AQA A-Level Chemistry: Energetics and Thermodynamics — Complete Revision Guide (7405)

Energetics is the bridge that carries AQA Chemistry students from AS to A2. The AS section (§3.1.4) introduces enthalpy change as a measurable quantity through calorimetry, bond enthalpies and Hess's law cycles. The A2 thermodynamics section (§3.1.8) then extends the same machinery to ionic lattices through Born-Haber cycles, to dissolving through enthalpies of solution and hydration, and finally to spontaneity through entropy and Gibbs free energy. Three big ideas run through the whole topic: enthalpy change is measured experimentally (and Required Practical 2 is examined every year), Hess's law and Born-Haber cycles let you reconstruct enthalpies you cannot measure directly, and the feasibility criterion ΔG = ΔH − TΔS distinguishes thermodynamic possibility from kinetic reality.

This topic is one of the most synoptic on the whole specification. The lattice enthalpies in Born-Haber cycles connect directly back to ionic and covalent bonding — Fajans's rules and polarisability govern whether experimental and theoretical lattice values agree. The activation energy that controls reaction rate is an energetics quantity examined again in kinetics and equilibrium, where the Arrhenius equation links Ea to rate constant. The relationship ΔG° = −RT ln K connects feasibility to the equilibrium constant. The thermal stability of Group 2 nitrates and carbonates, examined in the inorganic chemistry section, is a direct application of lattice enthalpy and polarising power. Time spent on energetics pays off across at least four other topics.

This guide walks through the energetics content in AQA 7405 sub-topic by sub-topic. It covers enthalpy changes and calorimetry; mean bond enthalpies; Hess's law cycles for combustion and formation; Born-Haber cycles for ionic lattices; enthalpies of solution and hydration; entropy and Gibbs free energy; the feasibility criterion in practice; and the experimental detail of Required Practical 2. For each topic you will find the core ideas, common pitfalls, a worked example and a link into the LearningBro Energetics and Thermodynamics course.

Synoptic Preview

Energetics is not a self-contained island. Lattice enthalpy values from Born-Haber cycles feed into bonding discussions about ionic character. Activation energy ties to the Arrhenius equation in kinetics and equilibrium. The ΔG° = −RT ln K relation links thermodynamics to chemical equilibrium. Group 2 carbonate stability sits inside inorganic chemistry. The energetics of redox reactions, including standard electrode potentials and their relation to ΔG = −nFE, anchor redox and electrochemistry. And the spectroscopic energy levels from atomic structure underpin the very idea of an ionisation enthalpy.

Guide Overview

The eight sub-topics covered in this guide are:

1. Enthalpy Changes and Calorimetry — the Required Practical 2 anchor.
2. Bond Enthalpies and Mean Bond Enthalpies.
3. Hess's Law and Enthalpy Cycles.
4. Born-Haber Cycles.
5. Enthalpy of Solution and Hydration.
6. Entropy and Gibbs Free Energy.
7. Free Energy and Feasibility Applications.
8. Required Practical 2: Enthalpy Determination.

Each maps to a specific LearningBro lesson and to a specific examinable area of AQA 7405.

AQA 7405 Specification Coverage

AQA A-Level Chemistry (7405) is examined through Paper 1 (Inorganic and Physical, 2h, 105 marks), Paper 2 (Organic and Physical, 2h, 105 marks) and Paper 3 (Synoptic and Practical, 2h, 90 marks). Energetics appears in §3.1.4 (AS, enthalpy changes, calorimetry, Hess's law, mean bond enthalpies) and §3.1.8 (A2, Born-Haber cycles, enthalpies of solution and hydration, entropy and Gibbs free energy). Required Practical 2 is the canonical practical anchor.

