The rate constant of a reaction changes with

Options

A. Pressure
B. Temperature
C. Initial concentration of reactants
D. Extent of reaction

Answer

To solve the question regarding what the rate constant of a reaction changes with, we will analyze the factors that influence the rate constant, particularly focusing on the Arrhenius equation.

### Step-by-Step Solution:

1. **Understanding the Rate Constant (k)**:
- The rate constant (k) is a proportionality factor in the rate law of a chemical reaction. It indicates how fast a reaction occurs.

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

3. **Analyzing the Factors**:
- From the Arrhenius equation, we can see that the rate constant \( k \) is influenced by:
- **Temperature (T)**: As temperature increases, the exponential term \( e^{-\frac{E_a}{RT}} \) increases, leading to an increase in \( k \).
- **Activation Energy (E_a)**: While \( E_a \) is a constant for a given reaction, it does not change with temperature or other factors.
- **Pre-exponential Factor (A)**: This is also a constant for a given reaction and does not change with temperature.

4. **Evaluating the Options**:
- **Pressure**: The rate constant does not depend on pressure for a given reaction at a constant temperature.
- **Temperature**: The rate constant is directly proportional to temperature, as established in the Arrhenius equation.
- **Initial Concentration of Reactant**: The rate constant is independent of the initial concentration of reactants.
- **Extent of Reaction**: The rate constant does not change with the extent of the reaction.

5. **Conclusion**:
- The only factor that affects the rate constant \( k \) is **temperature**. Therefore, the correct answer is:
- **Temperature** (Option 2).