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. `-1`

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
The rate of the reaction can be expressed as:
\[ R = k[A]^x \]
where \( R \) is the rate of reaction, \( k \) is the rate constant, \( [A] \) is the concentration of reactant A, and \( x \) is the order of the reaction with respect to A.

### Step 2: Set up the initial and new rates
Let the initial concentration of A be \( [A] \). The initial rate of reaction \( R_1 \) can be expressed as:
\[ R_1 = k[A]^x \]
When the concentration of A is increased by 1.5 times, the new concentration becomes \( 1.5[A] \). The new rate of reaction \( R_2 \) is:
\[ R_2 = k(1.5[A])^x = k \cdot 1.5^x \cdot [A]^x \]

### Step 3: Relate the rates
According to the problem, the new rate \( R_2 \) is 1.837 times the initial rate \( R_1 \):
\[ R_2 = 1.837 R_1 \]
Substituting the expressions for \( R_1 \) and \( R_2 \):
\[ k \cdot 1.5^x \cdot [A]^x = 1.837 \cdot k[A]^x \]

### Step 4: Simplify the equation
Since \( k[A]^x \) appears on both sides, we can cancel it out (assuming \( [A] \neq 0 \)):
\[ 1.5^x = 1.837 \]

### Step 5: Solve for \( x \)
To find \( x \), we take logarithms or recognize that \( 1.5^x = 1.837 \). We can express this as:
\[ x = \log_{1.5}(1.837) \]

Using the change of base formula:
\[ x = \frac{\log(1.837)}{\log(1.5)} \]

Calculating this gives:
\[ x \approx 1.5 \]

### Conclusion
Thus, the order of the reaction with respect to A is:
\[ \text{Order} = 1.5 \]