For a reaction A`to`B, the rate of reaction becomes twenty seven times when the concentration of A is increased three times. What is the order of the reaction?

Options

A. 2
B. 1
C. 3
D. 0

Explanation

To determine the order of the reaction A → B based on the information provided, we can follow these steps:

### Step 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,
- \( n \) is the order of the reaction.

### Step 2: Set up the initial and new conditions
According to the problem, when the concentration of A is increased three times, the rate of the reaction becomes 27 times the original rate. We can denote:
- Original concentration of A as \( [A] \)
- New concentration of A as \( 3[A] \)
- Original rate as \( R \)
- New rate as \( R' = 27R \)

### Step 3: Write the equations for the original and new rates
Using the rate equation for both conditions:
1. Original rate:
\[ R = k[A]^n \]
2. New rate:
\[ R' = k(3[A])^n = k \cdot 3^n \cdot [A]^n \]

### Step 4: Relate the two rates
Since \( R' = 27R \), we can substitute the expressions for \( R \) and \( R' \):
\[ k \cdot 3^n \cdot [A]^n = 27 \cdot k[A]^n \]

### Step 5: Cancel out common terms
We can cancel \( k \) and \( [A]^n \) from both sides (assuming \( [A] \neq 0 \)):
\[ 3^n = 27 \]

### Step 6: Express 27 as a power of 3
We know that:
\[ 27 = 3^3 \]
Thus, we can rewrite the equation as:
\[ 3^n = 3^3 \]

### Step 7: Equate the exponents
Since the bases are the same, we can equate the exponents:
\[ n = 3 \]

### Conclusion
The order of the reaction is \( n = 3 \).

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

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