Sub-topic	Spec area	Typical paper weight
Enthalpy changes and calorimetry	§3.1.4	4-6 marks
Bond enthalpies and mean bond enthalpies	§3.1.4	3-5 marks
Hess's law cycles	§3.1.4	4-6 marks
Born-Haber cycles	§3.1.8	6-10 marks
Enthalpy of solution and hydration	§3.1.8	4-6 marks
Entropy	§3.1.8	3-5 marks
Gibbs free energy and feasibility	§3.1.8	4-8 marks
Required Practical 2 (calorimetry)	RP2	4-6 marks

Weights are estimates modelled on recent 7405 papers. What is reliable is that an extended-response Born-Haber question — typically eight to ten marks — appears on Paper 1, and a feasibility calculation using ΔG = ΔH − TΔS appears on Paper 1 or Paper 3 with high frequency.

Enthalpy Changes and Calorimetry

The enthalpy change ΔH of a reaction is the heat exchanged with the surroundings at constant pressure. By convention ΔH is negative for exothermic reactions (heat released, surroundings warm) and positive for endothermic reactions (heat absorbed, surroundings cool). Standard enthalpy change ΔH° is measured at 100 kPa, with all species in their standard states, usually quoted at 298 K.

Several specific enthalpy changes recur throughout the specification: enthalpy of reaction (ΔrH°), formation (ΔfH°, one mole of compound from elements in standard states), combustion (ΔcH°, one mole burned in excess O2), neutralisation (one mole of water formed from H+ and OH−) and atomisation (one mole of gaseous atoms from the element in its standard state).

Calorimetric calculation uses q = mcΔT where q is heat absorbed by water (J), m is mass of water (g), c is specific heat capacity (4.18 J g⁻¹ K⁻¹ for water) and ΔT is temperature change (K). ΔH per mole is then −q / n, where n is moles of the limiting reactant. The negative sign converts a heat gained by the water into a heat lost by the reaction.

Worked example. 25.0 cm³ of 1.00 mol dm⁻³ NaOH is mixed with 25.0 cm³ of 1.00 mol dm⁻³ HCl. Temperature rises by 6.8 K. q = 50.0 × 4.18 × 6.8 = 1421 J. Moles of water formed = 0.025. ΔH = −1421 / 0.025 = −56.8 kJ mol⁻¹.

A common pitfall is to use moles of one solution rather than moles of water formed; another is to forget that the total mass of solution (50 g, not 25 g) appears in q = mcΔT. See the enthalpy changes and calorimetry lesson.

Bond Enthalpies and Mean Bond Enthalpies

A bond dissociation enthalpy is the energy required to break one mole of a specific bond in the gas phase. The mean bond enthalpy is the average over a range of molecules — for example, the mean C-H bond enthalpy is averaged across methane, ethane and many other molecules. Mean values are tabulated and used in approximate calculations.

For a gas-phase reaction, ΔrH ≈ Σ(bonds broken) − Σ(bonds formed). Bond breaking is endothermic (positive); bond formation is exothermic (negative); the sign convention sometimes confuses students. A reaction is exothermic when more energy is released forming new bonds than is absorbed breaking the old ones.

Worked example. Estimate ΔrH for CH4 + 2 O2 → CO2 + 2 H2O(g) using mean bond enthalpies: C-H 412, O=O 496, C=O 805, O-H 463 kJ mol⁻¹. Bonds broken: 4(C-H) + 2(O=O) = 4(412) + 2(496) = 1648 + 992 = 2640. Bonds formed: 2(C=O) + 4(O-H) = 2(805) + 4(463) = 1610 + 1852 = 3462. ΔrH = 2640 − 3462 = −822 kJ mol⁻¹. The true value is around −890 kJ mol⁻¹ — the difference reflects the averaging.

A common pitfall is to count bonds wrongly (each O=O is one bond, not two). Another is to claim mean bond enthalpies give exact answers — they give approximate values. The reaction must be in the gas phase for mean bond enthalpies to apply directly. See the bond enthalpies lesson.

Hess's Law and Enthalpy Cycles

Hess's law states that the total enthalpy change for a reaction is independent of the path taken. The implication: any enthalpy change can be calculated from a set of known enthalpy changes that connect the same initial and final states.

