For a reaction `2NO(g)+Cl_(2)(g) hArr 2NOCl(g)`.When concentration of `Cl_(2)` is doubled, the rate of reaction becomes two times of the original. When the concentration of `NO` is doubled the rate becomes four times. What is the order of the reaction

Options

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

Answer

To determine the order of the reaction for the equation \(2NO(g) + Cl_2(g) \rightleftharpoons 2NOCl(g)\), we will analyze how the rate of the reaction changes with varying concentrations of the reactants.

### Step-by-Step Solution:

1. **Write the Rate Law Expression**:
The rate law for the reaction can be expressed as:
\[ \text{Rate} = k [NO]^x [Cl_2]^y \]
where \(x\) is the order with respect to \(NO\) and \(y\) is the order with respect to \(Cl_2\).

2. **Analyze the Effect of Doubling \(Cl_2\)**:
According to the problem, when the concentration of \(Cl_2\) is doubled (i.e., \([Cl_2] \to 2[Cl_2]\)), the rate of the reaction becomes two times the original rate. Keeping \(NO\) constant, we can express this as:
\[ 2 \text{Rate} = k [NO]^x (2[Cl_2])^y \]
Simplifying, we have:
\[ 2 \text{Rate} = k [NO]^x 2^y [Cl_2]^y \]
Since the original rate is \(k [NO]^x [Cl_2]^y\), we can set the two equations equal to each other:
\[ k [NO]^x 2^y [Cl_2]^y = 2 k [NO]^x [Cl_2]^y \]
Dividing both sides by \(k [NO]^x [Cl_2]^y\) gives:
\[ 2^y = 2 \]
This implies that:
\[ y = 1 \]

3. **Analyze the Effect of Doubling \(NO\)**:
Next, we consider the case when the concentration of \(NO\) is doubled (i.e., \( [NO] \to 2[NO] \)). The problem states that the rate becomes four times the original rate. Keeping \(Cl_2\) constant, we can express this as:
\[ 4 \text{Rate} = k (2[NO])^x [Cl_2]^y \]
Simplifying, we have:
\[ 4 \text{Rate} = k 2^x [NO]^x [Cl_2]^y \]
Setting the two equations equal to each other:
\[ k 2^x [NO]^x [Cl_2]^y = 4 k [NO]^x [Cl_2]^y \]
Dividing both sides by \(k [NO]^x [Cl_2]^y\) gives:
\[ 2^x = 4 \]
This implies that:
\[ x = 2 \]

4. **Determine the Overall Order of the Reaction**:
The overall order of the reaction is the sum of the individual orders:
\[ \text{Overall Order} = x + y = 2 + 1 = 3 \]

### Final Answer:
The order of the reaction is **3**.