Hess's law and enthalpy cyclesEdexcel A-Level Chemistry: Revision notes

Section 1

Hess's law

Hess's law states that the enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions and states are the same. It is a consequence of the conservation of energy: a reaction cannot make or lose energy simply by going by a different route.

This lets us find the enthalpy change of reactions that cannot be measured directly (too slow, too hot, or giving mixtures of products) by combining enthalpy changes that can be measured.

Key termsHess's lawroute independent

Section 2

Key definitions you need

Standard enthalpy change of formation, $\Delta_f H^{\ominus}$ : the enthalpy change when one mole of a compound is formed from its elements in their standard states, under standard conditions (298 K, 100 kPa). The value for an element in its standard state is zero.

Standard enthalpy change of combustion, $\Delta_c H^{\ominus}$ : the enthalpy change when one mole of a substance is completely burned in oxygen, with everything in its standard state, under standard conditions.

Write the equation for each definition carefully: formation equations make exactly one mole of the compound from elements, so fractions such as ½O₂ are fine.

Key termsstandard enthalpy change of formationstandard enthalpy change of combustionstandard state

Common mistake

Writing a formation equation that starts from atoms or from compounds. The reactants must be elements in their standard states, e.g. C(s) and H₂(g), never C(g) or H(g).

Section 3

Constructing enthalpy cycles

An enthalpy cycle is a triangle (or similar) in which the direct reaction is one route and the indirect route goes through other species whose enthalpy changes are known. Arrows show the direction of each change.

To use the cycle, follow the route in the direction of the arrows: the direct arrow equals the sum of the arrows of the indirect route, with the sign reversed for any arrow followed backwards.

Cycle from formation data: elements sit at the bottom, reactants and products above them, so $\Delta_r H^{\ominus} = \sum \Delta_f H^{\ominus}(\text{products}) - \sum \Delta_f H^{\ominus}(\text{reactants})$ .

Cycle from combustion data: reactants and products both burn to the same combustion products, so $\Delta_r H^{\ominus} = \sum \Delta_c H^{\ominus}(\text{reactants}) - \sum \Delta_c H^{\ominus}(\text{products})$ .

Key termsenthalpy cycle

Exam tip

Notice the order reverses: formation is products minus reactants, combustion is reactants minus products. Check that elements have ΔfH = 0 and that CO₂ and H₂O have ΔcH = 0 (they do not burn).

Section 4

Worked example: enthalpy of formation of methane

Find $\Delta_f H^{\ominus}$ of methane from combustion data: C(s) −394, H₂(g) −286, CH₄(g) −890 kJ mol⁻¹.

Equation: C(s) + 2H₂(g) → CH₄(g)

$\Delta_f H^{\ominus} = \Delta_c H^{\ominus}(\text{C}) + 2\Delta_c H^{\ominus}(\text{H}_2) - \Delta_c H^{\ominus}(\text{CH}_4)$

= −394 + 2(−286) − (−890) = −394 − 572 + 890 = −76 kJ mol⁻¹.

Multiply the number of moles of each substance in the equation by its ΔcH. Always state the sign and units.

Key termsworked example

Section 5

Core practical 8: Hess's law in the laboratory

Enthalpy changes that cannot be measured directly (for example the decomposition of a carbonate) are found by measuring two reactions that can be done in a polystyrene cup, then combining them with Hess's law.

Method: measure a known volume of acid or solution; record the temperature for a few minutes; add a weighed mass of solid; stir; record the temperature until it falls; extrapolate the cooling curve back to the time of mixing to find the maximum temperature change ΔT.

Calculation: $q = mc\Delta T$ (m = mass of solution, c = 4.18 J g⁻¹ K⁻¹); moles of the limiting reagent; $\Delta H = -q \div n$ (negative if the temperature rises). Convert J to kJ before dividing.

Sources of error: heat lost to the surroundings, heat absorbed by the cup and thermometer, assuming the solution has the heat capacity and density of water, and mass or volume measurement errors. A lid, a polystyrene cup and extrapolation reduce heat-loss error.

Key termslimiting reagentextrapolate

Common mistake

Using the mass of the solid in q = mcΔT. The mass m is the mass of the solution being heated (volume of solution × 1.00 g cm⁻³).

Must Know

Hess's law: ΔH is independent of route
ΔfH of an element = 0; ΔcH of CO₂ and H₂O = 0
ΔrH = Σ ΔfH(products) − Σ ΔfH(reactants)
ΔrH = Σ ΔcH(reactants) − Σ ΔcH(products)
q = mcΔT, then ΔH = −q ÷ n, with the sign set by the temperature change
Give the sign and units (kJ mol⁻¹) with every answer

That's the notes covered.

Carry on to the next subtopic.

Exam questions on Hess's law and enthalpy cycles

A student wants the enthalpy change for a reaction that cannot be measured directly in a calorimeter, so she plans to use Hess's law with other reactions whose enthalpy changes can be measured.
Define the term standard enthalpy change of formation.2 marks
Ethanol, C₂H₅OH, is made on a large scale for use as a biofuel. Its standard enthalpy change of formation cannot be measured directly, but standard enthalpy changes of combustion are available: carbon (graphite) −394 kJ mol⁻¹, hydrogen −286 kJ mol⁻¹ and ethanol(l) −1367 kJ mol⁻¹.
Use an enthalpy cycle to calculate the standard enthalpy change of formation of ethanol.2 marks
Iron is extracted from iron(III) oxide in a blast furnace. One of the key reactions is Fe₂O₃(s) + 3CO(g) → 2Fe(s) + 3CO₂(g). Standard enthalpy changes of formation are: Fe₂O₃(s) −824 kJ mol⁻¹, CO(g) −111 kJ mol⁻¹, CO₂(g) −394 kJ mol⁻¹.
Calculate the standard enthalpy change of reaction.3 marks

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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).