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1.2.2—Hess's law

Syllabus
First assessment 2025
Objective
1.2.2
Level
HL

Hess's Law

Hess's law states that enthalpy change is independent of reaction pathway. Enthalpy values can therefore be combined through a balanced cycle.

Reverse an entire balanced equation by changing the sign of ΔH; scale every coefficient and ΔH by the same factor; then add equations and cancel identical species in identical physical states. Never change a chemical subscript, formula or state symbol merely to force cancellation. The surviving equation must exactly match the target before enthalpies are summed.

Treat chemical equations like algebra: reverse a step and reverse its ΔH sign; multiply all coefficients and ΔH by the same factor; then add and cancel species. The surviving overall equation must exactly match the target before the enthalpies are summed.

Worked example — Hess's law: target C(s)X2+HX2(g)X1+/2 OX2(g)→CHX3OH(l)\ce{C(s)+2H2(g)+1/2O2(g)->CH3OH(l)}. Use CX+OX2→COX2\ce{C+O2->CO2}, ΔH=−394 kJ mol−1\Delta H=-394\,\mathrm{kJ\,mol^{-1}}; double HX2X+1/2 OX2→HX2O(l)\ce{H2+1/2O2->H2O(l)} to give −572 kJ mol−1-572\,\mathrm{kJ\,mol^{-1}}; reverse methanol combustion to give +726 kJ mol−1+726\,\mathrm{kJ\,mol^{-1}}. After cancelling COX2\ce{CO2} and HX2O\ce{H2O}, ΔH=−394−572+726=−240 kJ mol−1\Delta H=-394-572+726=-240\,\mathrm{kJ\,mol^{-1}} for the target equation.

Solving Hess Cycles

Assessment in practice

Representative question

Question 1

[Maximum number: 1]

Determine the enthalpy change, ΔH\Delta H, in kJmol−1\mathrm{kJ} \mathrm{mol}^{-1}, for the hydration of solid anhydrous magnesium sulfate, MgSO4\mathrm{MgSO}_{4}.

Energy Cycles Summary

Retrieve the route: count bond breaking/forming, manipulate Hess equations, define standard formation/combustion values, apply product–reactant sums, and track every Born–Haber energy term.

Check equation direction, coefficients, signs, standard states, lattice enthalpy convention, and one-versus-two-electron steps.