You have studied the gas-phase oxidation of \(\mathrm{HBr}\) by \(\mathrm{O}_{2}\) : $$ 4 \mathrm{HBr}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{Br}_{2}(g) $$ You find the reaction to be first order with respect to \(\mathrm{HBr}\) and first order with respect to \(\mathrm{O}_{2}\). You propose the following mechanism: $$ \begin{aligned} \operatorname{HBr}(g)+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{HOOBr}(g) \\\ \mathrm{HOOBr}(g)+\mathrm{HBr}(g) & \longrightarrow 2 \mathrm{HOBr}(g) \\ \mathrm{HOBr}(g)+\mathrm{HBr}(g) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Br}_{2}(g) \end{aligned} $$ (a) Confirm that the elementary reactions add to give the overall reaction. (b) Based on the experimentally determined rate law, which step is rate determining? (c) What are the intermediates in this mechanism? (d) If you are unable to detect HOBr or HOOBr among the products, does this disprove your mechanism?

Step by step solution

01

(a) Confirming the elementary reactions add to the overall reaction

To confirm that the given elementary reactions add up to the overall reaction, we can simply add the equations for each reaction and then cancel out any species that appear on both the reactant and product sides. Let's do that: Step 1: HBr(g) + O2(g) → HOOBr(g) Step 2: HOOBr(g) + HBr(g) → 2 HOBr(g) Step 3: HOBr(g) + HBr(g) → H2O(g) + Br2(g) Adding all three equations: [HBr(g) + O2(g)] + [HOOBr(g) + HBr(g)] + [HOBr(g) + HBr(g)] → [HOOBr(g)] + [2 HOBr(g)] + [H2O(g) + Br2(g)] After canceling out the species that appear on both sides: 4 HBr(g) + O2(g) → 2 H2O(g) + 2 Br2(g) The overall reaction obtained by adding the elementary reactions is the same as the given overall reaction. So the answer is: yes, the elementary reactions add up to the overall reaction.

02

(b) Determining the rate-determining step

The reaction is found to be first order with respect to HBr and first order with respect to O2. The rate law can be expressed as: Rate = k[HBr]^1[O2]^1 To find the rate-determining step, we need to look at the proposed mechanism and identify the step that involves HBr and O2 as reactants. In this case, it is the first step: HBr(g) + O2(g) → HOOBr(g) Since the rate law agrees with this step's reactants, it is the rate-determining step.

03

(c) Identifying intermediates in the mechanism

Intermediates are the species that are produced in one step and consumed in a subsequent step. In the proposed mechanism, we can identify the following intermediates: 1. HOOBr(g): It is produced in Step 1 and consumed in Step 2. 2. HOBr(g): It is produced in Step 2 and consumed in Step 3. Hence, the intermediates in this mechanism are HOOBr(g) and HOBr(g).

04

(d) Impact of not detecting HOBr or HOOBr on the proposed mechanism

Not being able to detect HOBr or HOOBr among the products does not necessarily disprove the proposed mechanism. The reason is that these two species are intermediates, which means they are produced and consumed during the reaction process, and they might be present in very low concentrations. They could be consumed faster than they are produced or might decompose into other products during the reaction. Therefore, their absence in the final products does not disprove the proposed mechanism. Additional experiments and analyses would be required to confirm or disprove the mechanism.

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