R1.2 Energy cycles in reactionsIB Chemistry HL: Revision notes
Section 1
Bond enthalpies
Bond breaking absorbs energy; bond forming releases energy. Using average bond enthalpies for gaseous species:
ΔH = Σ(bonds broken) − Σ(bonds formed)
Example, N₂ + 3H₂ → 2NH₃: broken 945 + 3(436) = 2253; formed 6(391) = 2346; ΔH = −93 kJ. Values are approximate because average bond enthalpies are means over many compounds and apply only to gases.
Section 2
Hess's law
Hess's law: the enthalpy change for a reaction is independent of the pathway between the initial and final states. Combine given equations to reach the target: reverse an equation → change the sign of ΔH; multiply an equation → multiply ΔH. Every calculation below (formation data, combustion data, Born–Haber) is an application of Hess's law.
Section 3
Standard enthalpies of formation and combustion (HL)
Standard enthalpy of formation, ΔHf⦵: the enthalpy change when one mole of a compound is formed from its elements in their standard states under standard conditions (100 kPa, usually 298 K). ΔHf⦵ of an element in its standard state is zero. Example: ½N₂(g) + 1½H₂(g) → NH₃(g).
Standard enthalpy of combustion, ΔHc⦵: the enthalpy change when one mole of a substance is completely burned in oxygen under standard conditions. Example: C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(l).
Writing a formation equation that makes two moles, or starts from gaseous atoms, or gives the product in the wrong state.
Section 4
Calculations with ΔHf⦵ and ΔHc⦵ data (HL)
Both equations are in the data booklet:
- ΔH⦵ = Σ ΔHf⦵(products) − Σ ΔHf⦵(reactants)
- ΔH⦵ = Σ ΔHc⦵(reactants) − Σ ΔHc⦵(products)
Multiply each value by its coefficient. Combustion data are ideal for formation enthalpies that cannot be measured directly: for propane, 3C + 4H₂ → C₃H₈, ΔHf⦵ = [3(−394) + 4(−286)] − (−2219) = −107 kJ mol⁻¹.
Formation: products minus reactants. Combustion: reactants minus products. The order flips because combustion arrows point away from the substances.
Section 5
Born–Haber cycles (HL)
A Born–Haber cycle applies Hess's law to the formation of an ionic compound. Route from elements to gaseous ions:
- atomisation of the metal and of the non-metal (per atom formed);
- ionisation energies of the metal (IE₁ + IE₂ for M²⁺);
- electron affinities of the non-metal;
- ions come together to form the lattice (the reverse of the lattice enthalpy).
The sum equals ΔHf⦵. For KCl: lattice enthalpy = 437 + 89 + 419 + 121 − 349 = +717 kJ mol⁻¹.
Section 6
Interpreting Born–Haber values (HL)
First electron affinities are usually exothermic (the electron is attracted by the nucleus); second electron affinities (O⁻ → O²⁻) are endothermic because the electron is repelled by a negative ion.
For divalent ions, count everything: MgCl₂ needs IE₁ + IE₂ and two chlorine atomisations and electron affinities. Larger ionic charge and smaller ionic radius give a larger lattice enthalpy, which is why MgCl₂ (lattice 2526) forms rather than MgCl (about 753) despite the cost of IE₂.
Forgetting to double the atomisation and electron affinity of chlorine for MgCl₂.
Must know
- ΔH = Σ bonds broken − Σ bonds formed.
- Hess's law: ΔH is independent of the route.
- (HL) ΔHf⦵ of an element in its standard state = 0.
- (HL) Formation: products − reactants; combustion: reactants − products.
- (HL) Born–Haber: atomisation + IE + EA − lattice enthalpy = ΔHf⦵.
- (HL) Higher charge, smaller ions → larger lattice enthalpy.
That's the notes covered.
Carry on to the next subtopic.