For the reaction at 500 K, `"NO"_(2)(g)+"CO"(g)to"CO"_(2)(g)+"NO"(g)`, the proposed mechanism is as below :
(i) `"NO"_(2)+"NO"_(2)to"NO"+"NO"_(3)("slow")" ""(ii) ""NO"_(3)+"CO"to"CO"_(2)+"NO"_(2)("fast")`
What is the rate law for the reaction ?

Explanation

To determine the rate law for the given reaction and its proposed mechanism, we will follow these steps:

### Step 1: Identify the slow step in the mechanism
The proposed mechanism consists of two steps:
1. \( \text{NO}_2 + \text{NO}_2 \rightarrow \text{NO} + \text{NO}_3 \) (slow)
2. \( \text{NO}_3 + \text{CO} \rightarrow \text{CO}_2 + \text{NO}_2 \) (fast)

The first step is the slow step, which is crucial for determining the rate law.

### Step 2: Write the rate expression for the slow step
The rate of a reaction is generally expressed in terms of the concentration of the reactants involved in the slowest step. For the slow step:
\[ \text{Rate} = k[\text{NO}_2]^2 \]
Here, \( k \) is the rate constant and \( [\text{NO}_2] \) is the concentration of nitrogen dioxide.

### Step 3: Conclude the rate law
From the slow step, we can conclude that the rate law for the overall reaction is:
\[ \text{Rate} = k[\text{NO}_2]^2 \]

### Step 4: Determine the order of the reaction
The order of the reaction is determined by the sum of the powers of the concentration terms in the rate law. In this case, since the concentration of \( \text{NO}_2 \) is squared:
- The order of the reaction = 2.

### Final Answer
The rate law for the reaction is:
\[ \text{Rate} = k[\text{NO}_2]^2 \]
The order of the reaction is 2.

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