For a chemical reaction `A rarr B`, the rate of reaction increases by a factor of `1.837` when the concentration of `A` is increased by `1.5` time. The order of reaction with respect to `A` is:

Options

A. 1
B. 1.5
C. 2
D. 2.5

Explanation

To determine the order of the reaction with respect to A for the reaction \( A \rightarrow B \), we can follow these steps:

### Step 1: Write the rate law expression
For the reaction \( A \rightarrow B \), the rate of the 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 with respect to A.

### Step 2: Set up the initial and changed conditions
Let the initial concentration of A be \( [A] \) and the initial rate be \( r \). When the concentration of A is increased by 1.5 times, the new concentration becomes:
\[ [A]' = 1.5 [A] \]
The new rate of reaction becomes:
\[ r' = k [A']^n = k (1.5 [A])^n = k (1.5^n) [A]^n \]

### Step 3: Relate the rates before and after the change
According to the problem, the rate increases by a factor of 1.837:
\[ r' = 1.837 r \]
Substituting the expressions for \( r' \) and \( r \):
\[ k (1.5^n) [A]^n = 1.837 (k [A]^n) \]

### Step 4: Cancel out common terms
Since \( k \) and \( [A]^n \) are common on both sides, we can simplify:
\[ 1.5^n = 1.837 \]

### Step 5: Take logarithms
Taking the logarithm of both sides gives:
\[ \log(1.5^n) = \log(1.837) \]
Using the property of logarithms, we can rewrite this as:
\[ n \log(1.5) = \log(1.837) \]

### Step 6: Solve for \( n \)
Now, we can solve for \( n \):
\[ n = \frac{\log(1.837)}{\log(1.5)} \]

### Step 7: Calculate the logarithms
Using a calculator:
- \( \log(1.837) \approx 0.2641 \)
- \( \log(1.5) \approx 0.1761 \)

Substituting these values into the equation:
\[ n = \frac{0.2641}{0.1761} \approx 1.5 \]

### Conclusion
The order of the reaction with respect to A is:
\[ \boxed{1.5} \]