Problem 12-80

Mechanism identification:

The correct mechanism must meet three criteria:

1. All elementary steps are reasonable
2. The sum of the elementary steps must equal the rate law of the total reaction
3. The rate law of the complete reaction must correlate with the order of the slowest elementary step.

Complete reaction: 2NO(g) + O₂(g) → 2NO₂(g)

Mechanism (d) is incorrect because the total reaction is not the one expected: 3NO → 2NO₂ (not even balanced!)
However, mechanisms (a), (b), (c) meet criteria 1 and 2

Proposed mechanisms (a) and (c) both have a slow first step.
However, neither of these solutions corresponds to the expected rate law: rate = k[NO]²[O₂]

• (a) rate = k[NO][O₂]
• (c) rate = k[NO]²

The only remaining correct solution is (b)

Verification of criterion 3:

Since the first elementary step is fast, it is also an equilibrium waiting for the next step (slow) then:

K(equilibrium) = [product]/[reactant]  therefore  K = [NO₃]/[NO][O₂] (will be covered next chapter in equilibrium)

can be rearranged to: [NO₃] = K[NO][O₂]

and subtitute [NO₃] in the slow elementary step gives: rate = k[NO]²[O₂]
which is the expected rate law, therefore, mechanism (b) is correct.