Full chapter
Chemical Energetics
Track energy through bonds and cycles, then combine enthalpy and entropy to assess thermodynamic feasibility.
A-Level 9476 (2026-2027)
Breaking bonds costs energy; forming bonds releases it
The overall enthalpy change compares products with reactants, not the height of the barrier.
The reacting chemicals are the system; the solution, vessel and room can act as surroundings. At constant pressure, heat absorbed by the system corresponds to an increase in enthalpy. An exothermic reaction releases heat and has ΔH < 0; an endothermic reaction absorbs heat and has ΔH > 0. Bond breaking absorbs energy and bond formation releases it, so the difference between these contributions determines the overall sign.
Exothermic reaction profile
Reactants rise to a transition-state maximum before falling to lower-enthalpy products. Forward activation energy is measured upward from the reactant level to the maximum. Delta H points downward from reactants to products.
Endothermic reaction profile
The transition-state maximum lies above both endpoints. Products have higher enthalpy than reactants, so delta H is positive. Activation energy still measures from the reactant level to the maximum.
Worked example
Construct a profile from two energy measurements
A reaction has ΔH = -65 kJ mol-1 and forward activation energy 90 kJ mol-1. Sketch and label its profile, then determine the reverse activation energy.
- Draw axes labelled enthalpy, H / kJ mol-1, and reaction progress. Choose the reactant level as zero; this is a relative reference, not an assertion that reactants contain no energy.
- Draw a short horizontal reactant level at 0 and a product level at -65. Connect them by a smooth curve whose maximum is at +90, because forward activation energy is measured above the reactants.
- Draw the forward activation-energy arrow upwards from 0 to +90. Draw the enthalpy-change arrow downwards from 0 to -65. Label the two endpoints reactants and products.
- For the reverse reaction, start at the product level: draw its activation-energy arrow upwards from -65 to the same +90 maximum. The vertical difference is 90 - (-65) = 155.
- If asked to include a catalyst with forward activation energy 45 kJ mol-1, add a second curve peaking at +45 with the same endpoints. Its reverse barrier is 45 - (-65) = 110; the enthalpy change remains -65.
Ea,reverse = 155 kJ mol-1. Check the uncatalysed drawing using 90 - 155 = -65 = ΔH; both activation-energy arrows point upwards, even though the forward reaction is exothermic.
A catalyst provides a different mechanism with a lower activation barrier. It does not change the enthalpies of the initial and final states, so it leaves ΔH unchanged. In a multistep profile, minima between peaks represent intermediates; the highest absolute peak is not automatically the step with the largest barrier measured from its preceding intermediate.
An enthalpy value belongs to an exact equation and set of states
One mole means one mole of the specified event, not always one mole of the same substance.
Standard enthalpy changes refer to substances in their standard states at a specified temperature, commonly 298 K, with standard pressure 100 kPa. School calculations conventionally use 1 mol dm-3 for specified aqueous standard conditions. Temperature must still be stated: the standard symbol does not itself mean 298 K. Changing a state, multiplying an equation or reversing it changes the corresponding enthalpy value.
| Term | Process for one mole |
|---|---|
| Enthalpy change of reaction | Enthalpy change for the reaction as written, under stated conditions; coefficients define the amount of reaction. |
| Formation | One mole of a compound forms from its constituent elements in their standard states. Example: C(graphite) + O2(g) → CO2(g). |
| Combustion | One mole of substance is completely burnt in oxygen, with all products in specified states. |
| Hydration | One mole of gaseous ions becomes hydrated aqueous ions. Example: Na+(g) → Na+(aq). |
| Solution | One mole of solute dissolves in sufficient solvent that further dilution produces no appreciable enthalpy change. |
| Neutralisation | An acid and a base react to form one mole of water. |
| Atomisation | One mole of gaseous atoms forms from the element in its stated standard state. Example: 1/2 Cl2(g) → Cl(g). |
| Bond energy | Energy required to break one mole of a specified covalent bond in gaseous species; always positive for bond breaking. Tabulated mean bond energies average different environments. |
| Lattice energy in this syllabus | One mole of ionic solid forms from its constituent gaseous ions. Example: Na+(g) + Cl-(g) → NaCl(s); negative. |
For a strong acid and strong base in dilute aqueous solution, the main reaction is H+(aq) + OH-(aq) → H2O(l), so neutralisation enthalpies are similar. A weak acid or base also undergoes ionisation, changing the measured total. Do not assume every acid-base combination has exactly the same enthalpy.
