For the reaction `2H_(2) + 2NO rarr N_(2) + 2H_(2)O`, the following mechanism has been suggested :
`2NO ? N_(2)O_(2)` equilibrium constant `K_(1)` (fast)
`N_(2)O_(2) +H_(2) overset(k_(2)) rarr N_(2)O +H_(2)O` (slow)
`N_(2) O +H_(2) overset(k_(3)) rarr N_(2)+H_(2)O` (fast)
Establish the rate law for given reaction.

Explanation

To establish the rate law for the reaction \(2H_2 + 2NO \rightarrow N_2 + 2H_2O\) based on the provided mechanism, we will follow these steps:

### Step 1: Identify the Rate Determining Step (RDS)
The rate of the overall reaction is determined by the slowest step in the mechanism. From the given mechanism, the slow step is:
\[ N_2O_2 + H_2 \overset{k_2}{\rightarrow} N_2O + H_2O \]

### Step 2: Write the Rate Expression for the RDS
The rate of the reaction for the rate determining step can be expressed as:
...