Two standard cycles dominate AQA questions. The formation cycle: ΔrH° = Σ ΔfH°(products) − Σ ΔfH°(reactants). The combustion cycle: ΔrH° = Σ ΔcH°(reactants) − Σ ΔcH°(products). Note the reversed sign — combustion enthalpies are written for reactants on top because each reactant burns to give the same combustion products as the right-hand side of the target equation.

Worked example. Calculate ΔrH° for C2H5OH(l) + 3 O2(g) → 2 CO2(g) + 3 H2O(l) given ΔfH°: ethanol −277, CO2 −394, H2O −286 kJ mol⁻¹; O2 is zero (element in standard state). ΔrH° = [2(−394) + 3(−286)] − [(−277) + 3(0)] = [−788 − 858] − [−277] = −1646 + 277 = −1369 kJ mol⁻¹.

A common pitfall is to forget to multiply by stoichiometric coefficients. Another is to confuse the formation and combustion cycles — practise drawing the cycle diagram with arrows pointing from elements (formation) or to combustion products (combustion) until both feel automatic. Kirchhoff's law (temperature correction) is beyond 7405 but mentioned in some textbooks; you do not need it. See the Hess's law lesson.

Born-Haber Cycles

A Born-Haber cycle is a Hess's law cycle that decomposes the formation of an ionic compound from elements into a sequence of atomisation, ionisation, electron affinity and lattice formation steps. It is used to calculate the lattice enthalpy of an ionic compound — a quantity that cannot be measured directly.

The standard sequence for a 1:1 salt MX(s):

1. Atomisation of M(s) → M(g): ΔatH°(M), endothermic.
2. Ionisation of M(g) → M⁺(g) + e⁻: first ionisation enthalpy, endothermic.
3. Atomisation of ½X2 → X(g): ΔatH°(X), endothermic.
4. Electron affinity X(g) + e⁻ → X⁻(g): first electron affinity, exothermic.
5. Lattice formation M⁺(g) + X⁻(g) → MX(s): ΔLEH°, very exothermic.

The sum equals ΔfH°(MX). Rearranging gives the lattice enthalpy.

Worked example. For NaCl: ΔfH° = −411, ΔatH°(Na) = +109, IE1(Na) = +494, ΔatH°(Cl) = +121, EA1(Cl) = −364 kJ mol⁻¹. ΔLEH° = ΔfH° − [ΔatH°(Na) + IE1(Na) + ΔatH°(Cl) + EA1(Cl)] = −411 − [109 + 494 + 121 − 364] = −411 − 360 = −771 kJ mol⁻¹.

Two further subtleties matter at A2. First, for compounds with M²⁺ or X²⁻ ions you need the second ionisation enthalpy or second electron affinity (the second EA is typically endothermic because you are forcing an electron onto an already negative ion). Second, the theoretical lattice enthalpy calculated from a purely ionic model (Born-Landé approach) often disagrees with the experimental value from the cycle; the gap is a measure of covalent character, predicted by Fajans's rules on polarising power.

A common pitfall is to sign-flip lattice enthalpy — lattice formation is exothermic, lattice dissociation is endothermic, and AQA can ask for either. Another is to omit the second ionisation or to halve a diatomic atomisation incorrectly. See the Born-Haber cycles lesson.

Enthalpy of Solution and Hydration

When an ionic solid dissolves in water, two energy changes compete. The lattice enthalpy must be supplied to separate the ions from the crystal (endothermic, the reverse of lattice formation). The enthalpy of hydration is released as each gaseous ion is solvated by water dipoles (exothermic). The enthalpy of solution ΔsolH° is the sum: ΔsolH° = −ΔLEH° + ΔhydH°(cation) + ΔhydH°(anion).

Hydration enthalpy is more exothermic for ions with higher charge density (higher charge or smaller radius). Mg²⁺ has a much more exothermic ΔhydH° than Na⁺ because of its higher charge and smaller radius. Lattice enthalpy follows the same pattern, so the two terms partly cancel.

