Chemical Energetics: Hess's Law and Enthalpy Cycles

This guide covers Topic 5, Chemical energetics, subtopics 5.1 and 5.2, from Cambridge International AS & A Level Chemistry 9701, 2025–2027 series. This is AS Level content. It does not cover lattice energy, Born–Haber cycles, entropy or Gibbs free energy — those sit in Topic 23, A Level content, and are out of scope here.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL CHEMISTRY 9701 — AS Level, Topic 5

5.1 Enthalpy change, ΔH — that reactions are exothermic (ΔH negative) or endothermic (ΔH positive); constructing and interpreting reaction pathway diagrams showing enthalpy change and activation energy; standard conditions (298 K, 101 kPa, shown by the symbol ⦵) and standard enthalpy change of reaction, formation, combustion and neutralisation; that energy transfers occur because of bond breaking and bond making; using bond energies to calculate enthalpy change of reaction; that some bond energies are exact and some are averages; calculating enthalpy change from experimental results using q = mcΔT and ΔH = −mcΔT/n.

5.2 Hess’s law — applying Hess’s law to construct simple energy cycles; carrying out calculations using cycles and relevant energy terms, including determining enthalpy changes that cannot be found by direct experiment, and using bond energy data.

Standard enthalpy changes

An enthalpy change is measured under standard conditions — 298 K and 101 kPa — denoted by the ⦵ symbol. Four named standard enthalpy changes appear throughout AS and A Level energetics:

• ΔHr⦵, enthalpy change of reaction — for the reaction as written, in the molar quantities shown by the equation.
• ΔHf⦵, enthalpy change of formation — one mole of a compound formed from its elements in their standard states.
• ΔHc⦵, enthalpy change of combustion — one mole of a substance burned completely in oxygen.
• ΔHneut⦵, enthalpy change of neutralisation — formation of one mole of water from the reaction of an acid and a base.

Combustion and neutralisation are always exothermic; formation and reaction enthalpies can be either.

Bond energy calculations

Breaking a bond always requires energy (endothermic, ΔH positive); forming a bond always releases energy (exothermic, ΔH negative). The overall enthalpy change of a reaction is:

ΔHr = (sum of bond energies broken) − (sum of bond energies formed)

Worked example. Calculate the enthalpy change for H₂(g) + Cl₂(g) → 2HCl(g), given bond energies H–H = +436 kJ/mol, Cl–Cl = +243 kJ/mol, H–Cl = +432 kJ/mol.

Bonds broken:  1 × H-H + 1 × Cl-Cl = 436 + 243 = +679 kJ/mol
Bonds formed:  2 × H-Cl = 2 x 432 = +864 kJ/mol
ΔHr = 679 - 864 = -185 kJ/mol

The reaction is exothermic, ΔHr = −185 kJ/mol — bond energy values are always quoted as positive (the energy needed to break that bond), and the sign of the final answer comes from the subtraction, not from the individual values. Bond energies from a data book are usually averages across many compounds containing that bond, not exact values for the specific molecule in the question — which is precisely why a bond-energy calculation and an experimental enthalpy change for the same reaction rarely agree exactly.

Calculating from experimental data

For a reaction carried out in solution, the heat released or absorbed is calculated from the temperature change of the solution, then converted to an enthalpy change per mole:

q = mcΔT
ΔH = -mcΔT / n

where q is heat energy transferred (J), m is the mass of solution heated or cooled (g), c is the specific heat capacity (usually taken as 4.18 J g⁻¹ K⁻¹ for dilute aqueous solutions), ΔT is the temperature change (K), and n is the number of moles of the limiting reactant. The negative sign in the ΔH expression reflects that a temperature rise in the surroundings (the solution) means the reaction itself released energy — ΔH is negative for the exothermic reaction even though ΔT is positive.

Hess’s law

Hess’s law states that the total enthalpy change for a reaction is the same regardless of the route taken between reactants and products, provided the start and end conditions are the same. This makes it possible to find an enthalpy change that can’t be measured directly, by connecting it through enthalpy changes that can.

Worked example. Find ΔHf⦵ for methane, CH₄(g), given:

ΔHc(C, graphite) = -394 kJ/mol
ΔHc(H2) = -286 kJ/mol
ΔHc(CH4) = -890 kJ/mol

The formation reaction is C(graphite) + 2H₂(g) → CH₄(g). Route 1 (direct formation) and Route 2 (via combustion of the elements, then combustion of methane in reverse) must give the same overall enthalpy change:

Route 1: ΔHf(CH4)
Route 2: [ΔHc(C) + 2 x ΔHc(H2)] - ΔHc(CH4)
       = [(-394) + 2(-286)] - (-890)
       = [-394 - 572] - (-890)
       = -966 + 890
       = -76 kJ/mol

ΔHf⦵(CH₄) = −76 kJ/mol. This is the standard “combustion cycle” pattern: when the data given are combustion enthalpies, the cycle is built with the elements and target compound at the top, and their combustion products at the bottom, because every substance in the cycle can reach the same combustion products by a measurable route.

Common mistakes

• Getting the sign wrong in a combustion-data Hess cycle. The route through combustion products is subtracted, not added, because it runs in the reverse direction to formation.
• Forgetting that bond energies must be broken down per bond, not per molecule. H₂ has one H–H bond; O₂ has one O=O bond — miscounting bonds is the single most common arithmetic error in this topic.
• Treating bond-energy answers as if they were exact. Averaged bond energies give a good estimate, not the precise experimental value.
• Omitting the negative sign in ΔH = −mcΔT/n, which produces an enthalpy change with the wrong sign for an otherwise correct calculation.
• Confusing enthalpy of formation and enthalpy of combustion as data sources in a cycle — check which one the question actually gives before drawing the cycle.

Quick revision checklist

• The four standard enthalpy changes: reaction, formation, combustion, neutralisation, and standard conditions (298 K, 101 kPa)
• Reaction pathway diagrams showing ΔH and activation energy
• Bond energy calculations: bonds broken minus bonds formed, and why averaged values don’t match experiment exactly
• q = mcΔT and ΔH = −mcΔT/n for experimental data
• Hess’s law: constructing a cycle and choosing the correct route direction
• Both cycle patterns: from enthalpies of formation, and from enthalpies of combustion

Related resources

• Formulae, Equations and the Mole — mole calculations used throughout this topic
• Atoms, Molecules and Stoichiometry at AS — the previous AS topic
• Chemical Bonding: Shapes and Intermolecular Forces — bond energy used qualitatively there, quantitatively here
• Chemical Energetics: Lattice Energy, Entropy and Gibbs Free Energy — the A Level topic that continues this one
• Cambridge AS & A Level Chemistry hub

Written against Cambridge International AS & A Level Chemistry 9701, 2025–2027 series. Always check the current syllabus for your examination year.