The thermometer measures the surroundings, not the reaction directly
Find q for what warms or cools, reverse its sign, then divide by the reacting amount.
q = mcΔT, where m is the mass being warmed, c is its specific heat capacity and ΔT is final minus initial temperature. With m in g and c in J g-1 K-1, q is in J. A temperature interval of 1 K equals an interval of 1 °C. For an insulated arrangement, qreaction = -qsurroundings.
Worked example
Neutralisation measured in an insulated cup
50.0 cm3 of 1.00 mol dm-3 HCl is mixed with 50.0 cm3 of 1.00 mol dm-3 NaOH. The temperature rises by 6.80 K. Assume density 1.00 g cm-3, c = 4.18 J g-1 K-1 and negligible cup heat capacity.
- Total solution mass is 100.0 g, not 50.0 g.
- q(solution) = 100.0 × 4.18 × 6.80 = +2842.4 J, so q(reaction) = -2.8424 kJ.
- Both acid and base supply 0.0500 mol; 0.0500 mol water forms.
- Divide by the water amount: delta H = -2.8424/0.0500.
ΔHneut = -56.8 kJ mol-1 to three significant figures.
If the calorimeter heat capacity C is supplied, include its heat gain: qsurroundings = (mc + C)ΔT. In a combustion experiment, use the mass of water warmed and the amount of fuel actually burnt. In a dissolution experiment, use the appropriate solution mass and heat capacity, and divide by the amount of solute dissolved.
| Effect | Consequence for an exothermic result |
|---|---|
| Heat lost to the room or absorbed by an ignored vessel | Measured heat release is too small in magnitude; the calculated enthalpy is less negative. |
| Incomplete combustion | Less energy is released than for complete combustion to the stated products. |
| Fuel evaporates without burning | Apparent fuel consumption is too large; energy per measured mole is too small in magnitude. |
| Reactant concentrations or final temperature are mismeasured | Determine the direction from the actual calculation; there is no universal error direction. |
A temperature-time record before and after mixing can support extrapolation to estimate the temperature at mixing, reducing a systematic heat-loss error. Repeated trials reveal scatter but do not by themselves remove the same heat loss from every trial. Always identify the limiting reagent before dividing q by an amount.
Hess Law compares routes with identical endpoints
Enthalpy is a state function, so a direct route and an indirect route have the same total change.
Hess Law: the enthalpy change of a reaction depends on its initial and final states, not the route taken. Write the target equation first. Reverse any auxiliary equation that runs the wrong way and change its sign; multiply its enthalpy when multiplying its coefficients. Cancel identical species only when their states also match.
Worked example
Formation enthalpy from combustion data
Find the formation enthalpy of C2H5OH(l). Use combustion enthalpies C(graphite) = -394, H2(g) = -286 and ethanol(l) = -1367 kJ mol-1, all giving CO2(g) and H2O(l).
- Target: 2C(graphite) + 3H2(g) + 1/2 O2(g) → C2H5OH(l).
- Combusting the elements to 2CO2(g) + 3H2O(l) releases 2(-394) + 3(-286) = -1646 kJ.
- The alternative route is formation of ethanol followed by its combustion: delta Hf - 1367 = -1646.
- Rearrange without changing the endpoints.
ΔHf = -279 kJ mol-1 for the supplied rounded data.
With formation data, ΔHreaction = ΣνΔHf(products) - ΣνΔHf(reactants), where ν is the stoichiometric coefficient. Elements in their standard states have standard formation enthalpy zero by definition. This does not mean they contain no energy or have zero atomisation enthalpy.
