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R1.2

Energy cycles in reactions

3 SL · +5 HL (SL 1.2.1-1.2.2) (HL 1.2.3-1.2.5)

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Parent topic: What drives chemical reactions?

Guiding question

Guiding questionHow does application of the law of conservation of energy help us to predict energy changes during reactions?

The one big idea

Enthalpy is a state function, so the path does not matter. Hess's law lets you calculate ΔH for a reaction you cannot measure directly by combining cycles and summation equations from combustion, formation, and bond enthalpy data.

What this rests on

Our editorial judgement.The dependencies in this section are this site’s own assessment of what a sub-topic rests on. They have notbeen verified by a chemistry teacher and are not part of the official IB guide. By contrast, section 8 (Linking questions) reproduces the IB’s own wording verbatim.

What rests on this

Core concepts that must be mastered

  • Bond enthalpy and the source of ΔH(1.2.1)A reaction is exothermic when more energy is released forming product bonds than is absorbed breaking reactant bonds. Bond breaking always requires energy (endothermic); bond forming always releases it (exothermic). You can estimate ΔH from average bond enthalpy data: ΔH = Σ(bonds broken) − Σ(bonds formed). Tabulated bond enthalpies are averages across many compounds and apply to gaseous species only, so this method gives approximate results that diverge when liquids or solids are involved — for example, the O–H bond enthalpy in water differs slightly from the average O–H value because the molecular environment affects bond strength. The stronger the bond, the more energy is needed to break it — and bond enthalpy relates to bond length and polarity (shorter, more polar bonds are generally stronger). This is why the bond-enthalpy method is an estimate, not an exact calculation: actual bond enthalpies depend on the specific molecule, not just the bond type.
  • Hess's law(1.2.2)Hess's law states that ΔH is independent of the pathway taken. This works because enthalpy is a state function: only the start and end points matter, not the route between them. If a reaction can be expressed as the sum of two or more steps, its ΔH is the sum of the steps' ΔH values. This lets you calculate ΔH for reactions that are impractical to measure directly — for example, the formation of carbon monoxide from its elements is hard to stop at CO, but you can combine the combustion of C to CO₂ and CO to CO₂ to get there.
  • HL: Enthalpy of combustion and formation(1.2.3, 1.2.4)At HL, standard enthalpy of combustion ΔHc⦵ and standard enthalpy of formation ΔHf⦵ data are used in thermodynamic calculations. ΔHf⦵ is the enthalpy change when one mole of a compound forms from its elements in their standard states — so ΔHf⦵ of any element in its standard state is zero by definition. Hess's law applied via formation data gives: ΔH⦵ = ΣΔHf⦵(products) − ΣΔHf⦵(reactants). And via combustion data: ΔH⦵ = ΣΔHc⦵(reactants) − ΣΔHc⦵(products). The combustion equation is reversed because you burn the reactants and products separately and subtract — notice the reactants and products swap positions compared to the formation equation. Both sets of data are in the data booklet. Remember to multiply each ΔHf⦵ or ΔHc⦵ by the stoichiometric coefficient and to account for state symbols.
  • HL: Born–Haber cycles(1.2.5)A Born–Haber cycle is an application of Hess's law that shows the energy changes in forming an ionic compound from its elements. You must interpret and determine values from a Born–Haber cycle for compounds of univalent and divalent ions — for example NaCl or MgCl₂. The cycle includes: enthalpy of formation (the overall target), enthalpy of atomization (sublimation of the metal and/or bond enthalpy of the non-metal), ionization energy (removing electrons from the metal), electron affinity (adding electrons to the non-metal), and lattice enthalpy (the energy released when gaseous ions form the solid lattice). The cycle closes: the sum of all the steps equals ΔHf⦵. Lattice enthalpy depends on ion charge and ionic radius — higher charges and smaller ions give stronger lattices. Construction of a complete cycle will not be assessed — you will interpret or extract a single value, not draw the whole thing from scratch.
  • How this sub-topic connectsHess's law is the bridge between measuring enthalpy (R1.1) and predicting it without experiment. Bond enthalpies connect to the covalent model (S2.2: bond strength, bond length, polarity) and to reaction rates (R3.4: the C–halogen bond strength affects the rate of nucleophilic substitution). Born–Haber cycles connect to the ionic model (S2.1: lattice structure, ionic radius) and lattice enthalpy is a major factor in the properties of ionic compounds. At HL, these thermodynamic foundations feed directly into the entropy–Gibbs framework (R1.4): ΔH⦵ values calculated here become inputs to ΔG⦵ = ΔH⦵ − TΔS⦵.

Quantitative non-negotiables

  • Calculate ΔH from average bond enthalpy data and explain why the result is approximate.
  • Apply Hess's law to multi-step reactions.
  • At HL: use ΔH⦵ = ΣΔHf⦵(products) − ΣΔHf⦵(reactants) and ΔH⦵ = ΣΔHc⦵(reactants) − ΣΔHc⦵(products).HL
  • At HL: interpret and determine values from a Born–Haber cycle for univalent and divalent ionic compounds.HL

Common failure modes

  • M-30 — Bond breaking releases energy.

    Confidence: verified

    Why it’s wrong: Breaking bonds always requires energy input (endothermic); forming bonds always releases it.

    Correction: Exothermic overall means more energy released in forming than absorbed in breaking.

  • M-31 — Bond enthalpy calculations give the exact enthalpy change.

    Confidence: verified

    Why it’s wrong: Tabulated values are averages across many compounds and apply to gaseous species.

    Correction: Results are approximate and diverge when liquids or solids are involved.

What "HL standard" actually looks like

HLHL adds thermodynamic calculations from ΔHf⦵ and ΔHc⦵ data, the two Hess's-law summation equations, and Born–Haber cycles for ionic compounds (ionization energy, atomization enthalpy, electron affinity, lattice enthalpy). Construction of a complete cycle is not assessed, but interpreting one is. +5 HL hours.

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Linking questions

Official IB.The questions in this section are the IB’s own linking questions, reproduced verbatim from the guide. They are not this site’s editorial judgement — see section 3 for that distinction.

  1. Official IB

    How would you expect bond enthalpy data to relate to bond length and polarity?

    Reactivity 1.2.1 → S2.2 The covalent model

  2. Official IB

    How does the strength of a carbon–halogen bond affect the rate of a nucleophilic substitution reaction?

    Reactivity 1.2.1 → R3.4 Electron-pair sharing reactions

  3. Official IB

    Would you expect allotropes of an element, such as diamond and graphite, to have different ΔH⦵f values?

    Reactivity 1.2.3 → S2.2 The covalent model

  4. Official IB

    What are the factors that influence the strength of lattice enthalpy in an ionic compound?

    Reactivity 1.2.5 → S2.1 The ionic model

  5. Official IB

    Why do chlorofluorocarbons (CFCs) in the atmosphere break down to release chlorine radicals but typically not fluorine radicals?

    Reactivity 3.3.2 → R1.2 Energy cycles in reactions

Bridge: GCSE → IB HL

Derived. These are the bridge items tagged to this sub-topic— places where the GCSE model gets redefined, genuinely new territory, or carry-over strengths. The tagging is this site’s editorial judgement.

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