How can you determine the law of the following reaction?
`2NO(g) + O_(2) (g) to 2NO_(2) (g)`

Explanation

To determine the rate law for the reaction \( 2NO(g) + O_2(g) \rightarrow 2NO_2(g) \), we can follow these steps:

### Step 1: Write the Reaction
The first step is to clearly write down the balanced chemical equation for the reaction:
\[ 2NO(g) + O_2(g) \rightarrow 2NO_2(g) \]

### Step 2: Conduct Initial Experiments
To determine the rate law, we need to conduct experiments where we vary the concentrations of the reactants and measure the rate of the reaction.

### Step 3: Choose a Reactant to Vary
In the first experiment, we will take \( NO \) in excess and vary the concentration of \( O_2 \). Let’s denote the concentration of \( O_2 \) as \( x \) moles while keeping \( NO \) in excess.

### Step 4: Write the Rate Law for This Condition
When \( NO \) is in excess, its concentration does not change significantly during the reaction, and we can express the rate law as:
\[ \text{Rate} = k [O_2]^x \]
Here, \( x \) is the order of the reaction with respect to \( O_2 \).

### Step 5: Conduct Another Experiment
In the second experiment, we will take \( O_2 \) in excess and vary the concentration of \( NO \). Let’s denote the concentration of \( NO \) as \( y \) moles while keeping \( O_2 \) in excess.

### Step 6: Write the Rate Law for This Condition
When \( O_2 \) is in excess, we can express the rate law as:
\[ \text{Rate} = k [NO]^y \]
Here, \( y \) is the order of the reaction with respect to \( NO \).

### Step 7: Combine the Rate Laws
By combining both rate laws from the experiments, we can express the overall rate law for the reaction:
\[ \text{Rate} = k [NO]^y [O_2]^x \]

### Step 8: Determine the Overall Rate Law
To determine the overall rate law, we need to find the values of \( x \) and \( y \) from the experimental data. The overall rate law will be:
\[ \text{Rate} = k [NO]^y [O_2]^x \]

### Conclusion
The final step is to analyze the experimental data to find the values of \( x \) and \( y \) which will give us the complete rate law for the reaction.

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