Question

Consider benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) in the gas phase. (a) Write the reaction for breaking all the bonds in \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\), and use data in Appendix \(C\) to determine the enthalpy change for this reaction. (b) Write a reaction that corresponds to breaking all the carbon-carbon bonds in \(\mathrm{C}_{6} \mathrm{H}_{6}(g) .\) (c) By combining your answers to parts (a) and (b) and using the average bond enthalpy for \(C-H\) from Table \(8.4\), calculate the average bond enthalpy for the carbon-carbon bonds in \(\mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{~g}) .\) (d) Comment on your answer from part (c) as compared to the values for \(C-C\) single bonds and \(C=C\) double bonds in Table \(8.4 .\)

Short answer

In summary, the average bond enthalpy for carbon-carbon bonds in benzene is 522 kJ/mol. This value is between the bond enthalpies for C-C single bonds (346 kJ/mol) and C=C double bonds (611 kJ/mol) as expected, since the bonds in benzene are intermediate between single and double bonds due to the resonance structures.

Step-by-step solution

Reaction for bond breaking in benzene

The reaction for breaking all the bonds in benzene can be written as: C6H6(g) → 6C(g) + 6H(g) Calculating enthalpy change: We will use enthalpies of formation to determine the enthalpy change for this reaction. According to Appendix C: ΔfH°(C6H6, g) = +82.8 kJ/mol ΔfH°(C, g) = 716.7 kJ/mol ΔfH°(H, g) = 218.0 kJ/mol Now we can find the enthalpy change: ΔrxnH° = [6 × ΔfH°(C, g) + 6 × ΔfH°(H, g)] - ΔfH°(C6H6, g)

Calculating enthalpy change

Plug in the values and find the enthalpy change: ΔrxnH° = [6 × (716.7 kJ/mol) + 6 × (218.0 kJ/mol)] - (82.8 kJ/mol) = 5610 kJ/mol (b) Breaking all carbon-carbon bonds in benzene:

Reaction for breaking C-C bonds in benzene

For the reaction that corresponds to breaking all the carbon-carbon bonds in C6H6(g), we have: C6H6(g) + 3C2H2(g) → 6C(g) + 6H(g) (c) Calculating the average bond enthalpy for C-C bonds in benzene: We will combine the answers to (a) and (b) and use the given average bond enthalpy for C-H: Average bond enthalpy for C-H = 413 kJ/mol Enthalpy change for breaking C-H bonds: ΔH_CH = 6 × 413 kJ/mol = 2478 kJ/mol Enthalpy change for breaking C-C bonds: ΔH_CC = ΔrxnH° - ΔH_CH = 5610 kJ/mol - 2478 kJ/mol = 3132 kJ/mol Average bond enthalpy for C-C bonds in benzene: ΔH_CC / 6 bonds = 3132 kJ/mol / 6 = 522 kJ/mol (d) Comparing with C-C and C=C bond enthalpies:

Comparing with C-C and C=C bond enthalpies

From Table 8.4, the bond enthalpies for C-C single bonds and C=C double bonds are 346 kJ/mol and 611 kJ/mol, respectively. The average bond enthalpy for the carbon-carbon bonds in benzene (522 kJ/mol) is between these values, which is expected since the bonds in benzene are intermediate between single and double bonds due to the resonance structures.

Key concepts

Bond Enthalpy Calculation

When you're learning about energy changes in chemical reactions, bond enthalpy calculation plays a crucial role. Enthalpy change, often symbolized as ΔH, indicates the total heat change when bonds are broken and formed during a chemical reaction. It's a core part of thermochemistry, which involves the study of energy and heat associated with chemical reactions.

To calculate the enthalpy change of breaking bonds in benzene, we first need to list down the bonds broken and formed. Since bond enthalpies are provided for individual bonds, you can determine the total enthalpy change by summing up these bond enthalpies. Remember, breaking bonds requires energy and is endothermic (ΔH positive), while forming bonds releases energy and is exothermic (ΔH negative).

Here's a step to keep in mind: The enthalpy change for a reaction (ΔrxnH°) is found by adding together the enthalpies of all products and then subtracting the enthalpies of all reactants. It's important to use the correct signs (positive for bond breaking and negative for bond making) to get the right overall enthalpy change for the reaction.

Carbon-Carbon Bond Energy

The carbon-carbon bond energy reflects the strength of the C-C bond. It's a specific type of bond enthalpy that is essential when discussing organic molecules like benzene. In our benzene example, we are asked to focus on the energy needed to break all carbon-carbon bonds in a molecule of benzene.

The average C-C bond enthalpy can be found by calculating the total energy required to break these bonds, then dividing that energy by the number of C-C bonds broken. It's fascinating that in benzene, the carbon-carbon bond energy is not the same as that of a typical single or double bond. This is a unique aspect of benzene known as aromatic stability, which arises from its resonance structures - a concept that describes the delocalization of electrons over several atoms, allowing benzene to have bond lengths and energies that are intermediate between a single and a double bond.

Understanding the specific bond energy in molecules like benzene is crucial because it helps us predict the stability and reactivity of the molecule, key knowledge for anyone delving into organic chemistry or working on the synthesis of chemical compounds.

Benzene Thermochemistry

Let's dive into benzene thermochemistry, a fascinating topic that bridges the gap between the theoretical world of chemistry and real-world applications. Benzene is an organic chemical compound with a distinctly stable ring-like structure, and studying its thermochemistry involves understanding how energy changes when benzene reacts or transforms.

Benzene's thermochemical behavior is unique due to its resonance stabilization. When we calculate the average bond enthalpy for the C-C bonds in benzene, we find that it is higher than that of a single C-C bond but lower than that of a C=C double bond, reflecting benzene's resonance structure.

Not only does this intermediate energy contribute to benzene's remarkable stability, but it also affects its reactivity, making it less reactive than typical alkenes. Benzene's thermochemical data are crucial for industrial processes such as the production of polymers, dyes, and pharmaceuticals, and they're also important in environmental contexts, like understanding benzene's role as a pollutant.

Enthalpies of Formation

Understanding enthalpies of formation is like having a map that tells you the 'cost' of creating different chemical compounds from their elemental forms. An enthalpy of formation (ΔfH°) is defined as the heat change that occurs when one mole of a compound is formed from its elements in their standard states.

In our exercise, we use the enthalpies of formation for benzene and the gaseous forms of carbon and hydrogen to determine the energy involved in breaking down a mole of benzene into its elemental components. The sign convention for enthalpies of formation is important: if energy is released during the formation of a compound, the ΔfH° is negative, whereas if energy is absorbed, the ΔfH° is positive.

This concept not only helps you with calculations in the laboratory, but it also has practical implications, as it allows chemists and engineers to predict which reactions will be favorable for the synthesis of new compounds and to design processes that are energetically efficient. Learning how to use enthalpies of formation is crucial, both for academic purposes and for applications in real-world chemical industries.