e.g. Zn(s) | Zn2+(aq) || Cu2+(aq) | Cu(s) | Single lines separate phases, || is the salt bridge, and the highest oxidation states sit nearest the salt bridge. |
Spectroscopy & Analysis
| Formula / Equation | What it is / When to use it |
|---|
| A = εcl (Beer–Lambert law) | Colorimetry: absorbance A is proportional to concentration c and path length l, so a calibration curve converts absorbance into concentration. |
| Rf = distance moved by spot ÷ distance moved by solvent front | From thin-layer or paper chromatography; compare Rf values with known compounds run under identical conditions. |
| TMS (tetramethylsilane) is the NMR reference, δ = 0 ppm | Chemical shifts in 1H and 13C NMR are measured relative to TMS, which is inert, volatile and gives one sharp peak. |
| Number of peaks in a 13C NMR spectrum = number of different carbon environments | Equivalent carbons (in identical surroundings) give a single peak, so peak count reveals the symmetry of the molecule. |
Periodicity & Atomic Structure
| Formula / Equation | What it is / When to use it |
|---|
| First ionisation energy generally increases across a period | Nuclear charge rises while electrons enter the same shell, so shielding is similar and the outer electrons are held more tightly. |
| Drop at aluminium (Group 3) | The outer electron in Al is in a higher-energy 3p sub-shell, further from the nucleus than the 3s electron in Mg, so it is easier to remove. |
| Drop at sulfur (Group 6) | In S the removed electron is paired up in a 3p orbital; repulsion between the paired electrons makes it easier to remove than the single 3p electrons in P. |
| Relative atomic mass = Σ(m/z × % abundance) ÷ 100 | Weighted mean mass from a mass spectrum; relative intensities can replace % abundances if they are used consistently. |
| m/z = mass ÷ charge | Mass spectrometry axis; for singly charged ions it equals the ion mass, and the molecular ion peak gives the Mr of the compound. |
This formula sheet is an original revision aid produced by QuaidianPoint. It is not affiliated with, endorsed by, or produced by AQA.
