Question

Following is a balanced equation for bromination of toluene. (a) Using the values for bond dissociation enthalpies given in Appendix 3 , calculate \(\Delta H^{0}\) for this reaction. (b) Propose a pair of chain propagation steps and show that they add up to the observed reaction. (c) Calculate \(\Delta H^{0}\) for each chain propagation step. (d) Which propagation step is rate-determining?

Short answer

To find the rate-determining step in the bromination of toluene, you need to calculate the change in enthalpy, propose chain propagation steps, calculate the change in enthalpy for each propagation step, and identify the step with the highest change in enthalpy. The highest change in enthalpy corresponds to the rate-determining step.

Step-by-step solution

Calculate \(\Delta H^{0}\) for the reaction

Using the bond dissociation enthalpies from Appendix 3, we will calculate the \(\Delta H^{0}\) for the reaction by summing up the bond enthalpies for the bonds that are broken and subtracting the bond enthalpies for the bonds that are formed. The balanced equation for bromination of toluene is: \(\text{Toluene} + \text{Br}_2 \rightarrow \text{Bromotoluene} + \text{HBr}\) Broken bonds: - C-H bond in toluene - Br-Br bond Formed bonds: - C-Br bond in bromotoluene - H-Br bond Now, use the bond dissociation enthalpies to calculate \(\Delta H^{0}\): \(\Delta H^{0} = [\text{C-H} + \text{Br-Br}] - [\text{C-Br} + \text{H-Br}]\)

Propose chain propagation steps and show that they add up to the reaction

We will propose two chain propagation steps: Propagation step 1: \(\text{Toluene} + \text{Br}\cdot \rightarrow \text{Toluene}^{ \cdot } + \text{HBr}\) Propagation step 2: \(\text{Toluene}^{ \cdot } + \text{Br}_2 \rightarrow \text{Bromotoluene} + \text{Br}\cdot\) When we add these two propagation steps, we obtain the observed reaction: \(\text{Toluene} + \text{Br}_2 \rightarrow \text{Bromotoluene} + \text{HBr}\)

Calculate \(\Delta H^{0}\) for each chain propagation step

Using bond dissociation enthalpies, calculate the \(\Delta H^{0}\) for each propagation step. Propagation step 1: \(\Delta H_1^{0} = [\text{C-H} + \text{Br}\cdot] - [\text{H-Br} + \text{Toluene}^\cdot]\) Propagation step 2: \(\Delta H_2^{0} = [\text{Toluene}^\cdot + \text{Br-Br}] - [\text{C-Br} + \text{Br}\cdot]\)

Identify the rate-determining step

The rate-determining step is the propagation step with the highest \(\Delta H^{0}\). Compare \(\Delta H_1^{0}\) and \(\Delta H_2^{0}\): If \(\Delta H_1^{0} > \Delta H_2^{0}\), then the rate-determining step is the Propagation step 1. If \(\Delta H_2^{0} > \Delta H_1^{0}\), then the rate-determining step is the Propagation step 2. By comparing the values, you will identify the rate-determining step among the propagation steps.