A reaction has the following overall equation: 2 NO_2(g) + F_2(g) → 2 NO_2F(g). Experimental data show that the rate law is rate = k[NO_2][F_2]. Based on this information, how many elementary steps are most likely involved in the reaction mechanism?

• A. Four elementary steps
• B. Two elementary steps
• C. Three elementary steps
• D. One elementary step

Answer: (B)

Verified step by step guidance

1. Identify the overall reaction: \$2 \mathrm{NO}_2(g) + \mathrm{F}_2(g) \rightarrow 2 \mathrm{NO}_2\mathrm{F}(g)$.
2. Examine the given rate law: \(\text{rate} = k[\mathrm{NO}_2][\mathrm{F}_2]\). This indicates the reaction rate depends on the concentration of \(\mathrm{NO}_2\) and \(\mathrm{F}_2\) each to the first power.
3. Recall that for an elementary step, the rate law can be directly written from the molecularity of that step. For example, if an elementary step involves one \(\mathrm{NO}_2\) and one \(\mathrm{F}_2\) molecule colliding, the rate law would be \(\text{rate} = k[\mathrm{NO}_2][\mathrm{F}_2]\).
4. Since the overall reaction involves 2 \(\mathrm{NO}_2\) molecules but the rate law shows first order in \(\mathrm{NO}_2\), this suggests the reaction does not occur in a single elementary step involving both \(\mathrm{NO}_2\) molecules simultaneously.
5. Therefore, the reaction mechanism likely involves multiple elementary steps, and given the rate law, two elementary steps are most consistent: one step involving \(\mathrm{NO}_2\) and \(\mathrm{F}_2\) to form an intermediate, and a second step involving the intermediate reacting further to produce the final product.