Enthalpy Changes and Hess's Law

Enthalpy change

Enthalpy change (ΔH) is the heat energy transferred at constant pressure.

• Exothermic: releases heat, ΔH is negative (products lower in energy).
• Endothermic: absorbs heat, ΔH is positive (products higher in energy).

Standard conditions (⦵): 100 kPa, 298 K, solutions at 1 mol dm⁻³.

Key definitions

• Enthalpy of formation (ΔHf⦵): one mole of a compound formed from its elements in their standard states.
• Enthalpy of combustion (ΔHc⦵): one mole of a substance completely burned in oxygen.
• Enthalpy of reaction, neutralisation, atomisation — defined similarly, per mole.

Calorimetry

Measure enthalpy changes experimentally using:

q = m c ΔT

where q = heat energy (J), m = mass of solution (g), c = specific heat capacity (4.18 J g⁻¹ K⁻¹ for water), ΔT = temperature change. Divide by moles to get ΔH per mole. Heat loss to the surroundings makes measured values less exothermic than true values.

Hess's law

Hess's law: the total enthalpy change of a reaction is independent of the route taken, depending only on the initial and final states. This lets us calculate ΔH values that are hard to measure directly, using an enthalpy cycle.

• Using enthalpies of formation:

ΔH reaction = Σ ΔHf(products) − Σ ΔHf(reactants)

• Using enthalpies of combustion:

ΔH reaction = Σ ΔHc(reactants) − Σ ΔHc(products)

(note the reversed order compared with formation).

Bond enthalpies

The mean bond enthalpy is the energy to break one mole of a bond, averaged over different molecules.

ΔH = Σ(bonds broken) − Σ(bonds made)

Breaking bonds is endothermic; making bonds is exothermic. Values are averages, so bond-enthalpy answers are approximate.

Worked example

Given ΔHc: methane = −890, hydrogen = −286, and carbon = −394 kJ mol⁻¹, use Hess's law (combustion route) to find ΔHf of methane (C + 2H₂ → CH₄).

ΔHf = Σ ΔHc(reactants) − Σ ΔHc(products)
    = [(−394) + 2(−286)] − (−890)
    = (−966) − (−890) = −76 kJ mol⁻¹

✓

Common mistakes

• Getting the Hess's law direction wrong — formation: products − reactants; combustion: reactants − products.
• Forgetting to multiply by the number of moles/bonds in the balanced equation.
• Using q = mcΔT with the wrong mass (use the mass of the solution, not the solute).

Exam tips

• Draw a clear Hess cycle with arrows for the direct and indirect routes.
• State that bond enthalpies give approximate answers (mean values).
• Explain heat loss as the reason experimental values differ from data-book values.

Key facts to remember

• ΔH negative = exothermic, positive = endothermic; measured via q = mcΔT.
• Hess's law: ΔH is route-independent. Formation route = products − reactants; combustion route = reactants − products.
• Bond enthalpy ΔH = bonds broken − made (approximate, uses mean values).