5.2 Hess’s law
- Syllabus
- 9701–2028–2029
- Topic
- 5.2
- Level
- AS
Learning objectives
5.2.1Hess’s law to construct simple energy cycles• Apply Hess’s law to construct simple energy cycles5.2.2Calculations: cycles and relevant energy terms• Carry out calculations using cycles and relevant energy terms, including:: (a) determining enthalpy changes that cannot be found by direct experiment; (b) use of bond energy data
Construct a Hess cycle around one common intermediate state
Hess’s law states that the enthalpy change between fixed initial and final states is independent of the route taken. A cycle is valid only when every route begins and ends with the same substances, amounts and physical states.
| Available data | Useful common state for the cycle | Direction of known arrows |
|---|---|---|
| enthalpies of formation | constituent elements in their standard states | elements → compounds |
| enthalpies of combustion | common complete-combustion products, usually CO₂ and H₂O | substances → combustion products |
| bond energies | separated gaseous atoms | molecules → atoms for breaking; atoms → molecules for forming |
Write the balanced target equation across the top. Place the common intermediate state below or above it with the same total atoms, add known arrows in their defined directions, then label every arrow with its enthalpy change and coefficient. The two routes around the completed cycle must have equal total ΔH.
Treat chemical equations and enthalpy changes together: reversing an equation reverses the sign of ΔH; multiplying an equation multiplies ΔH by the same factor. Species that are unchanged on both sides must cancel before the remaining equation is accepted as the target.
The page layout does not determine plus or minus. Arrow direction, equation direction, coefficients and physical states do. Never draw a cycle first and then attach numbers without checking which chemical change each arrow actually represents.
Use signed routes to calculate inaccessible and bond-energy enthalpies
Choose one direction around the cycle from target reactants to target products. Add values when travelling with their defined arrows and subtract when travelling against them; equivalently, reverse and scale the known equations until they add to the target equation.
| Data set | Shortcut derived from the cycle |
|---|---|
| standard formation enthalpies | ΔHᵣ⦵ = ΣνΔHf⦵(products) − ΣνΔHf⦵(reactants) |
| standard combustion enthalpies | ΔHᵣ⦵ = ΣνΔHc⦵(reactants) − ΣνΔHc⦵(products) |
| bond energies | ΔHᵣ ≈ ΣE(bonds broken) − ΣE(bonds formed) |
The direct formation C(s) + 2H₂(g) → CH₄(g) is not conveniently measured. Combustion data give C: −394, H₂: −286 and CH₄: −890 kJ mol⁻¹. Both routes end at CO₂(g) + 2H₂O(l), so ΔH + (−890) = −394 + 2(−286), giving ΔH = −76 kJ mol⁻¹.
For H₂(g) + Cl₂(g) → 2HCl(g), using H–H 436, Cl–Cl 243 and H–Cl 431 kJ mol⁻¹, the gaseous-atom route gives ΔHᵣ ≈ (436 + 243) − 2(431) = −183 kJ mol⁻¹. Breaking to atoms is positive; forming product bonds is the reverse and therefore releases energy.
Finish by adding the manipulated equations: every intermediate must cancel and the result must reproduce the target equation exactly. A plausible sign is not proof; coefficients, state symbols and arrow directions are the decisive checks.