Worked example
Estimate a gas-phase reaction using mean bond energies
Estimate ΔH for H2(g) + Cl2(g) → 2HCl(g), using H-H = 436, Cl-Cl = 243 and H-Cl = 431 kJ mol-1.
- Break one H-H and one Cl-Cl bond: energy input = 436 + 243 = 679 kJ.
- Form two H-Cl bonds: energy released = 2 × 431 = 862 kJ.
- Subtract energy released from energy absorbed.
ΔH ≈ 679 - 862 = -183 kJ mol-1 of reaction as written.
The bond-energy route passes through separated gaseous atoms. Include extra phase-change terms if the target uses liquids or solids. Mean bond energies give estimates because bond strength depends on molecular environment; formation enthalpies for the exact substances and states can give a more specific value.
Build an ionic solid through gaseous atoms and ions
Born-Haber cycles keep atomisation, ionisation, electron affinity and lattice formation distinct.
A first electron affinity is the enthalpy change when one mole of gaseous atoms each gains an electron to form gaseous singly negative ions: Cl(g) + e- → Cl-(g). It is often negative. Adding an electron to an already negative ion, as in O-(g) + e- → O2-(g), requires energy to overcome repulsion and is positive. Ionisation energies always refer to removing electrons from gaseous species and are positive.
- Create gaseous atoms
Na(s) → Na(g): atomisation +108. 1/2 Cl2(g) → Cl(g): atomisation +122 kJ per mole of NaCl formed.
- Create gaseous ions
Na(g) → Na+(g) + e-: first ionisation +496. Cl(g) + e- → Cl-(g): electron affinity -349.
- Assemble the lattice
Na+(g) + Cl-(g) → NaCl(s): the unknown lattice energy, L.
Construct the two routes of a Born-Haber cycle
The direct left-hand route forms solid sodium chloride from solid sodium and half a mole of chlorine molecules, with enthalpy minus 411 kilojoules per mole. The indirect route first makes gaseous atoms, then removes an electron from sodium, transfers it to chlorine, and forms the ionic lattice. Both routes have exactly the same initial and final states.
Worked example
Calculate the lattice energy with the syllabus convention
Using the cycle above and ΔHf(NaCl,s) = -411 kJ mol-1, find L.
- The two routes give -411 = 108 + 122 + 496 - 349 + L.
- The non-lattice steps total +377 kJ mol-1.
- L = -411 - 377 = -788 kJ mol-1.
L = -788 kJ mol-1. Reversing the final step to separate the lattice would require +788 kJ mol-1.
For MgO, include Mg atomisation, half an O=O bond dissociation, both the first and second ionisation energies of Mg, and both electron affinities of oxygen. Each coefficient follows the target formula. A highly exothermic lattice-formation step can compensate for costly ion formation; do not omit a positive second electron affinity to make a cycle look easier.
A simple electrostatic model predicts a larger lattice-energy magnitude for greater ionic charge product and smaller interionic separation. Thus MgO has a much more negative lattice energy than NaCl, while MgO is generally more negative than CaO because Mg2+ is smaller. Use these comparisons for similar structures; appreciable covalent character can cause departures from a purely ionic model.
Worked example
Dissolution separates the lattice, then hydrates the ions
Using L = -788 kJ mol-1 and total hydration enthalpy -784 kJ mol-1 for Na+ and Cl-, estimate the solution enthalpy of NaCl.
- Separating NaCl(s) into gaseous ions reverses lattice formation, so the change is +788.
- Hydrating both gaseous ions releases 784 kJ mol-1.
- Add the two steps: delta Hsol = -L + sum(delta Hhyd).
ΔHsol = +4 kJ mol-1. A slightly endothermic dissolution can still occur because enthalpy is only one contribution to free energy.
Entropy describes how widely energy and particles can be distributed
Think of the number of accessible microscopic arrangements, not simply visible mess.
