Energetics & Thermodynamics
Enthalpy, entropy, Gibbs energy and thermochemical cycles.
Before you begin
Enthalpy, entropy, Gibbs energy and thermochemical cycles.
Learning goals
- Enthalpy Changes and Energy Profiles
- Calorimetry (q = mcΔT)
- Hess’ Law and Cycles
- Bond Enthalpy Calculations
- Lattice Energy and Born–Haber Cycles
- Entropy and Gibbs Free Energy
Syllabus statements covered
- explain that most chemical reactions are accompanied by energy changes, principally in the form of heat usually associated with the breaking and forming of chemical bonds; the reaction can be exothermic (∆H negative) or endothermic (∆H positive)
- construct and interpret an energy profile diagram, in terms of the enthalpy change of the reaction and of the activation energy (see also Section 8)
- explain and use the terms: — enthalpy change of reaction and standard conditions, with particular reference to: formation; combustion; hydration; solution; neutralisation; atomisation
- calculate enthalpy changes from appropriate experimental results, including the use of the relationship: heat change = mc∆T
- apply Hess’ Law to construct simple energy cycles, e.g. Born-Haber cycle, and carry out calculations involving such cycles and relevant energy terms (including ionisation energy and electron affinity), with particular reference to: — determining enthalpy changes that cannot be found by direct experiment, e.g. an enthalpy change of formation from enthalpy changes of combustion
- explain and use the terms: — bond energy (∆H positive, i.e. bond breaking) (see also Section 2)
- apply Hess’ Law to construct simple energy cycles, e.g. Born-Haber cycle, and carry out calculations involving such cycles and relevant energy terms (including ionisation energy and electron affinity), with particular reference to: — average bond energies
- explain and use the terms: — lattice energy (∆H negative, i.e. gaseous ions to solid lattice)
- explain, in qualitative terms, the effect of ionic charge and of ionic radius on the numerical magnitude of a lattice energy
- apply Hess’ Law to construct simple energy cycles, e.g. Born-Haber cycle, and carry out calculations involving such cycles and relevant energy terms (including ionisation energy and electron affinity), with particular reference to: — the formation of a simple ionic solid and of its aqueous solution
- explain and use the term entropy
- discuss the effects on the entropy of a chemical system by the following: — change in temperature
- discuss the effects on the entropy of a chemical system by the following: — change in phase
- discuss the effects on the entropy of a chemical system by the following: — change in the number of particles (especially for gaseous systems) [quantitative treatment is not required]
- predict whether the entropy change for a given process or reaction is positive or negative
- state and use the equation involving standard Gibbs free energy change of reaction, ∆G⦵: ∆G⦵ = ∆H⦵ − T∆S⦵ [the calculation of standard entropy change, ∆S⦵, for a reaction using standard entropies, S⦵, is not required]
- state whether a reaction or process will be spontaneous by using the sign of ∆G⦵
- understand the limitations in the use of ∆G⦵ to predict the spontaneity of a reaction
- predict the effect of temperature change on the spontaneity of a reaction, given standard enthalpy and entropy changes
Lessons
Work through them in order.
- Enthalpy Changes and Energy ProfilesDraw and read energy profiles, including the sign of ΔH, activation energy and catalysts.
- Calorimetry (q = mcΔT)Calculate ΔH from calorimetry data using q = mcΔT, with correct signs and units.
- Hess’ Law and CyclesConstruct Hess cycles to calculate enthalpy changes, avoiding sign and scaling errors.
- Bond Enthalpy CalculationsEstimate enthalpy changes from average bond energies.
- Lattice Enthalpy and Ionic AttractionDefine lattice formation and dissociation, and explain charge and radius trends.
- Constructing Born–Haber CyclesConstruct Born–Haber cycles with balanced species and signed enthalpy changes.
- Predicting Entropy ChangesPredict entropy changes from states, gaseous amounts and accessible arrangements.
- Gibbs Free Energy and FeasibilityUse entropy and Gibbs free energy, ΔG = ΔH − TΔS, to decide whether a reaction is feasible.
Practise and check
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Topic reference
This topic covers enthalpy changes, calorimetry, energy cycles and feasibility. The lessons build sign conventions and measurement first, then Hess’ law, bond enthalpy and Born–Haber cycles, and finish with entropy and Gibbs free energy.
Be comfortable with:
- Stoichiometry (A Level): amounts, equations and ratios.
- n = cV and unit conversions (cm³ ↔ dm³, J ↔ kJ).
- Rearranging algebra.
Quick Reference
| Task | Use | Unit check |
|---|---|---|
| calorimetry heat | q = mcΔ T | m in g, c in J g⁻¹ K⁻¹, Δ T in K (a °C change is numerically the same) |
| convert to enthalpy | Δ H = -qₛₒₗᵤₜᵢₒₙ/n | convert J → kJ; n in mol |
| Hess (formation) | Δ H_reaction⦵ = ∑ ν Δ H_f⦵(products) - ∑ ν Δ H_f⦵(reactants) | include coefficients |
| bond enthalpy estimate | Δ H ≈ ∑ E(broken) - ∑ E(formed) | estimate only |
| Gibbs feasibility | Δ G = Δ H - TΔ S | T in K; match kJ vs J |
| standard conditions | T = 298 K; p = 100 kPa; Δ S usually in J mol⁻¹ K⁻¹ (convert before Δ G) | quote conditions when using ⦵ data |
| Δ G temperature logic | feasible if Δ G < 0; increasing T favours feasibility when Δ S > 0 (since -TΔ S becomes more negative) | always use T in K |
| Born–Haber checklist | atomisation → IE₁/IE₂… → EA₁/EA₂… → lattice → formation | include signs and coefficients |
What You Must Memorise
- Exothermic vs endothermic: exothermic Δ H < 0; endothermic Δ H > 0.
- Standard conditions (A Level): typically 298 K and 100 kPa; solutions at 1.00 mol dm⁻³ when relevant.
- Calorimetry chain: qₛₒₗᵤₜᵢₒₙ = mcΔ T; q_reaction = -qₛₒₗᵤₜᵢₒₙ; Δ H = q_reaction/n (report in kJ mol⁻¹).
- Hess rules: reverse equation → change sign; multiply equation by k → multiply Δ H by k.
- Bond enthalpy estimate: Δ H ≈ ∑ E(broken) - ∑ E(formed) (mean values → estimate).
- Lattice enthalpy conventions: dissociation is the reverse of formation, so signs are opposite.
- Gibbs unit check: use T in K and make the energy units match before using Δ G = Δ H - TΔ S; feasibility requires Δ G < 0 under the stated conditions.
Common Exam Traps
- Mixing J and kJ (especially forgetting to convert Δ S before using Δ G).
- Using T in °C in Δ G = Δ H - TΔ S (must be K).
- Calorimetry sign errors: temperature rises but you give Δ H > 0 (or vice versa).
- Hess’ law sign/scale errors (reverse equation but forget sign; multiply coefficients but not Δ H).
- Born–Haber: missing IE₂ / EA₂ steps, or flipping electron affinity signs.
- Quoting Δ H without units (kJ mol⁻¹) or without “per mole of what?” clarity.
- Mixing standard and non-standard conditions: using Δ H⦵ values without stating standard conditions, or applying standard data when temperature/pressure/concentration differ.