In the reaction `A + B rarr` Products, keeping [A] constant if [B] is doubled , the rate becomes double and keeping [B] constant if [A] is doubled , the rate becomes four times. The order of reaction is :

Options

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

Explanation

To determine the order of the reaction given the information provided, we can follow these steps:

### Step 1: Write the rate law expression
The rate of the reaction can be expressed as:
\[ \text{Rate} = k [A]^m [B]^n \]
where \( k \) is the rate constant, \( m \) is the order with respect to reactant A, and \( n \) is the order with respect to reactant B.

### Step 2: Analyze the first condition
We are given that when the concentration of B is doubled (keeping A constant), the rate also doubles. This can be expressed mathematically as:
\[ \text{Rate}_1 = k [A]^m [B]^n \]
\[ \text{Rate}_2 = k [A]^m [2B]^n \]

Since the rate doubles:
\[ \text{Rate}_2 = 2 \cdot \text{Rate}_1 \]
Substituting the expressions:
\[ k [A]^m [2B]^n = 2 \cdot k [A]^m [B]^n \]

### Step 3: Simplify the equation
Cancelling \( k [A]^m \) from both sides (since they are constant):
\[ 2^n [B]^n = 2 [B]^n \]

Dividing both sides by \( [B]^n \) (assuming \( [B] \neq 0 \)):
\[ 2^n = 2 \]

This implies:
\[ n = 1 \]
Thus, the order with respect to B is 1.

### Step 4: Analyze the second condition
Now, we keep B constant and double the concentration of A. The rate becomes four times:
\[ \text{Rate}_3 = k [2A]^m [B]^n \]
Since the rate quadruples:
\[ \text{Rate}_3 = 4 \cdot \text{Rate}_1 \]
Substituting the expressions:
\[ k [2A]^m [B]^n = 4 \cdot k [A]^m [B]^n \]

### Step 5: Simplify the equation
Cancelling \( k [B]^n \) from both sides:
\[ [2A]^m = 4 [A]^m \]

### Step 6: Expand and compare
Expanding \( [2A]^m \):
\[ 2^m [A]^m = 4 [A]^m \]

Dividing both sides by \( [A]^m \) (assuming \( [A] \neq 0 \)):
\[ 2^m = 4 \]

This implies:
\[ 2^m = 2^2 \]
Thus:
\[ m = 2 \]
So, the order with respect to A is 2.

### Step 7: Determine the overall order of the reaction
The overall order of the reaction is the sum of the individual orders:
\[ \text{Overall order} = m + n = 2 + 1 = 3 \]

### Conclusion
The order of the reaction is **3**.

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