Mini-Lesson

Energy cycles, entropy and spontaneity (AHL)

This Additional Higher Level mini-lesson covers Reactivity 1.2 & 1.4: Born-Haber cycles and lattice enthalpy, entropy, and Gibbs energy and spontaneity.

Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. Press Start when you're ready.

AHL — Reactivity 1.2

Born-Haber cycles

A Born-Haber cycle applies Hess's law to ionic compounds, linking the enthalpy of formation to atomisation, ionisation energy, electron affinity and the lattice enthalpy — the energy to separate one mole of an ionic lattice into gaseous ions.

AHL — Reactivity 1.2

Lattice enthalpy trends

Lattice enthalpy is larger (more exothermic to form) when ions have higher charge and smaller radius — stronger electrostatic attraction. This also governs the enthalpies of solution and hydration in an energy cycle.

AHL — Reactivity 1.4

Entropy (S)

Entropy measures the number of ways energy and particles can be arranged. Gases have far more entropy than liquids or solids. For a reaction:

ΔS = ΣS(products) − ΣS(reactants)positive when disorder increases (e.g. more gas moles)

AHL calculate

Entropy change

1For N₂ + 3H₂ → 2NH₃, S°(N₂)=191.6, S°(H₂)=130.7, S°(NH₃)=192.8 J K⁻¹ mol⁻¹. Calculate ΔS (J K⁻¹ mol⁻¹).

J K⁻¹ mol⁻¹

ΔS = 2(192.8) − [191.6 + 3(130.7)] = 385.6 − 583.7.

AHL — Reactivity 1.4

Gibbs energy and spontaneity

The Gibbs energy change combines enthalpy and entropy:

ΔG = ΔH − TΔSspontaneous when ΔG < 0 (T in kelvin, ΔS in kJ K⁻¹ mol⁻¹)

Watch the units — convert ΔS from J to kJ before combining with ΔH.

AHL calculate

Gibbs energy

2For the same reaction ΔH = −92.2 kJ mol⁻¹ and ΔS = −198.1 J K⁻¹ mol⁻¹. Calculate ΔG at 298 K (kJ mol⁻¹).

kJ mol⁻¹

ΔG = ΔH − TΔS = −92.2 − 298 × (−0.1981).

AHL calculate

Crossover temperature

3Above what temperature (K) does ΔG become positive for this reaction? Use T = ΔH ÷ ΔS with ΔH = −92200 J and ΔS = −198.1 J K⁻¹.

K

T = ΔH ÷ ΔS = −92200 ÷ −198.1.

AHL check

Always spontaneous?

?Which combination makes a reaction spontaneous at ALL temperatures?

Sort it

Will it be spontaneous?

Tap a case, then when it is spontaneous.

✅ Spontaneous at all T

⛔ Never spontaneous

🌡️ Temperature dependent

Match it

Match the term to its expression

Tap an item on the left, then its match on the right.

Term

Expression

Recap

The big ideas to know

Born-Haber: Hess cycle giving lattice enthalpy; larger for higher charge, smaller ions

Entropy: ΔS = ΣS(products) − ΣS(reactants); + when more disorder/gas

Gibbs energy: ΔG = ΔH − TΔS; spontaneous when ΔG < 0

Crossover: T = ΔH ÷ ΔS gives where spontaneity switches

You've covered Energy cycles, entropy and spontaneity (AHL) for IB Diploma Chemistry HL. Press Finish to see your score.

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