In a reaction if the concentraion of reaction A is tripled, the rate of reaction becomes twety seven times. What is the order the reaction ?

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 Relationship Between Rate and Concentration**:
The rate of a reaction can be expressed as:
\[ r = k[A]^n \]
where \( r \) is the rate of the reaction, \( k \) is the rate constant, \( [A] \) is the concentration of reactant A, and \( n \) is the order of the reaction.

2. **Set Up the Initial Condition**:
Let the initial concentration of A be \( [A] \). Therefore, the initial rate of the reaction can be expressed as:
\[ r = k[A]^n \quad \text{(Equation 1)} \]

3. **Apply the Change in Concentration**:
When the concentration of A is tripled, it becomes \( 3[A] \). The new rate of the reaction becomes:
\[ 27r = k(3[A])^n \quad \text{(Equation 2)} \]

4. **Relate the Two Rates**:
From the problem, we know that the new rate is 27 times the initial rate:
\[ 27r = k(3[A])^n \]

5. **Divide Equation 2 by Equation 1**:
By dividing Equation 2 by Equation 1, we get:
\[ \frac{27r}{r} = \frac{k(3[A])^n}{k[A]^n} \]
Simplifying this gives:
\[ 27 = \frac{(3[A])^n}{[A]^n} \]

6. **Simplify the Expression**:
The right side simplifies to:
\[ 27 = \frac{3^n [A]^n}{[A]^n} = 3^n \]
Thus, we have:
\[ 27 = 3^n \]

7. **Express 27 as a Power of 3**:
We know that:
\[ 27 = 3^3 \]
Therefore, we can equate the powers:
\[ 3^3 = 3^n \]

8. **Solve for n**:
Since the bases are the same, we can equate the exponents:
\[ n = 3 \]

9. **Conclusion**:
The order of the reaction is:
\[ \text{Order of the reaction} = 3 \]