Worked example. For NaCl: ΔLEH° = −771 kJ mol⁻¹, ΔhydH°(Na⁺) = −406, ΔhydH°(Cl⁻) = −364. ΔsolH° = +771 + (−406) + (−364) = +1 kJ mol⁻¹. The near-zero value matches the experimental observation that NaCl dissolves with negligible heat change.

A common pitfall is to use the sign of lattice formation directly without flipping it for solution. The cycle dissolves the solid (lattice breaking, endothermic). Another is to forget there are two hydration terms (one per ion). See the enthalpy of solution and hydration lesson.

Entropy and Gibbs Free Energy

Entropy S is a measure of disorder, or more precisely (in Boltzmann's formulation) the number of microstates available to a system. Gases have higher entropy than liquids, which have higher entropy than solids. Dissolving an ionic solid increases entropy because the ordered crystal becomes a disordered solution. Combining two moles of gas into one mole of gas decreases entropy.

The standard entropy change ΔS° = Σ S°(products) − Σ S°(reactants), using tabulated standard molar entropies. Units are J K⁻¹ mol⁻¹ — note the J, not kJ, which trips up many students when combining with ΔH in kJ.

Gibbs's central equation is ΔG = ΔH − TΔS. A reaction is feasible (spontaneous) when ΔG < 0. Three patterns follow:

• ΔH negative and ΔS positive: feasible at all temperatures.
• ΔH positive and ΔS negative: never feasible.
• Both negative: feasible at low T (TΔS small); becomes unfeasible above T = ΔH/ΔS.
• Both positive: feasible at high T (TΔS large); becomes feasible above T = ΔH/ΔS.

Worked example. For CaCO3(s) → CaO(s) + CO2(g), ΔH° = +178 kJ mol⁻¹, ΔS° = +161 J K⁻¹ mol⁻¹. Set ΔG = 0: T = ΔH/ΔS = 178000/161 = 1106 K. CaCO3 decomposes above about 833 °C — consistent with industrial lime kiln operation.

A common pitfall is mixing J and kJ. Convert ΔS to kJ K⁻¹ mol⁻¹ before substituting into ΔG = ΔH − TΔS, or convert ΔH to J. See the entropy and Gibbs free energy lesson.

Free Energy and Feasibility Applications

Feasibility is a thermodynamic statement, not a kinetic one. A reaction with ΔG < 0 is thermodynamically possible but may proceed too slowly to observe. The combustion of diamond at room temperature is feasible (ΔG very negative) but kinetically frozen by the very high activation energy of C-C bond breaking.

Three application patterns recur on AQA papers. Decomposition temperatures of Group 2 carbonates and nitrates increase down the group because cation polarising power decreases — directly examined in inorganic chemistry. Extraction of metals by reduction with carbon depends on whether the carbothermic ΔG becomes more negative than the metal-oxide ΔG above some temperature — the basis of Ellingham diagrams (mentioned but not drawn in 7405). Equilibrium constants at a given temperature follow from ΔG° = −RT ln K, the link to kinetics and equilibrium.

Worked example. For N2(g) + 3 H2(g) ⇌ 2 NH3(g), ΔH° = −92, ΔS° = −198 J K⁻¹ mol⁻¹. At 298 K, ΔG° = −92 − 298(−0.198) = −92 + 59 = −33 kJ mol⁻¹. Feasible at room temperature. At 700 K, ΔG° = −92 − 700(−0.198) = −92 + 139 = +47 kJ mol⁻¹. Not feasible — explaining why the Haber process compromises at moderate temperature with a catalyst and high pressure rather than running thermodynamically.

A common pitfall is to treat feasibility as the same as observability. A 7405 mark scheme answer often requires the caveat "the reaction may have a high activation energy and therefore not occur at a measurable rate". See the free energy and feasibility applications lesson.

Required Practical 2: Enthalpy Determination

Required Practical 2 is the experimental anchor of the AS energetics section. The standard protocols are:

• Neutralisation: mix known volumes of strong acid and strong base; measure ΔT; calculate ΔH per mole of water formed.
• Displacement: add an excess of one metal to a solution of another's salt (e.g. Zn into CuSO4); measure ΔT; calculate ΔH per mole of the limiting metal-ion.
• Dissolution: dissolve a known mass of solid (e.g. NH4Cl) in a known mass of water; measure ΔT (may be a cooling for endothermic dissolution); calculate ΔH per mole of solid.

