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*Revision Materials* 1 Atomic Structure 2 Atoms, molecules and stoichiometry 3 Chemical Bonding 4 States of matter 5 Chemical energetics 6 Electrochemistry 7 Equilibria 8 Reaction kinetics 9 The Periodic Table, chemical periodicity 10 Group 2 11 Group 17 12 Nitrogen and sulfur 13 Organic 14 Hydrocarbons 15 Halogen compounds 16 Hydroxy compounds 17 Carbonyl compounds 18 Carboxylic acids and derivatives 19 Nitrogen compounds 20 Polymerisation 21 Organic synthesis 22 Analytical techniques 23 Chemical energetics 24 Electrochemistry 25 Equilibria 26 Reaction kinetics 27 Group 2 28 Chemistry of transition elements 29 Organic 30 Hydrocarbons 31 Halogen compounds 32 Hydroxy compounds 33 Carboxylic acids and derivatives 34 Nitrogen compounds 35 Polymerisation 36 Organic synthesis 37 Analytical techniques

5 Chemical energetics

5.1 Enthalpy change, ΔH 5.2 Hess’s law

Hess’s Law

Specification Reference Physical Chemistry: Chemical energetics 5.2

Quick Notes

  • Hess’s Law: The total enthalpy change in a chemical reaction is independent of the route taken, as long as the starting and ending conditions are the same.
  • We can use Hess (energy) cycles to determine enthalpy changes that can’t be found directly by experiment.
  • Key formulas:
    • ΔHr = ΣΔHf(products) – ΣΔHf(reactants)
    • ΔHr = ΣΔHc(reactants) – ΣΔHc(products)
    • ΔHr = Bonds broken – Bonds made

Full Notes

Hess’s Law has been outlined with more background theory and detail at this page.
This page is just what you need to know for CIE A-Level Chemistry :)

What is Hess’s Law?

Hess’s Law states:
“The total enthalpy change for a reaction is the same, no matter which route is taken, provided the starting and finishing conditions are the same.”

This is based on the Law of Conservation of Energy which states that energy cannot be created or destroyed, only transferred.

Hess’s Law is useful for finding enthalpy changes that cannot be measured directly by using Hess cycles (energy cycles).

CIE A-Level Chemistry Hess cycle diagram showing enthalpy routes for reactions.

A Hess’s cycle can be constructed for:

Hess’s Cycles Using Enthalpies of Formation (ΔHf)

The enthalpy of formation (ΔHf) is the enthalpy change when one mole of a compound is formed from its elements in their standard states.

Elements in their standard states (for example, O2(g)) have an enthalpy of formation, ΔHf, of zero — this is really important for calculations involving standard enthalpies of formation.

Formula for Hess’s Cycle using enthalpy of formation:
ΔHr = ΣΔHf(products) – ΣΔHf(reactants)

Worked Example

Calculate the enthalpy of formation of CO2

Reaction:
C(s) + O2(g) → CO2(g)

Given Data:
ΔHf(CO2) = –393 kJ mol⁻¹
ΔHf(O2) = 0 (since elements in their standard states have ΔHf = 0)

Using Hess’s Law:
ΔHr = ΔHf(CO2) – (ΔHf(C) + ΔHf(O))
ΔHr = –393 – (0 + 0)
ΔHr = –393 kJ mol⁻¹

Hess’s Cycles Using Enthalpies of Combustion (ΔHc)

Worked Example

Using enthalpies of combustion to find the enthalpy of formation of propane (C3H8)

Given Data:
ΔHc(C(s)) = –394 kJ mol⁻¹
ΔHc(H2(g)) = –286 kJ mol⁻¹
ΔHc(C3H8(g)) = –2220 kJ mol⁻¹

Draw a Hess Cycle showing two possible routes:

CIE A-Level Chemistry Hess cycle diagram for formation of propane using enthalpies of combustion.

Using Hess’s Law we know route 1 = route 2

ΔH1 = ΔH? + ΔH2
ΔH? = ΔH1 – ΔH2
ΔH? = (–2326) – (–2220) = –106 kJ mol⁻¹

Hess’s Law Using Bond Energies

Worked Example

Calculate the enthalpy change of formation (ΔHf) of methane, CH4(g) using bond enthalpies.

Bond enthalpies (kJ mol⁻¹):
C–H = +412
H–H = +436
C(s) → C(g) = +716
ΔHf of H2(g): 0.5H2(g) → H(g) + H(g), ΔH = +218

Overall reaction: C(s) + 2H2(g) → CH4(g)

Step 1: Draw the Hess Cycle

CIE A-Level Chemistry Hess cycle diagram for methane formation using bond energies.

Step 2: Apply Hess’s Law

CIE A-Level Chemistry Hess cycle showing energy terms for formation of methane.

ΔHf = ΔH1 (atomise C) + ΔH2 (atomise H2) – ΔH3 (form CH4)
ΔHf = +716 + 872 – 1648 = –60 kJ mol⁻¹

Final Answer:
ΔHf(CH4) = –60 kJ mol⁻¹


Photo of Matt
Matt’s exam tip

Always label arrows with enthalpy values and direction.
Make sure all equations in the cycle balance properly.
Pay careful attention to states — for example, if dealing with bond enthalpies make sure substances are atomised to get them into free, gaseous atoms. 0.5H2(g) isn’t the same as H(g).
Keep units consistent (usually kJ mol⁻¹).

Summary