1) Nitrogen dioxide reacts with hydrogen to give nitrogen and water according to the equation:
`2NO_(2) + H_(2) to N_(2) + H_(2)O_(2)` (slow)
`H_(2) + H_(2)O_(2) to 2H_(2)O` (fast)
What is the predicted rate law?
(1) Rate `=K[NO_(2)]`,
(2) Rate `=K[H_(2)]^(2)`
(3) Rate `=K[NO_(2)]^(2) [H_(2)]`
(4) Rate `=K[NO_(2)][H_(2)]`

Explanation

To determine the predicted rate law for the given reaction mechanism, we will analyze the steps involved in the reaction.

### Step 1: Identify the Rate-Determining Step
The reaction consists of two steps:
1. **Slow Step**: \( 2NO_2 + H_2 \rightarrow N_2 + H_2O_2 \)
2. **Fast Step**: \( H_2 + H_2O_2 \rightarrow 2H_2O \)

In chemical kinetics, the rate law is determined by the slowest step of the reaction, known as the rate-determining step. This is because the slow step will dictate the overall rate of the reaction.
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