# 6.2 Bond Energy When a chemical reaction occurs, chemical bonds in the reactant molecules are broken, and new bonds are formed in the product molecules. This process involves changes in energy. **Bond Breaking**: This process always requires an input of energy. The energy needed to break one mole of a particular bond to form neutral atoms is known as the **bond dissociation energy**. It is an endothermic process. **Bond Formation**: This process always releases energy. The energy released when one mole of a bond is formed from neutral atoms is called **bond energy**. It is an exothermic process. The overall energy change in a reaction, known as the **enthalpy change (ΔH)**, is the difference between the energy absorbed to break bonds and the energy released when new bonds are formed. The enthalpy change for a reaction can be calculated using the following formula: $$ \Delta H = \sum H_{\text{(bonds broken)}} - \sum H_{\text{(bonds formed)}} $$ Where: - $\sum H_{\text{(bonds broken)}}$ is the sum of the bond dissociation energies of all bonds in the reactants. - $\sum H_{\text{(bonds formed)}}$ is the sum of the bond energies of all bonds in the products. ## Worked Examples ### Example 1: Theoretical Bond Energy of H-Cl We can theoretically calculate the bond energy of a bond using known bond energy data. Calculate the bond energy for the Hydrogen Chloride (H-Cl) bond. The reaction is: $$ \mathrm{H_2} + \mathrm{Cl_2} \rightarrow 2\mathrm{HCl} $$ **Given values:** - Bond dissociation energy of $\mathrm{H_2}$ (H-H bond): $436 \, \text{kJ/mol}$ - Bond dissociation energy of $\mathrm{Cl_2}$ (Cl-Cl bond): $243 \, \text{kJ/mol}$ **Calculation:** 1. **Identify bonds broken (Reactants):** - 1 mole of H-H bonds - 1 mole of Cl-Cl bonds 2. **Identify bonds formed (Products):** - 2 moles of H-Cl bonds 3. **Apply the energy balance principle:** Total energy absorbed in bond breaking equals total energy released in bond formation. $$ (\text{Bond dissociation energy of H-H}) + (\text{Bond dissociation energy of Cl-Cl}) = 2 \times (\text{Bond energy of H-Cl}) $$ $$ 436 \, \text{kJ/mol} + 243 \, \text{kJ/mol} = 2 \times (\text{Bond energy of H-Cl}) $$ $$ 679 \, \text{kJ} = 2 \times (\text{Bond energy of H-Cl}) $$ $$ \text{Bond energy of H-Cl} = \frac{679}{2} = 339.5 \, \text{kJ/mol} $$ *Note:* The experimentally determined bond energy of $\mathrm{HCl}$ is $431.5 \, \text{kJ/mol}$. The difference exists because theoretical values are often averages and do not account for factors like the unequal distribution of electrons due to differences in electronegativity between atoms. ### Example 2: Enthalpy of Reaction for Water Formation Calculate the enthalpy change (ΔH) for the reaction between hydrogen and oxygen to produce water. $$ 2\mathrm{H_{2(g)}} + \mathrm{O_{2(g)}} \rightarrow 2\mathrm{H_2O_{(l)}} $$ **Given values:** - Bond dissociation energy of $\mathrm{H_2}$ (H-H): $436 \, \text{kJ/mol}$ - Bond dissociation energy of $\mathrm{O_2}$ (O=O): $493.6 \, \text{kJ/mol}$ - Bond energy of O-H: $460 \, \text{kJ/mol}$ **Calculation:** 1. **Energy of Bonds Broken (Reactants):** - 2 moles of H-H bonds: $2 \times 436 \, \text{kJ} = 872 \, \text{kJ}$ - 1 mole of O=O bonds: $1 \times 493.6 \, \text{kJ} = 493.6 \, \text{kJ}$ - Total energy absorbed: $872 + 493.6 = 1365.6 \, \text{kJ}$ 2. **Energy of Bonds Formed (Products):** - Each $\mathrm{H_2O}$ molecule has two O-H bonds. Since 2 moles of $\mathrm{H_2O}$ are formed, there are a total of $2 \times 2 = 4$ moles of O-H bonds. - Total energy released: $4 \times 460 \, \text{kJ} = 1840 \, \text{kJ}$ 3. **Calculate Enthalpy Change (ΔH):** $$ \Delta H = \sum H_{\text{(bonds broken)}} - \sum H_{\text{(bonds formed)}} $$ $$ \Delta H = (1365.6 \, \text{kJ}) - (1840 \, \text{kJ}) $$ $$ \Delta H = -474.4 \, \text{kJ} $$ The negative sign indicates that the reaction is exothermic, releasing 474.4 kJ of energy. ### Example 3: Average Bond Energy of C-H in Methane Calculate the average bond energy per mole of C-H bonds in methane ($\mathrm{CH_4}$). **Given reaction:** The complete dissociation of methane into its constituent atoms. $$ \mathrm{CH_{4(g)}} \rightarrow \mathrm{C_{(s)}} + 4\mathrm{H_{(g)}} \quad \Delta H^{\circ} = +1662 \, \text{kJ} $$ **Calculation:** 1. In this reaction, the enthalpy change ($+1662 \, \text{kJ}$) represents the total energy absorbed to break all the bonds in one mole of methane. 2. One molecule of $\mathrm{CH_4}$ contains four C-H bonds. Therefore, the energy absorbed corresponds to breaking 4 moles of C-H bonds. 3. To find the average bond energy for a single C-H bond, divide the total energy by the number of bonds broken. $$ \text{Average C-H bond energy} = \frac{\text{Total energy absorbed}}{\text{Moles of bonds broken}} $$ $$ \text{Average C-H bond energy} = \frac{1662 \, \text{kJ}}{4} $$ $$ \text{Average C-H bond energy} = +415.5 \, \text{kJ/mol} $$ ## 6.2.1 Variability in Bond Energies The tabulated values for bond energies are often averages, and their precision can vary depending on the specific molecule and its chemical environment. **Well-Defined Bond Energies:** For simple diatomic molecules composed of identical atoms (e.g., $\mathrm{H_2}, \mathrm{O_2}, \mathrm{N_2}, \mathrm{Cl_2}$), bond energies are highly accurate and precise. The bond dissociation energy is the same for every bond. For example, the H-H bond energy in $\mathrm{H_2}$ is reliably $436 \, \text{kJ/mol}$. **Approximate Bond Energies:** In more complex molecules, bond energies are approximate. The strength of a particular bond (e.g., C-H or C-C) can be influenced by several factors: - **Neighboring Atoms:** The other atoms or functional groups attached to the atoms in the bond. - **Molecular Geometry:** The overall 3D structure of the molecule. - **Inductive Effects:** The pulling or pushing of electron density by nearby functional groups. - **Bond Length and Multiplicity:** Generally, shorter bonds and multiple bonds (double, triple) have higher bond energies. **Examples of Variability:** - The C-C bond energy can differ between linear and branched alkanes. - The C-H bond energy in methane ($\mathrm{CH_4}$) is slightly different from the C-H bond energy in ethane ($\mathrm{C_2H_6}$) or chloroform ($\mathrm{CHCl_3}$). - The O-H bond energy in water ($\mathrm{H_2O}$) is different from the O-H bond energy in methanol ($\mathrm{CH_3OH}$) due to the different chemical environments. ## References (Derived from FBISE textbook)