Bond Enthalpies

This lesson covers: 

1. How bond breaking and bond making relate to reaction enthalpy
2. Mean bond enthalpy
3. How to calculate enthalpy changes for reactions using mean bond enthalpies

Reactions involve breaking and making bonds

Enthalpy changes in chemical reactions result from:

• Bond breaking - this process requires energy, making it endothermic (positive ΔH).
• Bond making - this process releases energy, making it exothermic (negative ΔH).

The overall enthalpy change (ΔH) of a reaction is the combined effect of both bond breaking and bond making.

More detail on breaking and making bonds

• To break chemical bonds, energy must be supplied, hence bond breaking is endothermic (ΔH positive). The strength of the bond correlates with the amount of energy needed to break it.
• The process of making chemical bonds results in energy release, hence bond formation is exothermic (ΔH negative). The formation of stronger bonds releases more energy.
• A reaction that requires more energy to break bonds than is released during new bond formation has a positive overall ΔH.
• Conversely, if breaking the bonds requires less energy than is released upon forming new bonds, then the reaction’s overall ΔH is negative.

Mean bond enthalpies

Mean bond enthalpy is defined as the energy required to break one mole of a specified type of covalent bond in a gaseous molecule. Although a specific type of bond always requires a particular amount of energy to break, the exact amount can vary based on the bond's molecular environment.

For example, breaking each O-H bond in H₂O involves different amounts of energy amounts. To account for these variations, chemists use mean bond enthalpy, which represents the average energy needed to break a type of bond across various molecular environments.

Important points regarding bond enthalpy values include:

1. They are always positive (endothermic) because breaking bonds requires energy.
2. They represent an average value across different molecular environments.

Calculating reaction enthalpy changes

The enthalpy change of a complete reaction (ΔH_r) is determined using average bond enthalpies for the bonds that are broken and those that are formed:

ΔH_r = Σ(bond enthalpies of bonds broken) - Σ(bond enthalpies of bonds formed)

where Σ = sum of

Alternatively, ΔH_r can be expressed in terms of the bond enthalpies in the reactants and products:

ΔH_r = Σ(bond enthalpies in reactants) - Σ(bond enthalpies in products)

Hess cycles provide more accurate ΔH_r values

Calculating ΔH_r using mean bond enthalpies is less accurate than using Hess cycles because average bond enthalpies do not account for the unique molecular environment of each bond in a specific molecule. Hess cycles, in contrast, consider the actual enthalpy changes associated with the specific bonds in the reactants and products, providing a more precise estimation of ΔH_r.

Worked example 1 - Calculating ΔH for the combustion of methane

Calculate the enthalpy change (ΔH) for the combustion of methane (CH₄) with oxygen to form carbon dioxide and water. The balanced chemical equation is:

CH₄ + 2O₂ ➔ CO₂ + 2H₂O

Given the mean bond enthalpies:

Step 1: Identify and count the bonds broken and formed

Bonds broken: 4 x C-H and 2 x O=O

Bonds formed: 2 x C=O and 4 x O-H

Step 2: Calculate total energy absorbed in breaking bonds

Energy to break bonds = (4 x 414) + (2 x 498) = 1,656 + 996 = 2,652 kJ mol^-1

Step 3: Calculate total energy released in forming bonds

Energy released in bond formation = (2 x 799) + (4 x 464) = 1,598 + 1,856 = 3,454 kJ mol^-1

Step 4: Calculate ΔH for the reaction

ΔH = Σbond enthalpies of bonds broken - Σbond enthalpies of bonds formed

ΔH = 2,652 - 3,454 = -802 kJ mol^-1

The negative sign indicates that the reaction is exothermic, releasing 802 kJ mol^-1 of energy.

Worked example 2 - Calculating ΔH for the synthesis of ammonia

Calculate the enthalpy change (ΔH) for the synthesis of ammonia (NH₃) from nitrogen and hydrogen. The balanced chemical equation is:

N₂ + 3H₂ ➔ 2NH₃

Given the mean bond enthalpies:

Step 1: Identify and count the bonds broken and formed

Bonds broken: 1 x N≡N and 3 x H-H

Bonds formed: 6 x N-H

Step 2: Calculate total energy absorbed in breaking bonds

Energy to break bonds = (1 x 945) + (3 x 436) = 945 + 1,308 = 2,253 kJ mol^-1

Step 3: Calculate total energy released in forming bonds

Energy released in bond formation = (6 x 391) = 2,346 kJ mol^-1

Step 4: Calculate ΔH for the reaction

ΔH = Σbond enthalpies of bonds broken - Σbond enthalpies of bonds formed

ΔH = 2,253 - 2,346 = -93 kJ mol^-1

The negative sign indicates that the reaction is exothermic, releasing 93 kJ mol^-1 of energy.