For reactions that are slow (e.g. Zn + CuSO4 takes several minutes), cooling-curve extrapolation is required. Plot temperature against time; extrapolate the cooling section backwards to the moment of mixing; subtract from the initial temperature to obtain the true maximum ΔT. This corrects for heat losses to the surroundings during the reaction.

CPAC (Common Practical Assessment Criteria) checkpoints examiners look for: accurate use of measuring cylinder or pipette for volumes; thermometer read to 0.1 K resolution; insulated polystyrene cup as calorimeter; minimum 30-second cooling-curve data after maximum; clearly drawn extrapolation; assumption that solution density = 1 g cm⁻³ and c = 4.18 J g⁻¹ K⁻¹ stated explicitly.

A common pitfall is to use the initial peak temperature directly rather than the extrapolated value — usually gives an answer numerically smaller than the textbook value. Another is to give an answer in J rather than kJ — always per mole, always kJ mol⁻¹. See the Required Practical 2 lesson.

Common Mark-Loss Patterns

• Forgetting the negative sign when converting q (heat absorbed by solution) to ΔH (heat released by reaction).
• Using moles of the wrong reactant in q/n — should be moles of the limiting reactant (or moles of water for neutralisation).
• Mixing J and kJ in ΔG = ΔH − TΔS calculations.
• Mis-counting bonds in mean-bond-enthalpy questions.
• Sign-flipping lattice enthalpy between formation and dissociation contexts.
• Omitting the second ionisation enthalpy for 2+ cations in Born-Haber cycles.
• Treating feasibility as proof of observability; activation energy is a separate consideration.
• Forgetting cooling-curve extrapolation in slow reactions.
• Using mass of the reactant rather than mass of the solution in q = mcΔT.
• Quoting "Hess law" or "Born-Haber" without naming a quantity — the mark scheme wants the specific enthalpy term.

How to Revise This Topic

• Drill calorimetric arithmetic daily. Five q = mcΔT problems per day for a fortnight makes the bookkeeping automatic.
• Build a Born-Haber flashcard set. One card per step; one per common salt (NaCl, MgCl2, MgO, CaF2); one for the second ionisation/electron affinity subtlety.
• Practise Hess cycles in both directions. Calculate ΔrH from ΔfH; calculate one ΔfH from a ΔrH and the others.
• Memorise the four ΔH/ΔS sign combinations and the temperature-dependence pattern of feasibility.
• Sketch cooling curves for at least three of the standard RP2 protocols; mark the extrapolation explicitly.
• Use the LearningBro practice quizzes to test under timed conditions.

Linking to Other Topics

Energetics ramifies across the rest of the course. Lattice enthalpies feed back into bonding discussions of ionic character and Fajans's rules. The activation energy Ea sits inside the Arrhenius equation in kinetics and equilibrium, where ΔG° = −RT ln K joins thermodynamics to the equilibrium constant. Group 2 carbonate and nitrate decomposition trends in inorganic chemistry are direct lattice-enthalpy arguments. The Nernst relation between ΔG and cell potential in redox and electrochemistry extends the feasibility framework. Even the ionisation enthalpies in Born-Haber cycles trace back to the orbital energy levels from atomic structure. Master energetics and at least four other topics open up.

Final Word

Energetics rewards systematic study. The calorimetric arithmetic is formulaic, Hess and Born-Haber cycles reduce to careful bookkeeping, and the Gibbs feasibility criterion fits onto a single line. The trap is sign errors and unit slips — practise enough that signs become automatic. The full LearningBro Energetics and Thermodynamics course walks through every sub-topic with worked examples, AI tutor feedback and the Required Practical 2 protocol drilled to CPAC standard. Get this section fluent and the thermodynamic backbone of the rest of the A-Level falls into place.