The rate constant of a reaction varies :

Options

A. with temperature
B. with concentration of reaction
C. with both temperature and concentration of the reactants
D. with neither temperature nor concentration of the reactants.

Explanation

To solve the question regarding how the rate constant of a reaction varies, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Rate Constant (k)**:
The rate constant (k) is a crucial factor in chemical kinetics that indicates the speed of a reaction. It is influenced by various factors, primarily temperature.

2. **Arrhenius Equation**:
The relationship between the rate constant and temperature is described by the Arrhenius equation:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) = rate constant
- \( A \) = pre-exponential factor (frequency factor)
- \( E_a \) = activation energy
- \( R \) = universal gas constant
- \( T \) = temperature (in Kelvin)

3. **Effect of Temperature**:
From the Arrhenius equation, it is clear that the rate constant \( k \) varies with temperature \( T \). As the temperature increases, the exponential term \( e^{-\frac{E_a}{RT}} \) increases, leading to a higher rate constant.

4. **Comparing Rate Constants at Different Temperatures**:
If we want to compare the rate constants at two different temperatures \( T_1 \) and \( T_2 \), we can use the following relationship derived from the Arrhenius equation:
\[ \ln \left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right) \]
where:
- \( k_1 \) = rate constant at temperature \( T_1 \)
- \( k_2 \) = rate constant at temperature \( T_2 \)

5. **Conclusion**:
Therefore, we conclude that the rate constant of a reaction varies primarily with temperature. The activation energy \( E_a \) remains constant for a given reaction, while \( k \) changes as \( T \) changes.