Hess’s Law and Enthalpy Cycles

A concise revision guide to Hess’s law: building enthalpy cycles, calculating enthalpy changes from formation and combustion data, and using unfamiliar cycles, for AQA A Level Chemistry.

Paper 1 and 2 AQA

3.1.4 Energetics

7405/1 and 7405/2

Written by:
Dr. Mohammed Al-Fatah

Chemistry specialist revision notes for A Level Chemistry.

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Hess’s Law

Hess’s law states that the total enthalpy change for a reaction is independent of the route taken, provided the starting and finishing conditions are the same. It follows from the conservation of energy: if two routes between the same reactants and products gave different energy changes, energy could be created by going round the cycle.

This allows enthalpy changes that cannot be measured directly, such as the enthalpy change of formation of methane or the hydration of an anhydrous salt, to be calculated from values that can be measured.

Definition: Hess’s law: the enthalpy change for a reaction is independent of the route taken from reactants to products.

Building an Enthalpy Cycle

An enthalpy cycle links the reaction you want to a set of reactions whose enthalpy changes are known. Draw the target reaction across the top, then an alternative route through a common intermediate.

Write the balanced target equation across the top with an arrow labelled with the unknown ΔH.
Choose the connecting species: the elements when you have enthalpies of formation, or the combustion products when you have enthalpies of combustion.
Draw arrows from each side to the connecting box and label them with the known values, multiplied by the number of moles in the equation.
Go round the cycle the long way: follow an arrow and add its value; go against an arrow and subtract it.

[IMAGE NEEDED: SHARED FIGURE, used on all five boards, draw once: a formation cycle (elements in a box at the bottom, arrows up) beside a combustion cycle (CO₂ and H₂O in a box at the bottom, arrows down) for the same reaction]

Formation arrows point up from the elements; combustion arrows point down to the combustion products. The direction decides whether each value is added or subtracted.

Exam focus: Show the cycle and the working. A correct final answer with no cycle scores less than a cycle with one arithmetic slip.

Using Enthalpy Changes of Formation

When the data are enthalpy changes of formation, the cycle reduces to one rule:

Δ_rH^⦵ = ΣΔ_fH^⦵(products) − ΣΔ_fH^⦵(reactants)

Worked example. Calculate the enthalpy change for the thermal decomposition of sodium hydrogencarbonate.

2NaHCO₃(s) → Na₂CO₃(s) + H₂O(l) + CO₂(g)

Substance	Δ_fH^⦵ / kJ mol⁻¹
NaHCO₃(s)	−951
Na₂CO₃(s)	−1131
H₂O(l)	−286
CO₂(g)	−394

ΣΔ_fH^⦵(products) = −1131 + (−286) + (−394) = −1811 kJ mol⁻¹
ΣΔ_fH^⦵(reactants) = 2 × (−951) = −1902 kJ mol⁻¹
Δ_rH^⦵ = −1811 − (−1902) = +91 kJ mol⁻¹

Common mistake: Forgetting to multiply by the coefficient (2 × NaHCO₃) or giving elements a non-zero value. Elements in their standard states have an enthalpy change of formation of zero.

Using Enthalpy Changes of Combustion

When the data are enthalpy changes of combustion, the arrows point the other way, so the rule is reversed:

Δ_rH^⦵ = ΣΔ_cH^⦵(reactants) − ΣΔ_cH^⦵(products)

Worked example. Calculate the enthalpy change of formation of propane from the enthalpies of combustion of carbon (−394), hydrogen (−286) and propane (−2220 kJ mol⁻¹).

3C(s) + 4H₂(g) → C₃H₈(g)

ΣΔ_cH^⦵(reactants) = 3 × (−394) + 4 × (−286) = −1182 − 1144 = −2326 kJ mol⁻¹
ΣΔ_cH^⦵(products) = −2220 kJ mol⁻¹
Δ_fH^⦵(C₃H₈) = −2326 − (−2220) = −106 kJ mol⁻¹

This is exactly the kind of value that cannot be measured directly, because carbon and hydrogen do not react to give propane alone.

Key idea: Formation: products minus reactants. Combustion: reactants minus products. If you draw the cycle, you never need to remember which.

Unfamiliar Cycles and Practical Hess

Exam questions often give a cycle you have not seen before. The method does not change: identify the route, follow the arrows, reverse the sign of any step you travel against, and multiply by the moles.

A classic practical use is finding the enthalpy change for the hydration of anhydrous copper(II) sulfate, CuSO₄(s) + 5H₂O(l) → CuSO₄·5H₂O(s), which cannot be measured directly because the solid cannot be given exactly five moles of water without dissolving. Instead, the enthalpy changes of solution of the anhydrous and hydrated salts are measured separately, and Hess’s law combines them.

Hess’s law applied in the laboratory: two measurable enthalpy changes of solution give the hydration enthalpy that cannot be measured directly.

Exam sentence: The enthalpy change cannot be measured directly, so Hess’s law is used: the enthalpy changes of two reactions that can be measured are combined, because the total enthalpy change is independent of the route.

Common Exam Points

State Hess’s law

The enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same.

Calculate an enthalpy change from formation data

Products minus reactants, each multiplied by its coefficient; elements count as zero.

Calculate an enthalpy change from combustion data

Reactants minus products, each multiplied by its coefficient.

Explain why a value must be found indirectly

The reaction does not happen cleanly on its own, or gives other products, so it cannot be measured by experiment.

Check Your Understanding

Use cycles for reactions and data that do not appear in the worked examples.

FAQs

Use these quick answers to check the Hess’s law methods AQA questions test.

What does Hess’s law say?

The enthalpy change for a reaction is independent of the route taken, provided the starting and finishing conditions are the same.

When do I use products minus reactants?

When the data are enthalpy changes of formation, because the arrows point up from the elements to both sides.

When do I use reactants minus products?

When the data are enthalpy changes of combustion, because the arrows point down from both sides to carbon dioxide and water.

What happens to the sign when I go against an arrow?

It is reversed. Going against a step is the reverse reaction, so its enthalpy change has the opposite sign.

Why use Hess cycles at all?

Many enthalpy changes cannot be measured directly because the reaction does not happen cleanly, so they are calculated from values that can be measured.

Copyright and author footprint: This OLS revision page was written for Online Learning System by Dr. Mohammed Al-Fatah. It is designed for A Level Chemistry revision and should not be copied or redistributed without permission.