Entropy, S, measures the dispersal of energy among accessible microscopic arrangements. A state with more accessible arrangements has greater entropy. Qualitative predictions work best when a large change, such as gas production or a phase change, dominates; do not infer a precise value from appearance.
| Change | Reasoning | Typical sign for the system |
|---|---|---|
| Temperature rises | More energy levels and microscopic arrangements become accessible. | Positive |
| Solid melts; liquid vaporises | Particles gain greater freedom of position and movement, especially on becoming gas. | Positive |
| Gas is compressed at fixed temperature | The particles have less available volume and fewer positional arrangements. | Negative |
| More moles of gas are formed in a reaction | Usually greatly increases possible particle arrangements. | Positive, other contributions permitting |
| Gas is consumed to form a liquid or solid | A large loss of translational freedom usually dominates. | Negative |
Worked example
Compare two reactions using their gaseous particles
Predict the signs of ΔS for CaCO3(s) → CaO(s) + CO2(g), and N2(g) + 3H2(g) → 2NH3(g).
- Carbonate decomposition produces gas from solids; accessible arrangements increase strongly.
- Ammonia formation reduces the gas amount from four moles to two moles per equation.
- Count gaseous coefficients, not every coefficient regardless of phase.
Carbonate decomposition has positive ΔS; ammonia formation has negative ΔS under the usual conditions considered.
Dissolution often increases positional dispersal, but strongly hydrated ions can order nearby water molecules. The net entropy of dissolution is not guaranteed positive. If gas amounts are unchanged or competing changes are similar, supplied entropy data is stronger evidence than a simple counting rule. The syllabus does not require calculating reaction entropy from tables of absolute standard entropies.
Free energy combines the enthalpy and entropy contributions
Use Kelvin and match the energy units before subtracting.
ΔG° = ΔH° - TΔS°. T is absolute temperature in K. If ΔH is in kJ mol-1 and ΔS in J mol-1 K-1, divide the entropy by 1000 first. At constant temperature and pressure, a negative actual ΔG favours the forward process; zero corresponds to equilibrium; a positive value favours the reverse process.
The standard value ΔG° assesses the driving tendency from standard-state conditions. A negative standard value is often described as thermodynamically feasible or spontaneous under standard conditions. It does not promise that all reactant turns into product, that the change is fast, or that the same direction remains favoured at every composition.
Worked example
An endothermic process can be favourable
For a process, ΔH° = +36.0 kJ mol-1 and ΔS° = +120 J mol-1 K-1. Calculate ΔG° at 298 K and 350 K, treating these values as temperature-independent.
- Convert entropy to +0.120 kJ mol-1 K-1.
- At 298 K: delta G = 36.0 - 298(0.120) = +0.24 kJ mol-1.
- At 350 K: delta G = 36.0 - 350(0.120) = -6.00 kJ mol-1.
Slightly unfavourable at 298 K and favourable at 350 K under standard conditions. The larger entropy contribution at higher temperature outweighs the positive enthalpy change.
Spontaneous does not mean rapid, complete or condition-independent
Use a sign table for temperature trends, then state what the calculation cannot decide.
| ΔH | ΔS | When ΔG is negative |
|---|---|---|
| Negative | Positive | At all temperatures within the range where these signs and phases apply. |
| Positive | Negative | At no positive temperature under this approximation. |
| Negative | Negative | At sufficiently low temperature; the positive -T delta S term grows on heating. |
| Positive | Positive | At sufficiently high temperature; the negative -T delta S term becomes dominant. |
If ΔH and ΔS have the same sign, solve T = ΔH/ΔS for the crossover where ΔG = 0, using consistent units. For the +36.0 kJ mol-1, +120 J mol-1 K-1 example, T = 300 K. The direction of the inequality depends on the signs: positive/positive is favourable above the crossover; negative/negative below it.
| Limit | What to say |
|---|---|
| Kinetics | A large activation barrier can make a favourable reaction immeasurably slow; a catalyst changes the rate, not the endpoint free-energy difference. |
| Non-standard composition | Actual concentrations and partial pressures affect the driving tendency. Standard delta G is not the actual delta G at every composition. |
| Extent | A favourable forward tendency does not mean 100% conversion; equilibrium composition matters. |
| Temperature range and phase | Enthalpy and entropy vary with temperature, and a phase change can invalidate a simple extrapolation. |
Check your understandingA conversion is thermodynamically favourable, yet no change is seen over a lesson. Is the free-energy calculation necessarily wrong?Think it through, then reveal the answer
Quick revision
Revisit the essentials, then return to an explanation when you need it.
