Hess's law and enthalpy cyclesEdexcel International A Level Chemistry: Revision notes
Section 1
Hess's law
Hess's law: the total enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions (and states) are the same.
This is a consequence of the conservation of energy: if two routes gave different values, energy could be created by going round a cycle.
It matters because many enthalpy changes (such as the formation of methane from carbon and hydrogen) cannot be measured directly. They can be calculated from values that can be measured.
Section 2
Cycles from enthalpy changes of formation
The route via the elements: reactants → elements → products.
ΔrH = Σ ΔfH(products) – Σ ΔfH(reactants)
Worked example: CaCO₃(s) → CaO(s) + CO₂(g) ΔfH: CaCO₃ –1207, CaO –635, CO₂ –394 kJ mol⁻¹. ΔrH = (–635 – 394) – (–1207) = +178 kJ mol⁻¹.
Multiply each ΔfH by the number of moles in the equation. Elements in their standard states have ΔfH = 0.
Subtracting the wrong way round. For formation data it is products minus reactants.
Section 3
Cycles from enthalpy changes of combustion
The route via the combustion products: reactants and products can both be burned to the same products.
ΔrH = Σ ΔcH(reactants) – Σ ΔcH(products)
Worked example: C₂H₄ + H₂ → C₂H₆ ΔcH: C₂H₄ –1411, H₂ –286, C₂H₆ –1560 kJ mol⁻¹. ΔrH = (–1411 – 286) – (–1560) = –137 kJ mol⁻¹.
For combustion data it is reactants minus products, the opposite of the formation rule.
Draw the cycle first: the arrows show which way each ΔH goes, so you do not need to memorise which way round to subtract.
Section 4
Cycles from other reaction data
Any set of reactions that link the same starting and finishing materials can be used. Write each equation with its ΔH, then add or reverse equations (reversing changes the sign; multiplying changes the size) until they sum to the target equation.
Example: to find ΔfH of MgO from ΔH₁ (Mg + 2HCl) and ΔH₂ (MgO + 2HCl) and ΔfH of H₂O:
ΔfH(MgO) + ΔH₂ = ΔH₁ + ΔfH(H₂O)
Section 5
Core Practical 2: using Hess's law to find an enthalpy change
Because the enthalpy change of formation of magnesium oxide cannot be measured directly, two reactions with excess hydrochloric acid are measured:
- Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)
- MgO(s) + 2HCl(aq) → MgCl₂(aq) + H₂O(l)
Method for each: measure a known volume of excess acid into a polystyrene cup, record the temperature, add a weighed mass of the solid, stir and record the temperature. Use a cooling-curve correction if needed. Then q = mcΔT and ΔH = –q ÷ n (n = moles of the solid, which is limiting).
Combine with ΔfH(H₂O) = –286 kJ mol⁻¹: ΔfH(MgO) = ΔH₁ + ΔfH(H₂O) – ΔH₂ ≈ –607 kJ mol⁻¹.
Sources of error: heat loss, an oxide layer on the magnesium ribbon, and the assumption that the solution has the properties of water.
Use the same volume of the same acid in both experiments so the results can be combined fairly.
Must Know
- Hess's law: ΔH independent of route; follows from conservation of energy
- Formation data: ΔrH = ΣΔfH(products) – ΣΔfH(reactants)
- Combustion data: ΔrH = ΣΔcH(reactants) – ΣΔcH(products)
- Multiply by moles in the equation; reverse a step = change sign
- Core Practical 2: Mg and MgO with excess HCl give ΔfH(MgO)
- Data must be at the same conditions and states
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Hess's law and enthalpy cycles
- A gas company wants the standard enthalpy change of formation of methane, CH₄(g). Carbon and hydrogen do not react to give pure methane in the laboratory, so the value must be found indirectly. The standard enthalpy changes of combustion are: C(graphite) –394 kJ mol⁻¹, H₂(g) –286 kJ mol⁻¹ and CH₄(g) –890 kJ mol⁻¹, with CO₂(g) and H₂O(l) as the products.Explain why Hess's law is used to find the enthalpy change of formation of methane rather than measuring it directly.2 marks
- A cement works heats limestone in a kiln: CaCO₃(s) → CaO(s) + CO₂(g). The standard enthalpy changes of formation are: CaCO₃(s) –1207 kJ mol⁻¹, CaO(s) –635 kJ mol⁻¹ and CO₂(g) –394 kJ mol⁻¹. (Ar: Ca = 40.0, C = 12.0, O = 16.0.)Calculate the energy transferred when 250 g of calcium carbonate is decomposed in the kiln, and state whether it is taken in or given out.2 marks
- A student determines the standard enthalpy change of formation of magnesium oxide, which cannot be measured directly. She measures the enthalpy change for two reactions with excess hydrochloric acid: (1) Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g), ΔH₁ = –467 kJ mol⁻¹; and (2) MgO(s) + 2HCl(aq) → MgCl₂(aq) + H₂O(l), ΔH₂ = –146 kJ mol⁻¹. The standard enthalpy change of formation of H₂O(l) is –286 kJ mol⁻¹.Describe how the student finds the enthalpy change for reaction 2 in a laboratory experiment.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).