Bond Enthalpies

Carson West

Hess Law

Thermodynamics

Bond enthalpy (or bond energy) is the average amount of energy required to break one mole of a specific type of bond in the gaseous phase. It’s an important concept in thermochemistry, allowing us to estimate the enthalpy change ( $ \Delta H $ ) of reactions without needing to directly measure it experimentally. Remember that bond enthalpies are average values, as the actual energy required to break a specific bond can vary slightly depending on the molecule’s structure and surrounding atoms.

Understanding the Concept

Bond formation is an exothermic process (releases energy), while bond breaking is an endothermic process (requires energy). Bond enthalpy is always a positive value because it represents the energy required to break a bond. We can use bond enthalpies to estimate the enthalpy change of a reaction using Hess’s Law, essentially by summing the energy required to break bonds in the reactants and subtracting the energy released by forming bonds in the products.

The equation for calculating the enthalpy change ( $ \Delta H_{rxn} $ ) using bond enthalpies is:

$ \Delta H_{rxn} \approx \sum \text{Bond enthalpies of bonds broken} - \sum \text{Bond enthalpies of bonds formed} $

Using Bond Enthalpies to Estimate $ \Delta H_{rxn} $

Let’s illustrate with an example: Consider the reaction between methane ( $ CH_4 $ ) and chlorine ( $ Cl_2 $ ) to form chloromethane ( $ CH_3Cl $ ) and hydrogen chloride ( $ HCl $ ):

$ CH_4(g) + Cl_2(g) \rightarrow CH_3Cl(g) + HCl(g) $

To estimate $ \Delta H_{rxn} $ :

  1. Bonds Broken: We break one C-H bond in $ CH_4 $ and one Cl-Cl bond in $ Cl_2 $ .
  2. Bonds Formed: We form one C-Cl bond in $ CH_3Cl $ and one H-Cl bond in $ HCl $ .

We would then look up the average bond enthalpies for each bond type in a data table (usually provided in your textbook or on an AP Chemistry exam). Let’s assume (for this example):

Therefore:

$ \Delta H_{rxn} \approx [(413 \text{ kJ/mol}) + (242 \text{ kJ/mol})] - [(339 \text{ kJ/mol}) + (431 \text{ kJ/mol})] = -115 \text{ kJ/mol} $

This calculation provides an estimate of the enthalpy change. The actual value may differ slightly due to the limitations of using average bond enthalpies.

Limitations of Using Bond Enthalpies

Average vs. Actual Bond Enthalpies The use of average bond enthalpies inherently involves some error. The strength of a bond can vary depending on the molecule’s structure and the surrounding atoms. For example, a C-H bond in methane will have a slightly different bond enthalpy than a C-H bond in benzene.

Phase Changes and Standard Conditions Bond enthalpies are typically given for gaseous phase molecules. If the reactants and products are in different phases (solid, liquid, or gas) then additional energy terms (heat of fusion or vaporization) will need to be considered. The calculations are usually based on standard conditions (298 K and 1 atm).

Resonance Structures In molecules with resonance structures, the actual bond enthalpy may differ from the average calculated using individual bond enthalpies.