Bond dissociation energy (BDE) quantifies the strength of a specific chemical bond. It represents the energy input required to break one mole of a particular bond in a molecule. This bond cleavage must occur homolytically, meaning the two electrons that formed the covalent bond are split evenly, with one electron remaining on each resulting fragment, forming highly reactive radicals.
Because energy must be absorbed to break a bond, BDE is always a positive value. A higher BDE indicates a stronger chemical bond that is more difficult to cleave. The standard units used to express this energy are kilojoules per mole (\(\text{kJ/mol}\)) or kilocalories per mole (\(\text{kcal/mol}\)).
The Primary Calculation Method Using Enthalpy Data
The most common method for calculating BDE leverages established thermodynamic principles, particularly the application of Hess’s Law using standard enthalpy of formation data (\(\Delta H_f^\circ\)). This approach treats the homolytic bond cleavage as a chemical reaction, allowing the energy change to be determined from the difference between the thermodynamic properties of the products and the reactants.
The general homolytic reaction for a molecule \(\text{A-B}\) is \(\text{A-B} \rightarrow \text{A}^\bullet + \text{B}^\bullet\), where \(\text{A}^\bullet\) and \(\text{B}^\bullet\) are the resulting radicals. The standard enthalpy change for the reaction is calculated using the formula: \(\text{BDE} = \sum \Delta H_f^\circ (\text{products}) – \sum \Delta H_f^\circ (\text{reactants})\). This calculation requires consulting specialized tables that contain the pre-determined \(\Delta H_f^\circ\) values for the parent molecule and the specific radicals formed.
Consider the breaking of a single C-H bond in ethane (\(\text{CH}_3\text{CH}_2\text{-H}\)), which yields an ethyl radical (\(\text{CH}_3\text{CH}_2^\bullet\)) and a hydrogen radical (\(\text{H}^\bullet\)). The calculation involves taking the sum of the standard enthalpies of formation for the ethyl radical and the hydrogen radical, and then subtracting the standard enthalpy of formation for the ethane molecule.
This thermodynamic calculation is highly dependent on the accuracy of the tabulated enthalpy values for the transient radical species. Because radicals are short-lived and highly reactive, obtaining precise experimental data for their enthalpy of formation is a challenging task. The calculated BDE is a direct measure of how much less stable the resulting radicals are compared to the starting molecule.
Specific Bond Dissociation Energy Versus Average Bond Energy
The specific BDE refers to the energy needed to break one particular bond in a molecule, which is formally called the sequential BDE. This value is highly specific to the chemical environment of that one bond.
In polyatomic molecules, the energy required to break bonds of the same type in sequence is not constant. Using methane (\(\text{CH}_4\)) as an example, the energy needed to break the first C-H bond is different from the energy needed to break the second C-H bond. Each successive bond cleavage changes the molecular structure and the stability of the remaining radical, affecting the energy required for the next step.
The average bond energy (ABE), conversely, is calculated as the total energy required to break all bonds of a particular type divided by the number of those bonds. For methane, the ABE for the C-H bond is the sum of the four sequential BDEs divided by four. This average value is useful for estimating the enthalpy change of a reaction where multiple bonds are broken and formed, but it does not represent the actual strength of any single bond within the molecule.
Most general chemistry tables list ABEs, as these values offer a convenient way to approximate bond strengths across a variety of compounds. Researchers seeking to understand the precise thermodynamics of a specific reaction step, such as the initiation of a free-radical process, must use the specific BDE for that single bond.
Experimental Measurement Techniques
Thermodynamic calculations of BDE rely on data derived from precise experimental measurements performed in specialized laboratories. These techniques provide the foundation by physically determining the energy needed to cleave a bond.
One powerful approach is Photoionization Mass Spectrometry (PIMS), which involves irradiating a gaseous sample with photons of known energy. PIMS measures the minimum energy, known as the Appearance Energy (AE), required for a photon to cause a molecule to break and form a specific fragment ion. By tracking the precise energy at which the fragment ion first appears in the mass spectrometer, scientists can determine the BDE.
Kinetic methods offer another route to BDE determination by studying the rates of chemical reactions involving radicals. These methods measure the speed of a reaction over a range of temperatures, often involving radical chain reactions. Analyzing the temperature dependence of the reaction rate allows researchers to infer the activation energy, which can then be related to the BDE using established kinetic models.