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Lesson 0 of this course established that enthalpy changes can be measured directly by calorimetry. This lesson develops a complementary, model-based route to ΔH: estimating reaction enthalpies from the energies required to break and make individual covalent bonds. Two related but conceptually distinct quantities matter. The exact bond enthalpy is the energy required to break one mole of a specific bond in a specific gaseous molecule — for example, the first C–H bond in methane. The mean bond enthalpy is the average bond-breaking energy of one type of bond (e.g. C–H) taken across many different gaseous compounds. Tabulated databooks list mean values because they are the only practical choice when the exact molecular environment is not known. From these tabulated means we can estimate the enthalpy change of any reaction using the well-known approximation ΔH ≈ Σ(bonds broken) − Σ(bonds formed). This lesson works through the algebra, four worked examples, and the systematic reasons why bond-enthalpy estimates almost always disagree with direct calorimetric measurements.
Spec mapping (AQA 7405): This lesson maps to §3.1.4 (energetics — bond enthalpies and mean bond enthalpies). It builds directly on lesson 0 (calorimetry: q = mcΔT) by offering an indirect estimation route to the same quantity, and on lesson 2 (Hess's law and enthalpy cycles) which provides a third, rigorous indirect route via formation or combustion enthalpies. Covalent bonding fundamentals are anchored in lesson 1 of the bonding course (§3.1.3) — students should already be confident with σ/π bonds and bond multiplicity before estimating bond-energy sums. Forward links: §3.3 (organic chemistry) uses mean bond enthalpies to predict the heats of combustion of alkanes and the relative exothermicity of free-radical halogenation steps. Refer to the official AQA specification document for the exact wording of each section.
Assessment objectives: AO1 (recall): define exact and mean bond enthalpy; state that bond breaking is endothermic so mean bond enthalpies are always positive; state the formula ΔH ≈ Σ(bonds broken) − Σ(bonds formed). AO2 (application): given a databook of mean bond enthalpies, calculate ΔH for combustion, hydrogenation, halogenation, and other simple gas-phase reactions. AO3 (analysis): explain quantitatively why the estimated ΔH differs from the experimental value; evaluate when the approximation is least reliable (liquid or solid reactants/products, resonance-stabilised molecules such as benzene, ionic intermediates). The bond-enthalpy approximation appears every cycle on AQA Paper 2.
Key Definition: The bond enthalpy (also called bond dissociation enthalpy) is the enthalpy change required to break one mole of a specific covalent bond in the gas phase, with all reactants and products as isolated gaseous species. Units: kJ mol⁻¹. Bond breaking is always endothermic, so bond enthalpies are always positive.
Key Definition: The mean bond enthalpy is the average value of the bond enthalpy of a particular type of bond (e.g. C–H) taken across a wide range of gaseous compounds in which that bond appears. It is what databooks tabulate; it is not exact for any individual molecule.
A representative process for the bond enthalpy of the H–H bond is:
H–H(g) → 2 H(g) ΔH = +436 kJ mol⁻¹
For homonuclear diatomic molecules such as H₂, Cl₂, O₂ or N₂, the tabulated value is exact — there is only one molecule containing the bond, so the "mean" is taken over a population of one. For polyatomic molecules the situation is more subtle, as the next section shows.
The actual energy required to break a C–H bond is not a single universal number. It depends on the rest of the molecule — specifically, on the electron density at the carbon atom, the hybridisation, the substituents bonded to the same carbon, and the stability of the radical fragments left behind. Some illustrative exact bond enthalpies:
| Molecule | Bond broken | Bond enthalpy (kJ mol⁻¹) |
|---|---|---|
| CH₄ | First C–H | 438 |
| CH₃• → CH₂• + H | C–H in methyl radical | ~462 |
| CHCl₃ | C–H (in chloroform) | ~395 |
| C₂H₆ | C–H (in ethane) | ~410 |
| HCN | C–H (in hydrogen cyanide) | ~528 |
| (CH₃)₃C–H | tertiary C–H | ~400 |
The chemical environment can shift a C–H bond enthalpy by over 130 kJ mol⁻¹ between extremes. The mean value across the most common organic compounds is approximately 413 kJ mol⁻¹, and this is the value an A-Level databook will list. When we use it to estimate the enthalpy change of a reaction involving CHCl₃ (where the true value is closer to 395), the calculation carries a small but systematic error. This is the fundamental, irreducible source of inaccuracy in bond-enthalpy estimates.
