Question

What is the rate law for the reaction that has the following mechanism? step 1: no(g) + no(g) → N₂O₂(g) (fast) step 2: N₂O₂ (g) + O₂(g) → 2NO₂(g) (slow)

1) rate = k[no][N₂O₂]
2) rate = k[no]2
3) rate = k[no]2[O₂]
4) Cannot be determined

Answer 1

The correct rate law for the given reaction mechanism, where step 2 is the slow, rate-determining step, is rate = k[NO]²[O₂]. This reflects the dependence of the reaction rate on the concentrations of both NO and O₂, as they are the reactants involved in the slow step of the reaction.

Step-by-step explanation:

The question at hand involves determining the rate law for a reaction based on its mechanism. In chemical kinetics, the rate-determining step of a reaction, which is the slowest step, controls the speed of the overall reaction. Therefore, the rate law of the entire reaction reflects the rate law of the slow step, as the other steps quickly equilibrate.

Given the proposed mechanism:

• Step 1: NO(g) + NO(g) → N₂O₂(g) (fast)
• Step 2: N₂O₂(g) + O₂(g) → 2NO₂(g) (slow)
  

Since Step 2 is the slow step and the rate-determining step, the rate law is based on the reactants involved in this step. The correct rate law for the overall reaction, reflecting the mechanism provided, would thus be rate = k[NO][O₂], where 'k' is the rate constant specific to this step. However, since [N₂O₂] is generated from NO in the fast step, it is not included in the rate law for the overall reaction. Rate = k[NO]²[O₂] accurately reflects how the concentration of NO and O₂ affects the rate of the slow, and hence rate-determining, step 2.