The rate constant of a reaction will be equal to the pre-exponential factor when

Options

A. Temperature in centigrade is zero.
B. The absolute temperature is zero.
C. The absolute temperature is infinity.
D. No suitable answer.

Explanation

To determine when the rate constant \( k \) of a reaction is equal to the pre-exponential factor \( A \), we can use the Arrhenius equation:

\[ k = A e^{-\frac{E_a}{RT}} \]

Where:
- \( k \) is the rate constant,
- \( A \) is the pre-exponential factor,
- \( E_a \) is the activation energy,
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin.

### Step-by-Step Solution:

1. **Set the equation for equality**:
We want to find when \( k = A \). Therefore, we can set up the equation:
\[ A = A e^{-\frac{E_a}{RT}} \]

2. **Divide both sides by \( A \)**:
Assuming \( A \neq 0 \), we can divide both sides by \( A \):
\[ 1 = e^{-\frac{E_a}{RT}} \]

3. **Take the natural logarithm**:
To solve for the exponent, we take the natural logarithm of both sides:
\[ \ln(1) = -\frac{E_a}{RT} \]
Since \( \ln(1) = 0 \), we have:
\[ 0 = -\frac{E_a}{RT} \]

4. **Rearranging the equation**:
Rearranging gives us:
\[ \frac{E_a}{RT} = 0 \]

5. **Analyzing the equation**:
For the fraction \( \frac{E_a}{RT} \) to be zero, the numerator \( E_a \) must be zero or the denominator \( RT \) must approach infinity. Since \( E_a \) is a constant for a given reaction, we focus on \( RT \).

6. **Conclusion about temperature**:
The only way for \( RT \) to approach infinity is for the temperature \( T \) to approach infinity. Therefore, we conclude that:
\[ k = A \text{ when } T \to \infty \]

### Final Answer:
The rate constant \( k \) will be equal to the pre-exponential factor \( A \) when the absolute temperature \( T \) approaches infinity.

---