The following reaction exhibits the rate law: Rate = k[NO2]^2[Cl2].
2NO(g)+Cl2(g)---->2NOCl (g)
(a) Explain why the following mechanism is not plausible for this reaction.
Fast: NO + Cl2<-->NOCl + Cl
Slow: NO + Cl---->NOCl
(b) Propose a two-step mechanism involving one fast reversible step and one slow step that is consistent with the net equation and the observed rate law.
No2
(a) In order for a mechanism to be plausible for a reaction, it must satisfy two conditions: (1) it must lead to the overall balanced equation, and (2) it must explain the observed rate law.
Looking at the proposed mechanism, we see that the overall balanced equation matches the net equation, which is a good start. However, when we examine the rate law, we see that it involves the concentrations of both NO2 and Cl2 raised to the power of 2.
In the proposed mechanism, the only step that involves both NO2 and Cl2 is the fast reversible step: NO + Cl2 <--> NOCl + Cl. The rate law for this step would be proportional to the concentrations of NO and Cl2. However, in the overall rate law we have the concentrations of NO2 and Cl2 raised to the power of 2. Therefore, the proposed mechanism does not explain the observed rate law, and it is not plausible for this reaction.
(b) In order to propose a two-step mechanism that is consistent with the observed rate law, we need to find a step that involves the concentrations of NO2 and Cl2 raised to the power of 2. One possible mechanism that satisfies this condition is:
Fast: NO2 + Cl2 <--> NO2Cl + Cl
Slow: NO2Cl + NO2Cl --> 2NO2 + 2Cl
In the first step, NO2 reacts with Cl2 to form NO2Cl and Cl. This step is fast and reversible.
In the second step, the slow step, two molecules of NO2Cl combine to form two molecules of NO2 and two molecules of Cl. This step is slow and irreversible.
The overall balanced equation for this proposed mechanism is:
2NO2 + Cl2 --> 2NO2Cl + Cl
2NO2Cl --> 2NO2 + 2Cl
Adding these equations gives us the net equation for the reaction:
2NO2 + Cl2 --> 2NO2Cl + Cl
The rate law for this mechanism can be determined by examining the slow step. We see that the concentration of NO2Cl is involved in the slow step and is raised to the power of 2. Therefore, the rate law for this mechanism would be rate = k[NO2Cl]^2, which matches the observed rate law.
Thus, this proposed two-step mechanism is consistent with the net equation and the observed rate law for the reaction.