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J. W. Hill, R. H. Petrucci, T. W. McCreary, & S. S. Perry General Chemistry, 4th edition.

Problem 13.65.

The following reaction exhibits the rate law: Rate = k[NO]2[Cl2].
2NO(g) + Cl2(g) 2NOCl(g)

Explain why the following mechanism is not plausible for this reaction.
Fast:
NO(g) + Cl2NOCl(g) + Cl(g)
Slow:
NO(g) + Cl(g) NOCl(g)





Answer:

The rate law is determined by the slow step: Rate = kslow[NO][Cl]

However, this rate law includes and intermediate that cannot be part of the rate law for the overall reaction - only NO or Cl2 can be part of the rate law. The [Cl] term can be eliminated using the fast, reversible step where the rate of the forward reaction is the same as the rate of the reverse reaction:

Rateforward = Ratereverse

Rateforward = kforward[NO][Cl2]

Ratereverse = kreverse[NOCl][Cl]

so kforward[NO][Cl2] = kreverse[NOCl][Cl]

substituting for [Cl] in the slow step rate law gives:

This rate does not match the experimental rate law so this cannot be a plausible mechanism.