Core Definitions and Sign Convention

🟢 Lite — Quick Review (1h–1d)

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Topic 10: Chemical Energetics — the study of heat changes in physical changes, chemical reactions, and the formation of ionic and covalent bonds. Enthalpy change (ΔH) measures heat exchanged at constant pressure; exothermic reactions give ΔH < 0, endothermic reactions give ΔH > 0, both expressed in kJ mol⁻¹.

Calorimetry formula: q = mcΔT, where q = heat (J), m = mass of water/solution (g), c = specific heat capacity (4.2 J g⁻¹ K⁻¹), ΔT = temperature change (K).
Molar enthalpy: ΔH = mcΔT / n, with n = moles of limiting reactant.
Hess’s Law (path-independence): ΔH(overall) = ΔH₁ + ΔH₂ + ΔH₃.
Standard formation: ΔH°reaction = Σ ΔH°f(products) − Σ ΔH°f(reactants).
Bond-energy estimate: ΔH = Σ BE(broken) − Σ BE(formed).

🟡 Standard — Regular Study (2d–2mo)

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Core Definitions and Sign Convention

Enthalpy (H) is the heat content of a system at constant pressure. The change ΔH = H(products) − H(reactants). A reaction that releases heat to the surroundings has H(products) < H(reactants), giving a negative ΔH (exothermic). Melting ice, photosynthesis, and the thermal decomposition of calcium carbonate are endothermic (+ΔH); combustion of fuels and neutralisation of strong acid by strong base are exothermic (−ΔH).

Calorimetry: From Temperature Rise to ΔH

In a simple polystyrene-cup calorimeter, the heat released by the reaction warms a known mass of water. Use q = mcΔT, then divide by the moles of limiting reagent to obtain ΔH in kJ mol⁻¹. A reaction mixture of 50 cm³ of 1.0 mol dm⁻³ HCl with 50 cm³ of 1.0 mol dm⁻³ NaOH, with ΔT = +6.8 K, gives:

mass ≈ 100 g, c = 4.2 J g⁻¹ K⁻¹ → q = 100 × 4.2 × 6.8 = 2856 J ≈ 2.86 kJ
moles of water formed = 0.050 mol → ΔH = −2.86 / 0.050 = −57.1 kJ mol⁻¹

Compare this with the accepted standard value of −57.3 kJ mol⁻¹; the small shortfall reflects heat loss to the surroundings.

Hess’s Law and Bond Energies

Because enthalpy is a state function, ΔH depends only on initial and final states, not the route. This is the basis of Hess’s Law, allowing calculation of an indirect enthalpy change by summing stepwise ΔH values along any convenient pathway.

Mnemonic for Hess cycles: “Products minus Reactants” — always subtract the enthalpy of the starting materials from that of the final materials.

For gas-phase reactions, estimate ΔH from mean bond energies using bonds broken minus bonds formed. Mean values are averages across many compounds, so results are approximate (typically within ±10 kJ mol⁻¹).

Quantity	Symbol	Typical Sign (kJ mol⁻¹)
Enthalpy of combustion	ΔH°c	Negative (exothermic)
Enthalpy of formation	ΔH°f	Compound-dependent
Bond dissociation energy	BE	Positive (always endothermic)
Electron affinity	EA	Negative for halogens

Exam Pattern for UNEB UACE

Paper 1 carries 1–2 structured questions (6–8 marks) on this topic. Expect (a) a calorimetry calculation, (b) an enthalpy profile diagram showing Eₐ (activation energy) and ΔH, and (c) a Hess’s Law cycle drawing. Use correct state symbols (g, l, s, aq) — they are compulsory in UACE cycles.

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The Born–Haber Cycle for Ionic Solids

The Born–Haber cycle applies Hess’s Law to the formation of an ionic crystal from its elements in their standard states. For NaCl(s):

Na(s) + ½Cl₂(g) → NaCl(s) ΔH°f

The cycle decomposes this into: sublimation of Na(s) → Na(g) (ΔH_sub), ionisation to Na⁺(g) (+IE), atomisation of ½Cl₂ → Cl(g) (+½ D(Cl–Cl)), electron affinity of Cl (EA, negative), and finally lattice formation (ΔH_latt, large and negative).

Applying Hess’s Law around the cycle:

ΔH°f = ΔH_sub + ½D(Cl–Cl) + IE(Na) + EA(Cl) + ΔH_latt

For MgO the cycle is doubled (Mg²⁺ requires 2×IE; O²⁻ requires 2×EA and a large endothermic step for O(g) + 2e⁻ → O²⁻(g)). The lattice enthalpy of MgO (~~−3850 kJ mol⁻¹) dwarfs that of NaCl (~~−787 kJ mol⁻¹) because lattice energy scales with the product of ionic charges and inversely with ionic radius.

Trends in Lattice Energy

Charge increases → lattice energy rises sharply (NaCl < MgO < Al₂O₃).
Radius increases → lattice energy falls (NaCl > KCl > RbCl).
Polarising cations (small, high charge) distort anions, adding covalent character and reducing measured lattice energy compared with the purely ionic model.

Connection to Bonding and Periodicity

This topic links directly to Period 3 oxide acid–base behaviour (Topic on s-Block/p-Block), where the exothermic lattice energy of MgO is offset by endothermic atomisation and ionisation terms, giving an overall negative ΔH°f. It also bridges to electrochemistry, since ΔH values feed directly into entropy and Gibbs free-energy calculations: ΔG = ΔH − TΔS.

Common Mistakes in UACE Scripts

Sign reversal on combustion data: when using ΔH°c in a Hess cycle for a formation problem, reverse the equation and flip the sign.
Forgetting the ½ factor for diatomic molecules in atomisation steps (½ O₂ → O, not O₂ → 2O gives ΔH_atom).
Treating bond-energy ΔH as exact — examiners accept ±10 kJ mol⁻¹ tolerance; do not write answers to 4 sig figs.
Drawing activation energy as if it were the same as ΔH — Eₐ is the peak of the profile; ΔH is the net difference between reactants and products.

Practice Prompts

A 1.20 g sample of methanol (CH₃OH, M = 32 g mol⁻¹) raised the temperature of 250 g of water from 22.4 °C to 36.7 °C in a calorimeter. Calculate the standard enthalpy of combustion of methanol in kJ mol⁻¹, stating one assumption made.
Using ΔH°f values (C₂H₅OH(l) = −277, CO₂(g) = −394, H₂O(l) = −286 kJ mol⁻¹), determine ΔH°c of ethanol and comment on how your answer would differ from the experimental calorimetric value.

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Core Definitions and Sign Convention