Bond Energy and Enthalpy Change

 
This is part of Year 11 HSC Chemistry course under the topic of Enthalpy and Hess's Law. 

HSC Chemistry Syllabus

  • Explain the enthalpy changes in a reaction in terms of breaking and reforming bonds, and relate this to:

– The Law of Conservation of Energy 

        Bond Energy and Enthalpy Change

        This video will explore the concept of bond energy, defining what it is and explaining its importance in chemical reactions. It'll also examine how bond energy relates to enthalpy change and how enthalpy change for chemical reactions can be estimated using bond energies. 

        What is Bond Energy?

        Bond energy is the average energy required to break a specific chemical bond. Consider methane (`CH_4`), which consists of four C-H bonds. 

         

        Figure 1. tetrahedral structure of methane (`CH_4`)

           

        The bone energy of the C–H bond is 413 kJ/mol which means one mole of C–H bond requires 413 kJ to break. This means that to break all C–H bonds of one mole of `CH_4`, a total of 1652 kJ/mol of energy is needed. This information is usually presented in tables showing bond types and their respective energies. 

         

        Bond type

        Bond energy (kJ/mol)

        C=O

        746

        O–H

        464

        C–H

        413

        O=O

        495
        Table 1. Bond energies of a range of different bond types

         

        What is Enthalpy Change of Reaction? 

        The enthalpy change of a reaction (ΔH) is the overall change in the internal energy of chemical species during a chemical reaction. While enthalpy values are typically measured, we can estimate them theoretically by examining bond breaking and forming. Breaking bonds in reactants is an endothermic (energy absorbing) process, while forming bonds in products is an exothermic (energy releasing) process. The enthalpy change ΔH represents the difference between these absorbed and released energies.

        Bond Energy and Enthalpy Change Relationship 

        Enthalpy is defined by the formula

        $$H = U + PV$$

         

        where:

        H is enthalpy
        U is the internal energy of the substance
        P is the pressure of the system
        V is the volume of the system

        The internal energy of substances consists of potential energy primarily in the form of bond energy. PV in the formula represents work in thermodynamics which is done when a system expands or contracts against external pressure.

        Change in enthalpy that occurs in a chemical reaction is defined by the formula

        $$\Delta  = \Delta U + P \times \Delta V$$

         

        For most chemical reactions that occur in school laboratories, the work associated with changes in pressure and volume can be assumed to be negligible compared to changes in bond energy.

        Thus, `\Delta H` can often be approximated using changes in bond energies. However, discrepancies can arise between calculated and measured enthalpy values due to factors such as bond-breaking order. For instance, breaking the first bond in `CH_4` requires the most energy as the molecule is initially stable. As more bonds break, the molecule destabilises and its molecular geometry changes, requiring less energy for each subsequent bond.

         

        Calculating Enthalpy Using Bond Energy

        Steps:

        1. List all bonds broken in the reactants
        2. List all bonds formed in the products
        3. Sum the bond energies for broken bonds (endothermic, positive enthalpy)
        4. Sum the bond energies for formed bonds (exothermic, negative enthalpy)
        5. Add the positive and negative enthalpy values together.
        6. Adjust for state changes if applicable (e.g. if products condense from gas form)

        Example 1: Synthesis of hydrogen fluoride (HF) (More detailed explanation in video) 

        Use the bond energy values in the table to calculate the enthalpy change of the following chemical reaction.

         

        Bond type

        Bond energy (kJ/mol)

        H–H

        432

        H–F

        565

        F–F

        154

         

        Calculate the energy absorbed when breaking bonds in reactant molecules:

        $$432 + 154 = 586 \; kJ$$ 

        Calculate the energy released when forming bonds in product molecules:

        $$-565 \times 2 = -1130 \; kJ$$

        Determine the enthalpy change calculating the difference in energy:

        $$586 - 1130 = -544 \; kJ$$

        No changes in states of atoms are involved in this reaction as both reactants and products are gaseous. Therefore -544 kJ of energy is released for every 2 moles of HF molecules formed. 

        The molar enthalpy of reaction is given by

        $$\Delta H = \frac{-544}{2} = -272 \; \text{kJ/mol of HF}$$

        Example 2: Combustion of methane (`CH_4`) (More detailed explanation in video) 

        Use the bond energy values in the table to calculate the enthalpy change of the following chemical reaction.

         

         

        Bond type

        Bond energy (kJ/mol)

        C=O

        +746

        O–H

        +464

        C–H

        +413

        O=O

        +495
        Let's calculate the enthalpy change in one step for this example, by considering the energy absorbed and released during bond breaking and formation respectively at the same time.
        $$\Delta H = 413 \times 4 + 495 \times 2 + (-746 \times 2 -464 \times 2 \times 2)$$
        $$\Delta H = -706 \; kJ$$
         
        Since this calculation is for the formation of 1 mole of carbon dioxide, the molar enthalpy change is also given by:
        $$\Delta H = -706 \; \text{kJ/mol of} \; CO_2$$
         
        The energy changes associated with each process of the reaction can be better visualised in the following diagram.
         

          

        The diagram demonstrates that there's a discrepancy between the calculated enthalpy change value and the actual experimental (measured) value for combustion of methane. The discrepancy is explained below.

        Measured vs Calculated Enthalpy (ΔH)

        In some cases, the measured enthalpy change for a reaction can differ from the calculated value. For example the measured enthalpy change for the combustion of methane by calorimetry is -802 kJ/mol but using bond energies a value of -706 kJ/mol is calculated.

        This discrepancy often arises due to multiple energetic processes involved in the reaction. For example, the enthalpy of vaporisation of water has a specific value for the transition between liquid and gaseous states:

         

        • `H_2O(l) \rightarrow H_2O(g)`: ΔH = 40.7 kJ/mol (endothermic, as energy is absorbed to vaporise water)
        • `H_2O(g) \rightarrow H_2O(l)`: ΔH = –40.7 kJ/mol (exothermic, as energy is released when vapour condenses)

         

        Additionally, bond energy values in tables are average values – they represent an average for a particular bond type, derived from multiple reactions. This averaging process can introduce minor difference between the theoretical enthalpy calculated from bond energies and the actual measured enthalpy as the specific context of each bond (e.g. surrounding atoms, molecular stability) affects its exact energy requirement. 

        Lastly, it is important to remember, although the work done associated with changes in pressure and volume during a chemical reaction are negligible compared to bond energies, they still do contribute to the change in enthalpy. When these are not considered, there will inevitably be discrepancies between calculated and theoretical values.

        In the calculation of ∆H above, the aforementioned factors were not considered, hence resulting in a discrepancy between the calculated and theoretical value.

         

        Previous Section: ΔH of Combustion and Neutralisation, Calorimetry

        Next Section: Enthalpy of formation and Bond Energy (COMING)

         

         

        BACK TO MODULE 4: DRIVERS OF REACTION