If the rate of reaction `A to B` triples on increasing the concentration of A by 9 times, then the order of reaction is

Options

A. 2
B. 1
C. `1/2`
D. 4

Explanation

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

### Step-by-Step Solution:

1. **Understand the Rate Law**:
The rate of a reaction can be expressed using the rate law:
\[ \text{Rate} = k[A]^n \]
where \( k \) is the rate constant, \( [A] \) is the concentration of reactant A, and \( n \) is the order of the reaction.

2. **Initial and New Conditions**:
Let the initial concentration of A be \( [A] \) and the initial rate be \( R \):
\[ R = k[A]^n \]
When the concentration of A is increased by 9 times, the new concentration becomes \( 9[A] \). The new rate \( R' \) is given to be three times the initial rate:
\[ R' = 3R \]

3. **Express the New Rate**:
The new rate can also be expressed using the rate law:
\[ R' = k(9[A])^n = k \cdot 9^n \cdot [A]^n \]

4. **Set Up the Equation**:
Now, we can set the two expressions for the new rate equal to each other:
\[ 3R = k \cdot 9^n \cdot [A]^n \]
Substituting \( R = k[A]^n \) into the equation gives:
\[ 3(k[A]^n) = k \cdot 9^n \cdot [A]^n \]

5. **Cancel Common Terms**:
We can cancel \( k \) and \( [A]^n \) from both sides (assuming \( [A] \neq 0 \)):
\[ 3 = 9^n \]

6. **Rewrite 9 in Terms of 3**:
Since \( 9 = 3^2 \), we can rewrite the equation:
\[ 3 = (3^2)^n = 3^{2n} \]

7. **Equate Exponents**:
Since the bases are the same, we can equate the exponents:
\[ 1 = 2n \]

8. **Solve for n**:
Dividing both sides by 2 gives:
\[ n = \frac{1}{2} \]

9. **Conclusion**:
The order of the reaction is \( n = 0.5 \) or \( \frac{1}{2} \).

### Final Answer:
The order of the reaction is \( \frac{1}{2} \) or 0.5.