In the following reaction:
`2NO(g)+O_(2)(g) overset(k')rarr2NO_(2)(g)`
What is the predicted rate law, if the mechanism is
`NO+O_(2)(g) overset(k_(eq))hArr NO_(3) ("fast")` (fast)
`NO_(3) + NO overset(k_(1))rarr NO_(2) + NO_(2)` (slow)

Explanation

To determine the predicted rate law for the reaction \(2NO(g) + O_2(g) \overset{k'}{\rightarrow} 2NO_2(g)\) based on the given mechanism, we will follow these steps:

### Step 1: Identify the Rate-Determining Step
The mechanism provided consists of two steps:
1. \(NO + O_2(g) \overset{k_{eq}}{\rightleftharpoons} NO_3\) (fast)
2. \(NO_3 + NO \overset{k_1}{\rightarrow} NO_2 + NO_2\) (slow)

The slow step is the rate-determining step, which means the rate of the overall reaction is governed by this step.
...