For reaction `aA rarr xP`, when `[A] = 2.2 mM`, the rate was found to be `2.4mM s^(-1)`. On reducing concentration of `A` to half, the rate changes to `0.6 mM s^(-1)`. The order of reaction with respect to `A` is

Options

A. 1.5
B. `2.0 `
C. `2.5`
D. `3.0`

Explanation

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

### Step 1: Write the Rate Law Expression
The rate law for the reaction can be expressed as:
\[ \text{Rate} = k[A]^x \]
where \( k \) is the rate constant, \( [A] \) is the concentration of A, and \( x \) is the order of the reaction with respect to A.

### Step 2: Set Up the Equations
From the problem, we have two scenarios:

1. When \( [A] = 2.2 \, \text{mM} \), the rate is \( 2.4 \, \text{mM/s} \):
\[ 2.4 = k(2.2)^x \quad \text{(Equation 1)} \]

2. When \( [A] \) is reduced to half, \( [A] = 1.1 \, \text{mM} \), the rate is \( 0.6 \, \text{mM/s} \):
\[ 0.6 = k(1.1)^x \quad \text{(Equation 2)} \]

### Step 3: Divide the Two Equations
To eliminate \( k \), we can divide Equation 1 by Equation 2:
\[ \frac{2.4}{0.6} = \frac{k(2.2)^x}{k(1.1)^x} \]
This simplifies to:
\[ 4 = \left(\frac{2.2}{1.1}\right)^x \]

### Step 4: Simplify the Fraction
Calculating the fraction:
\[ \frac{2.2}{1.1} = 2 \]
Thus, we have:
\[ 4 = 2^x \]

### Step 5: Solve for \( x \)
We can express 4 as \( 2^2 \):
\[ 2^2 = 2^x \]
Since the bases are the same, we can equate the exponents:
\[ x = 2 \]

### Conclusion
The order of the reaction with respect to A is \( 2 \).

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