5.2 Hess’s Law
Candidates should be able to:
- apply Hess’s Law to construct simple energy cycles
- carry out calculations using cycles and relevant energy terms, including:
- determining enthalpy changes that cannot be found by direct experiment
- use of bond energy data
You can’t set a match to a mountain path and measure how much height you “burn” — but you could measure the height at the start and the height at the end, however you got there. Enthalpy works the same way. Keep that in mind as you read Hess’s Law below.
1 Hess’s Law: The Principle
The law of conservation of energy states that energy cannot be created or destroyed — this is also known as the first law of thermodynamics. It applies just as much to chemical reactions as to anything else: the total energy of the chemicals and their surroundings must stay constant.
In 1840, the chemist Germain Hess applied this idea specifically to enthalpy changes, giving us:
“The enthalpy change accompanying a chemical change is independent of the route by which the chemical change occurs,” provided the initial and final conditions are the same.
In other words: it doesn’t matter whether reactants turn into products in one step, or via several intermediate steps — the overall enthalpy change is exactly the same either way, because enthalpy only depends on the initial and final states, not the path taken.
Why Hess’s Law matters: an enthalpy change you cannot measure directly
Some standard enthalpy changes simply cannot be found by direct experiment. A classic example is the standard enthalpy change of formation of carbon monoxide, ΔHf⦵(CO):
C(s) + ½O2(g) → CO(g)
This can’t be measured directly, because burning carbon in a limited supply of oxygen always produces a mixture of CO and CO2 — never pure CO. However, two related enthalpy changes can be measured directly by burning each substance in excess oxygen:
Calculate ΔHf⦵(CO) from the following data:
CO(g) + ½O2(g) → CO2(g) ΔH2 = −283.0 kJ mol−1
2 Enthalpy Change from Enthalpy Changes of Formation
Every compound can be related back to elements in their standard states via its standard enthalpy change of formation, ΔHf⦵. Because every reactant and every product can be “built” from elements, elements make a convenient common reference point for a Hess cycle — one that works for any reaction, as long as you have formation data for every substance involved.
Calculate the enthalpy change of reaction for the complete combustion of methane:
CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)
This matches the experimental value used for methane combustion in Topic 5.1 — the same reaction, calculated by a completely different route.
3 Enthalpy Change from Enthalpy Changes of Combustion
For many organic reactions — especially converting one hydrocarbon or alcohol into another — formation data may not be available, but standard enthalpy changes of combustion, ΔHc⦵, usually are, since they’re easy to measure directly by burning a substance in a bomb calorimeter. Combustion cycles use the combustion products (typically CO2 and H2O) as the common reference point instead of elements.
Calculate the enthalpy change for the hydrogenation of ethene to ethane:
C2H4(g) + H2(g) → C2H6(g)
4 Bond Energy Cycles & Solving Any Hess Cycle
When you used bond energies to calculate ΔH by breaking bonds in the reactants (endothermic) and forming new bonds in the products (exothermic), you were already using a Hess cycle — just with a set of gaseous atoms as the intermediate step, instead of elements or combustion products.
A general method for any Hess cycle question
Whatever data you’re given — formation, combustion, or bond energies — the same method solves every Hess cycle problem:
Write out the equation for the reaction you want ΔH for, and draw it as the top edge of a triangle.
Look at the data you’ve been given and decide which type of cycle it fits: formation data → elements at the bottom; combustion data → combustion products at the bottom; bond energies → gaseous atoms at the bottom.
Draw in the two remaining arrows in the correct direction for that data (formation arrows point away from elements; combustion arrows point towards combustion products).
Apply Hess’s Law: the enthalpy change going one way around the cycle equals the enthalpy change going the other way.
Rearrange to find the unknown ΔH, remembering to reverse the sign of any arrow you travel against.
Reversing the direction you travel along an arrow reverses the sign of that enthalpy change. This is the single most common source of errors in Hess cycle questions — always check whether you’re travelling with or against each arrow before adding or subtracting it.
Practice questions
State Hess’s Law.
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The enthalpy change accompanying a chemical change is independent of the route by which the change occurs (1), provided the initial and final conditions (states) are the same (1).
Use the enthalpy changes of formation below to calculate ΔH for the complete combustion of ethanol, C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(l). (ΔHf: C2H5OH(l) = −277.6, CO2(g) = −393.5, H2O(l) = −285.8, O2(g) = 0, all in kJ mol−1)
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ΣΔHf(products) = 2(−393.5) + 3(−285.8) = −787.0 − 857.4 = −1644.4 kJ mol−1 (1)
ΣΔHf(reactants) = −277.6 + 0 = −277.6 kJ mol−1 (1)
ΔHr = −1644.4 − (−277.6) = −1366.8 kJ mol−1 (1)
Use the enthalpy changes of combustion below to calculate ΔH for the hydrogenation of propene, C3H6(g) + H2(g) → C3H8(g). (ΔHc: C3H6(g) = −2058, H2(g) = −286, C3H8(g) = −2220, all in kJ mol−1)
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ΣΔHc(reactants) = −2058 + (−286) = −2344 kJ mol−1 (1)
ΣΔHc(products) = −2220 kJ mol−1 (1)
ΔHr = −2344 − (−2220) = −124 kJ mol−1 (1)
Sulfur dioxide can be oxidised to sulfur trioxide: SO2(g) + ½O2(g) → SO3(g). Given ΔHf[SO2(g)] = −296.8 kJ mol−1 and ΔHf[SO3(g)] = −395.7 kJ mol−1, calculate ΔHr.
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ΔHr = ΣΔHf(products) − ΣΔHf(reactants) (1)
ΔHr = (−395.7) − (−296.8) = −98.9 kJ mol−1 (1). (O2(g) is an element in its standard state, so contributes zero.) (1)
Explain, in terms of the law of conservation of energy, why Hess’s Law must be true.
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Energy cannot be created or destroyed (1). If two different routes between the same initial and final states gave different overall enthalpy changes, energy could be created or destroyed simply by choosing a different route — which would violate the law of conservation of energy (1). So the enthalpy change must be the same regardless of route (1).
Exam Tips & Quick Summary
Do remember
- Hess’s Law: ΔH depends only on initial and final states, not the route taken.
- Formation cycles: elements sit at the bottom, with both arrows pointing up (elements → compound).
- Combustion cycles: combustion products sit at the bottom, with both arrows pointing down (substance → combustion products).
- Bond energy cycles: gaseous atoms sit at the bottom — one arrow down (breaking, endothermic), one arrow up (making, exothermic).
- Reversing an arrow reverses the sign of that ΔH.
Do not confuse
- Formation formula: products − reactants. Combustion formula: reactants − products — the order flips.
- A Hess cycle is not “extra working” — it’s the only way to find some enthalpy changes at all (e.g. ΔHf of CO).
- Elements in their standard states always have ΔHf = 0, but this is not true of ΔHc — elements still burn and release energy.
- Don’t forget to multiply each ΔH by the correct stoichiometric number of moles from the balanced equation.
Recap in 20 seconds
Hess’s Law says enthalpy change depends only on the start and end points, not the path — a direct result of energy conservation. This lets you calculate enthalpy changes that are hard or impossible to measure directly, by building a triangular cycle through a common reference point: elements (formation data, arrows up), combustion products (combustion data, arrows down), or gaseous atoms (bond energies, one arrow each way). Whichever cycle you draw, the enthalpy change going one way round always equals the enthalpy change going the other way.