Key Point: When you use a databook mean bond enthalpy in a calculation, you are implicitly assuming the bond in the molecule of interest has the average strength. Real bonds may deviate by ±10–15% from that average, and the error propagates linearly into the final estimated ΔH.
The following values, all in kJ mol⁻¹ and all referring to gaseous species at 298 K, are representative of an AQA databook. Question stems will normally provide the values you need — these are for fluency.
| Bond | Mean bond enthalpy (kJ mol⁻¹) | Bond | Mean bond enthalpy (kJ mol⁻¹) |
|---|---|---|---|
| C–C | 347 | O–H | 463 |
| C=C | 612 | N–H | 391 |
| C≡C | 838 | H–H | 436 |
| C–H | 413 | F–F | 158 |
| C–O | 358 | Cl–Cl | 242 |
| C=O (in CO₂) | 805 | Br–Br | 193 |
| C=O (in carbonyls) | 745 | I–I | 151 |
| C–N | 305 | O=O | 498 |
| C=N | 615 | N=N | 158 |
| C–F | 484 | N≡N | 945 |
| C–Cl | 327 | H–F | 568 |
| C–Br | 285 | H–Cl | 432 |
| C–I | 213 | H–Br | 366 |
Two values warrant special attention. The C=O bond in CO₂ is 805 kJ mol⁻¹, significantly stronger than the C=O in aldehydes and ketones (745 kJ mol⁻¹). This is because the two C=O bonds in CO₂ are part of a linear, cumulated system with partial triple-bond character (each C=O has ~50% extra π density delocalised across the molecule). Using 745 for CO₂ is a classic exam mistake that costs marks on combustion calculations. The second is N≡N at 945 kJ mol⁻¹ — the strongest common diatomic bond and the reason atmospheric nitrogen is so kinetically unreactive, despite being thermodynamically capable of forming many oxides.
The estimation formula is:
Key Equation: ΔH ≈ Σ(bond enthalpies of bonds broken) − Σ(bond enthalpies of bonds formed)
Why the minus sign? Bond breaking requires energy input (endothermic, positive contribution to the system enthalpy). Bond formation releases energy (exothermic, negative contribution). Since tabulated values are all positive (bond breaking), the formula must subtract the energies of bonds formed to give them the correct negative sign. An equivalent way of writing it is:
ΔH ≈ Σ(reactant bonds) − Σ(product bonds)
where both sums use the tabulated positive bond enthalpies. The two forms are identical algebra. The sign of ΔH is determined entirely by which side has more stored bond energy: if the products are more strongly bonded than the reactants, ΔH < 0 (exothermic).
Reaction: CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(g)
(Note: H₂O is taken as gaseous to match the databook conventions for bond enthalpy; the experimental ΔcH° refers to liquid H₂O.)
Bonds broken (reactants):
Bonds formed (products):
ΔH estimate: 2648 − 3462 = −814 kJ mol⁻¹
(Some databooks with slightly different values give the often-quoted −698; using 805 for C=O in CO₂ gives the more accurate −814.) The experimental standard enthalpy of combustion is −890 kJ mol⁻¹. The bond-enthalpy estimate is 70–190 kJ mol⁻¹ less exothermic, depending on the databook. Two reasons account for the gap. First, mean bond enthalpies for C–H and the various other bonds carry residual error from molecular-environment averaging. Second, ΔcH° is defined with H₂O as a liquid; the latent heat of vaporisation of water (≈ 44 kJ mol⁻¹ × 2 = 88 kJ mol⁻¹ of additional release on condensation) is not captured by the gas-phase bond-enthalpy approach. Adding 88 kJ mol⁻¹ to our −814 estimate gives roughly −902 kJ mol⁻¹, comfortably within 1% of the experimental −890.
Reaction: C₂H₄(g) + H₂(g) → C₂H₆(g)
Bonds broken:
Bonds formed:
ΔH estimate: 2700 − 2825 = −125 kJ mol⁻¹
The experimental value is −137 kJ mol⁻¹. The agreement is good (within 10%) because both reactant and product are simple alkenes/alkanes with C–H bonds close to the mean.
A faster shortcut for hydrogenation problems: the only bonds that change are one C=C breaking (+612) and one H–H breaking (+436), making one C–C (−347) and two new C–H bonds (−2 × 413 = −826). ΔH = +612 + 436 − 347 − 826 = −125 kJ mol⁻¹. The four pre-existing C–H bonds in ethene appear on both sides and cancel. Spotting cancellations is the single best speed-up on exam questions of this type.
