Chemistry

The key is distinguishing between reactants in the overall equation and reactants in the rate-determining step. Since step (2) is slow, it controls the reaction rate—but $\text{F}$ is an intermediate produced in the fast step (1), not a starting material. By writing $[\text{F}]$ in terms of the equilibrium from step (1), you can eliminate it and express the rate using only the initial reactants $\text{NO}_{2}$ and $\text{F}_{2}$. The fact that $\text{F}_{2}$ appears in a fast pre-equilibrium rather than the slow step is why it doesn't show up in the final rate law.

The key is distinguishing between reactants in the overall equation and reactants in the rate-determining step. Since step (2) is slow, it controls the reaction rate—but $\text{F}$ is an intermediate produced in the fast step (1), not a starting material. By writing $[\text{F}]$ in terms of the equilibrium from step (1), you can eliminate it and express the rate using only the initial reactants $\text{NO}_{2}$ and $\text{F}_{2}$. The fact that $\text{F}_{2}$ appears in a fast pre-equilibrium rather than the slow step is why it doesn't show up in the final rate law.