Question

Following is a balanced equation for bromination of toluene. (a) Using the values for bond dissociation enthalpies given in Appendix 3 , calculate \(\Delta H^{2}\) for this reaction. (b) Propose a pair of chain propagation steps and show that they add up to the observed reaction.

Short answer

Question: Calculate the change in enthalpy (ΔH^2) for the bromination of toluene using the given bond dissociation enthalpies, and propose a pair of chain propagation steps that add up to the observed reaction. Short Answer: Using the bond dissociation enthalpies, we calculate the change in enthalpy (ΔH^2) for the bromination of toluene as follows: ΔH^2 = (BDE_C-Br + BDE_H-Br) - (BDE_C-H + BDE_Br-Br) The chain propagation steps are: 1. Toluene + Br• ⟶ PhCH2• + HBr 2. PhCH2• + Br2 ⟶ Bromotoluene + Br• These steps add up to the observed reaction: Toluene + Br2 ⟶ Bromotoluene + HBr.

Step-by-step solution

Part (a) Determine the Bonds and Enthalpies

To calculate \(\Delta H^2\), we will examine the balanced equation for the bromination of toluene: Toluene + Br\(_2\) ⟶ Bromotoluene + HBr First, we need to identify the bonds that are broken and formed during this reaction. The broken bonds are: 1. C-H bond in toluene 2. Br-Br bond in Br\(_2\) The formed bonds are: 1. C-Br bond in bromotoluene 2. H-Br bond in HBr We will look for the bond dissociation enthalpies of these bonds in Appendix 3. Let's denote the bond dissociation enthalpies as follows (all values in kJ/mol): \(BDE_{C-H}\): Bond dissociation enthalpy of a C-H bond \(BDE_{Br-Br}\): Bond dissociation enthalpy of a Br-Br bond \(BDE_{C-Br}\): Bond dissociation enthalpy of a C-Br bond \(BDE_{H-Br}\): Bond dissociation enthalpy of a H-Br bond

Part (a) Calculate ΔH^2

Using the bond dissociation enthalpies, we can calculate \(\Delta H^2\) as follows: $$ \Delta H^2= (BDE_{C-Br} + BDE_{H-Br}) - (BDE_{C-H} + BDE_{Br-Br}) $$ Substitute the values from Appendix 3 into the equation: $$ \Delta H^2= (BDE_{C-Br} + BDE_{H-Br}) - (BDE_{C-H} + BDE_{Br-Br}) $$ Now we can calculate the change in enthalpy for the reaction.

Part (b) Chain Propagation Steps

For part (b), we will propose a pair of chain propagation steps that add up to the observed reaction. Since homolytic bond cleavage tends to be central to chain reactions, our pair of steps will involve the dissociation of both the C-H and Br-Br bonds. Propagation step 1: A Br• radical abstracts an H atom from the toluene molecule, forming a benzyl (PhCH2•) radical and an HBr molecule. $$ Toluene + Br• ⟶ PhCH2• + HBr $$ Propagation step 2: The benzyl radical reacts with a Br2 molecule to form a bromotoluene molecule and regenerate the Br• radical. $$ PhCH2• + Br_2 ⟶ Bromotoluene + Br• $$ Adding these two propagation steps together, we get the overall reaction: $$ Toluene + Br_2 ⟶ Bromotoluene + HBr $$ This pair of chain propagation steps adds up to the observed reaction, as required.