Reaction: CH₃OH(g) + 1½ O₂(g) → CO₂(g) + 2 H₂O(g)
Bonds broken:
Bonds formed:
ΔH estimate: 2807 − 3462 = −655 kJ mol⁻¹
The experimental ΔcH°(CH₃OH, l) = −726 kJ mol⁻¹. Once again the gap (~71 kJ mol⁻¹) is dominated by the gas-vs-liquid state difference: liquid methanol → gaseous methanol costs ~+38 kJ mol⁻¹, and gaseous H₂O → liquid H₂O releases ~−88 kJ mol⁻¹ overall.
Reaction: CH₄(g) + Cl₂(g) → CH₃Cl(g) + HCl(g)
This is the overall outcome of the first step of the free-radical chain mechanism studied in §3.3.
Bonds broken:
(Three of the four C–H bonds in CH₄ are spectators — they appear unchanged on both sides.)
Bonds formed:
ΔH estimate: 655 − 759 = −104 kJ mol⁻¹ (exothermic).
The experimental value is −99 kJ mol⁻¹. Agreement is excellent because all four species are simple gases with well-behaved mean bonds. The exothermicity drives chlorination forward thermodynamically (although kinetics — the UV initiation step — controls how fast it happens).
Three systematic reasons account for the disagreement between bond-enthalpy estimates and direct calorimetric values, in roughly decreasing order of importance:
(a) Mean values vs exact values — the molecular environment effect. The mean C–H bond enthalpy of 413 kJ mol⁻¹ is an average; the actual C–H bond in any specific molecule can differ by ±10%. For a reaction involving several C–H bonds the errors compound. For unusual bonds (vinyl, aromatic, allylic) the deviation can exceed 15%.
(b) The gas-phase requirement. Tabulated bond enthalpies refer to bond breaking with all species in the gas phase. Real reactions often involve liquids (e.g. water in combustion, ethanol fuel cells), solids (combustion of solid sugars), or solutions (acid–base reactions). To compare a bond-enthalpy estimate to an experimental measurement, the latent heats of vaporisation, fusion or dissolution must be added in. For water, ΔvapH° ≈ +44 kJ mol⁻¹ per mole — significant in a combustion calculation that produces 2 mol of H₂O per mol of fuel.
(c) Resonance stabilisation and other electronic effects. Some molecules are more stable than the sum of their classical localised bonds would predict. Benzene is the textbook case (see next section). Conjugated dienes, carboxylates, amides and many other resonance-stabilised species fall in the same category. Bond enthalpies built from classical Lewis structures cannot capture this extra stability.
A fourth, smaller contributor is the assumption that all reactants and products are in their standard states at 298 K. Real combustion at 1500 K obviously involves species at very different temperatures, but this matters less for ΔH (a state function) than for kinetics.
The bond-enthalpy approach predicts the hydrogenation of benzene as if it were three discrete C=C bonds:
C₆H₆(g) + 3 H₂(g) → C₆H₁₂(g)
A Kekulé-structure calculation, or a simpler proxy of 3 × (hydrogenation of one alkene C=C ≈ −120 kJ mol⁻¹), would predict ΔH ≈ −360 kJ mol⁻¹. The experimental value for benzene hydrogenation is only −208 kJ mol⁻¹.
The 152 kJ mol⁻¹ shortfall is benzene's aromatic resonance stabilisation energy. The six π-electrons in benzene are delocalised over the whole ring rather than localised in three discrete double bonds; the delocalised system is much lower in energy than three isolated C=C bonds would be. To break this delocalisation (which hydrogenation does), an extra 152 kJ mol⁻¹ of energy is required beyond what classical bond enthalpies predict. Bond-enthalpy estimates therefore systematically overestimate the exothermicity of benzene's hydrogenation. The same effect explains why benzene resists addition reactions and prefers substitution — addition would destroy aromaticity and pay this large energy penalty.
Forward link: §3.3.10 develops aromatic chemistry in detail and quantifies this stabilisation through alternative experimental routes (heat of hydrogenation of cyclohexene, cyclohexadiene and benzene compared).
Practical-skills box — When to trust a bond-enthalpy estimate. The bond-enthalpy method is best used for relative comparisons: deciding which of two related reactions is more exothermic, or whether a given reaction will be exothermic at all. It is poor at giving precise absolute values. For absolute ΔH, prefer (i) direct calorimetry (lesson 0) for well-behaved systems, or (ii) Hess's law via formation enthalpies (lesson 2) for systems involving condensed-phase species. Bond enthalpies are an excellent tool for predicting trends (e.g. why fluorination releases more energy than iodination) and for mechanistic reasoning, but treat any individual numerical value as accurate only to ±10%.
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