A proposed mechanism for the reaction 2O3 --- 3O2 is shown below.

NO + O3 --- NO2 + O2 (slow)

NO2 + O3 --- NO + 2O2 (fast)

What is the rate law consistent with this mechanism?

Question

A proposed mechanism for the reaction 2O3 ---> 3O2 is shown below.

NO + O3 ---> NO2 + O2              (slow)

NO2 + O3 ---> NO + 2O2           (fast)

What is the rate law consistent with this mechanism?

BlackTom AI · Accepted Answer

Begin by identifying the rate-determining step in the provided mechanism. The slow step is NO + O3 -> NO2 + O2, which means the overall reaction rate is controlled by this step.

Option 1: rate = k[NO][O3]. This directly matches the rate expression for the slow, elementary step, since the rate depends on the concentrations of NO and O3 present in that step. This is a strong candidate for the correct rate law.

Option 2: rate = k[NO2][O3]. This would imply that NO2, a product from the slow step, participates in the rate law. However, intermediates like NO2 do not appear in the rate law unless the mechanism provides a scenario where they are involved in the slow step or in a pre-equilibrium that feeds the slow step. Here, NO2 is produced in the slow step and consumed in the fast step, so it should not be in the rate law.

Option 3: rate = k[NO][O3]2[NO2]. This expression includes a squared O3 term and also NO2, an intermediate, which is inconsistent with the rate-determining step being a single bimolecular elementary step. The squared concentration is not justified by the mechanism.

Option 4: rate = k[O3]2. This asserts dependence solely on O3, with a squared concentration, ignoring NO entirely. Since the slow step requires both NO and O3 as reactants, a rate law depending only on O3 is incorrect.

In summary, the correct rate law must reflect the rate-determining (slow) step NO + O3 -> NO2 + O2, and therefore depends on both [NO] and [O3] in first power. The other options misrepresent the role of intermediates, the stoichiometry, or the involvement of the reactants within the rate-determining step.

CHEM 110 Lecture Quiz Week 6

A proposed mechanism for the reaction 2O3 ---> 3O2 is shown below. NO + O3 ---> NO2 + O2 (slow) NO2 + O3 ---> NO + 2O2 (fast) What is the rate law consistent with this mechanism?

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