In a reaction `AtoB` when the concentration of reaction is made 8 times, the rate got doubled. The order of reaction is

Options

A. `1//3`
B. `1`
C. `1//2`
D. `2`

Answer

To determine the order of the reaction \( A \to B \) based on the given information, we can follow these steps:

### Step 1: Understand the relationship between rate and concentration
The rate of a reaction can be expressed as:
\[ \text{Rate} = k [A]^n \]
where \( k \) is the rate constant, \( [A] \) is the concentration of reactant A, and \( n \) is the order of the reaction.

### Step 2: Set up the initial condition
Let the initial concentration of A be \( [A] \). Therefore, the initial rate \( R \) can be expressed as:
\[ R = k [A]^n \]

### Step 3: Set up the condition after changing the concentration
When the concentration of A is increased 8 times, the new concentration becomes \( 8[A] \). The new rate \( R' \) can be expressed as:
\[ R' = k (8[A])^n = k \cdot 8^n \cdot [A]^n \]

### Step 4: Relate the new rate to the old rate
According to the problem, the new rate \( R' \) is double the initial rate \( R \):
\[ R' = 2R \]
Substituting the expressions for \( R \) and \( R' \):
\[ k \cdot 8^n \cdot [A]^n = 2(k [A]^n) \]

### Step 5: Simplify the equation
We can cancel \( k \) and \( [A]^n \) from both sides (assuming \( [A] \neq 0 \)):
\[ 8^n = 2 \]

### Step 6: Solve for \( n \)
To solve for \( n \), we can rewrite the equation:
\[ 8^n = 2^1 \]
Since \( 8 \) can be expressed as \( 2^3 \):
\[ (2^3)^n = 2^1 \]
This simplifies to:
\[ 2^{3n} = 2^1 \]
By equating the exponents:
\[ 3n = 1 \]
Thus,
\[ n = \frac{1}{3} \]

### Conclusion
The order of the reaction is \( \frac{1}{3} \).

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