A bond enthalpy (or bond dissociation energy) is the enthalpy change required to break a chemical bond in the gas phase and separate the bonded atoms completely.
For a diatomic molecule,
\[ A{-}B(g) \rightarrow A(g) + B(g) \]
\[ \Delta H_{\mathrm{rxn}} = D(A{-}B) \]
Because bond breaking requires energy, bond enthalpies are always positive. The larger the bond enthalpy, the stronger the bond.
Examples:
| Bond | Average Bond Enthalpy (kJ/mol) |
|---|---|
| H–H | 436 |
| Cl–Cl | 243 |
| C–H | 413 |
| O=O | 498 |
In a molecule containing several bonds, not all bonds of a given type are exactly identical. The energy required to break a bond depends on the molecular environment surrounding that bond.
For example, a C–H bond in methane, \(CH_4\), is not exactly the same as a C–H bond in acetylene, \(C_2H_2\), or ethanol, \(C_2H_5OH\).
As a result, most bond enthalpies reported in tables are average bond enthalpies obtained by averaging measurements from many different molecules containing that type of bond.
Because average values are used, reaction enthalpies calculated from bond enthalpies are generally approximate. Typical errors are on the order of 5–10%, although larger errors can occur for unusual molecules.
Standard enthalpies of formation usually provide more accurate reaction enthalpies, but bond enthalpies are often useful when formation enthalpy data are unavailable.
Bond enthalpies can be used to estimate the enthalpy change of a reaction by considering the bonds that are broken and the bonds that are formed.
The process consists of three steps:
Breaking bonds requires energy:
\[ \text{Energy absorbed} = \sum D(\text{bonds broken}) \]
Forming bonds releases energy:
\[ \text{Energy released} = \sum D(\text{bonds formed}) \]
The estimated reaction enthalpy is therefore
\[ \Delta H_{\mathrm{rxn}} = \sum D(\text{bonds broken}) - \sum D(\text{bonds formed}) \]
If more energy is released by bond formation than is required for bond breaking, the reaction is exothermic and \(\Delta H_{\mathrm{rxn}}<0\). If more energy is required to break bonds than is released by forming new bonds, the reaction is endothermic and \(\Delta H_{\mathrm{rxn}}>0\).
When using bond enthalpies, it is often helpful to draw structural formulas for both reactants and products and physically count the bonds that must be broken and formed.
For example, in the combustion of methane,
\[ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g) \]
the calculation begins by identifying:
The bond enthalpies are then inserted into the equation above to estimate the reaction enthalpy.
Big picture: Bond enthalpies provide a molecular picture of reaction energetics. By comparing the energy required to break bonds with the energy released when new bonds form, reaction enthalpies can be estimated even when detailed thermodynamic data are unavailable.
| Bond | Average Bond Enthalpy (kJ/mol) |
Bond | Average Bond Enthalpy (kJ/mol) |
|---|---|---|---|
| H–H | 436 | O–H | 463 |
| H–F | 567 | O–O | 146 |
| H–Cl | 431 | O=O | 498 |
| H–Br | 366 | C–C | 347 |
| H–I | 299 | C=C | 614 |
| N–H | 391 | C≡C | 839 |
| N–N | 163 | C–H | 413 |
| N=N | 418 | C–O | 358 |
| N≡N | 945 | C=O (carbonyl) | 743 |
| F–F | 159 | C=O (CO₂) | 799 |
| Cl–Cl | 243 | C–Cl | 338 |
| Br–Br | 193 | C–Br | 276 |
| I–I | 151 | C–N | 305 |
| C=N | 615 | ||
| C≡N | 891 |
Note: These values are average bond enthalpies obtained by averaging measurements from many different molecules. Consequently, reaction enthalpies calculated using bond enthalpies are approximate and are typically accurate to within about 5–10% of experimentally measured values.
Estimate the reaction enthalpy for the addition of HBr to ethene:
\[ C_2H_4(g) + HBr(g) \rightarrow C_2H_5Br(g) \]
First identify the bonds that change during the reaction.
| Bonds broken | Average bond enthalpy |
|---|---|
| 1 C=C bond | \(614\ \mathrm{kJ\,mol^{-1}}\) |
| 1 H–Br bond | \(366\ \mathrm{kJ\,mol^{-1}}\) |
| Bonds formed | Average bond enthalpy |
|---|---|
| 1 C–C bond | \(347\ \mathrm{kJ\,mol^{-1}}\) |
| 1 C–H bond | \(413\ \mathrm{kJ\,mol^{-1}}\) |
| 1 C–Br bond | \(276\ \mathrm{kJ\,mol^{-1}}\) |
The estimated reaction enthalpy is
\[ \Delta H_{\mathrm{rxn}} = \sum D(\text{bonds broken}) - \sum D(\text{bonds formed}) \]
Substitute the bond enthalpies, keeping units attached to each term:
\[ \Delta H_{\mathrm{rxn}} = \left[ 614\ \mathrm{kJ\,mol^{-1}} + 366\ \mathrm{kJ\,mol^{-1}} \right] - \left[ 347\ \mathrm{kJ\,mol^{-1}} + 413\ \mathrm{kJ\,mol^{-1}} + 276\ \mathrm{kJ\,mol^{-1}} \right] \]
\[ \Delta H_{\mathrm{rxn}} = 980\ \mathrm{kJ\,mol^{-1}} - 1036\ \mathrm{kJ\,mol^{-1}} \]
\[ \Delta H_{\mathrm{rxn}} = -56\ \mathrm{kJ\,mol^{-1}} \]
Therefore,
\[ \boxed{ \Delta H_{\mathrm{rxn}} \approx -56\ \mathrm{kJ\,mol^{-1}} } \]
Physical interpretation: The reaction is estimated to be exothermic because the bonds formed in bromoethane release more energy than is required to break the C=C and H–Br bonds in the reactants. Since average bond enthalpies are used, this value should be treated as an approximation.
Use average bond enthalpies to estimate \(\Delta H_{\mathrm{rxn}}\). Choose the correct answer.
Big picture: Bond enthalpies provide a molecular view of reaction energetics. Reaction enthalpies can be estimated by comparing the energy required to break bonds in the reactants with the energy released when new bonds form in the products. Although approximate, this method provides valuable insight into why reactions are exothermic or endothermic.