For a reaction `2NO(g) +Cl_(2)(g) rarr 2NOCl(g)`, when concentration of `Cl_(2)` is doubled, the rate becomes four times. What is the order of reaction with respect to `Cl_(2)` ?

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To determine the order of the reaction with respect to \( \text{Cl}_2 \) for the reaction \( 2\text{NO}(g) + \text{Cl}_2(g) \rightarrow 2\text{NOCl}(g) \), we can follow these steps:

### Step 1: Understand the relationship between concentration and rate
The rate of a reaction can be expressed in terms of the concentrations of the reactants raised to their respective orders. For this reaction, we can write the rate law as:
\[ \text{Rate} = k [\text{NO}]^m [\text{Cl}_2]^n \]
where \( m \) is the order with respect to \( \text{NO} \) and \( n \) is the order with respect to \( \text{Cl}_2 \).

### Step 2: Analyze the effect of doubling the concentration of \( \text{Cl}_2 \)
According to the problem, when the concentration of \( \text{Cl}_2 \) is doubled, the rate of the reaction becomes four times the original rate. Let's denote the initial rate as \( R \) and the new rate after doubling \( [\text{Cl}_2] \) as \( R' \):
\[ R' = 4R \]

### Step 3: Set up the equation for the new rate
If we double the concentration of \( \text{Cl}_2 \), we can express the new rate as:
\[ R' = k [\text{NO}]^m [2\text{Cl}_2]^n \]
This can be rewritten as:
\[ R' = k [\text{NO}]^m [2^n \cdot \text{Cl}_2^n] = 2^n \cdot k [\text{NO}]^m [\text{Cl}_2]^n \]
Thus, we can relate the new rate to the original rate:
\[ R' = 2^n \cdot R \]

### Step 4: Equate the two expressions for the new rate
Since we know that \( R' = 4R \), we can set the two expressions equal to each other:
\[ 2^n \cdot R = 4R \]
Dividing both sides by \( R \) (assuming \( R \neq 0 \)):
\[ 2^n = 4 \]

### Step 5: Solve for \( n \)
We know that \( 4 = 2^2 \), so we can equate the exponents:
\[ 2^n = 2^2 \implies n = 2 \]

### Conclusion
The order of the reaction with respect to \( \text{Cl}_2 \) is \( n = 2 \).

### Final Answer
The order of reaction with respect to \( \text{Cl}_2 \) is **2**.

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