Heat gained by the solution is heat lost by the reaction. Hess cycles require identical endpoint states. Bond-energy estimates use gaseous bonds broken minus gaseous bonds formed. The syllabus lattice energy is negative for lattice formation; dissolution uses its reverse plus hydration.
ΔG° = ΔH° - TΔS° with T in K and matching units. Heating favours processes with positive ΔS. A negative standard free-energy change indicates a thermodynamic tendency under standard conditions, not a guaranteed fast or complete reaction.
Scope and references
Learning outcomes and sources
7. Chemical Energetics: Thermochemistry and Thermodynamics. Use the outcome map to find the explanation for a particular syllabus requirement.
See the learning outcome map
7(a) Explain heat changes through bond breaking and formation.
- Exothermic: negative delta H
- Endothermic: positive delta H
- Breaking absorbs and forming releases energy
7(b) Construct and interpret reaction energy profiles.
- Reaction enthalpy
- Forward/reverse activation energies
- Reaction progress is not time
7(c) Define the specified enthalpy terms and standard conditions.
- (i) Reaction, formation, combustion, hydration, solution, neutralisation, atomisation
- (ii) Positive bond-breaking energy
- (iii) Negative lattice energy for gaseous ions forming solid
An enthalpy value belongs to an exact equation and set of statesBuild an ionic solid through gaseous atoms and ions
7(d) Calculate enthalpy from experimental heat measurements.
- q = mc delta T
- Reaction amount and sign
- Appropriate heat-capacity and measurement assumptions
The thermometer measures the surroundings, not the reaction directly
7(e) Explain lattice-energy magnitudes qualitatively.
- Ionic charges
- Ionic radii
- Limits of simple electrostatic comparison
7(f) Construct Hess and Born-Haber cycles and calculate energies.
- Ionisation energies and electron affinities
- (i) Indirect enthalpies, including formation from combustion
- (ii) Simple ionic solid formation and aqueous solution
- (iii) Average bond energies
Hess Law compares routes with identical endpointsBuild an ionic solid through gaseous atoms and ions
7(g) Explain entropy.
- Energy dispersal and accessible microscopic arrangements
Entropy describes how widely energy and particles can be distributed
7(h) Explain qualitative effects on system entropy.
- (i) Temperature
- (ii) Phase
- (iii) Particle numbers, especially gases
- No quantitative microstate treatment required
Entropy describes how widely energy and particles can be distributed
7(i) Predict the sign of an entropy change.
- Processes and reactions
- Dominant phase/gas changes and limits of simple rules
Entropy describes how widely energy and particles can be distributed
7(j) Use the standard Gibbs-energy equation.
- delta G = delta H - T delta S
- Kelvin and consistent units
- No calculation of reaction delta S from absolute standard entropies required
7(k) Infer spontaneity from the sign of Gibbs energy.
- Negative, zero and positive signs
- Standard-state scope
7(l) Explain limits of standard Gibbs-energy predictions.
- Rate versus feasibility
- Non-standard conditions and equilibrium extent
- Temperature/phase assumptions
Spontaneous does not mean rapid, complete or condition-independent
7(m) Predict how temperature changes spontaneity.
- All four enthalpy/entropy sign combinations
- Crossover temperature with stated approximations
Spontaneous does not mean rapid, complete or condition-independent
- SEAB H2 Chemistry 9476, examination 2026
Topic 7, printed pages 18-19. All 13 lettered outcomes, named enthalpies, three Hess-cycle applications, entropy variables and stated exclusions inspected.
- Grail: RI Chemical Energetics I, 2022
Pages 4-5 visually inspected for energy-level and profile conventions. The numerical construction example is original. This older resource informs presentation only; current 9476 defines scope and feasibility language.