For a reaction, `2NO + 2H_(2) to N_(2) + 2H_(2) O`, the possible mechanism is
`NO hArr N_(2)O_(2)`
`N_(2)O_(2) + H_(2) overset("Slow")(to) N_(2)O + H_(2) O`
`N_(2) O + H_(2) O overset("fast")(to) N_(2) + H_(2) O`
What is the rate law and order of the reaction?

Options

A. Rate = `[N_(2)O_(2)]`, order = 1
B. Rate = `[N_(2)O_(2)][H_(2)]`, order = 2
C. Rate = `[N_(2)O_(2)]^(2)` order = 2
D. Rate = `[N_(2)O_(2)]^(2) [H_(2)]`, order = 3

Explanation

To determine the rate law and order of the reaction given the mechanism, we will follow these steps:

### Step 1: Identify the Rate-Determining Step
The rate of a reaction is determined by its slowest step, known as the rate-determining step. In this case, the slow step is:
\[ N_2O_2 + H_2 \overset{\text{Slow}}{\to} N_2O + H_2O \]

### Step 2: Write the Rate Law
The rate law can be expressed based on the reactants involved in the rate-determining step. For the slow step, the rate law can be written as:
\[ \text{Rate} = k [N_2O_2]^1 [H_2]^1 \]
Here, \( k \) is the rate constant, and the exponents correspond to the stoichiometric coefficients of the reactants in the rate-determining step.

### Step 3: Simplify the Rate Law
Since the exponents are both 1, we can simplify the rate law to:
\[ \text{Rate} = k [N_2O_2] [H_2] \]

### Step 4: Determine the Overall Order of the Reaction
The overall order of the reaction is the sum of the exponents in the rate law. In this case:
- The exponent for \( [N_2O_2] \) is 1.
- The exponent for \( [H_2] \) is 1.

Thus, the overall order is:
\[ 1 + 1 = 2 \]

### Final Answer
- **Rate Law**: \( \text{Rate} = k [N_2O_2] [H_2] \)
- **Order of the Reaction**: 2

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