According to the Arrhenius equation,

Options

A. a high activation energy usually implies a fast reaction.
B. rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy.
C. higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant.
D. the pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy

Explanation

### Step-by-Step Solution:

1. **Understanding the Arrhenius Equation**:
The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) = rate constant
- \( A \) = pre-exponential factor (related to collision frequency and orientation)
- \( E_a \) = activation energy
- \( R \) = universal gas constant
- \( T \) = temperature (in Kelvin)

2. **Analyzing Activation Energy**:
- Activation energy (\( E_a \)) is the minimum energy required for a reaction to occur.
- A high activation energy typically indicates that the reaction is slower because fewer molecules will have sufficient energy to overcome this barrier at a given temperature.

3. **Effect of Temperature on Rate Constant**:
- According to the Arrhenius equation, as temperature (\( T \)) increases, the term \( e^{-\frac{E_a}{RT}} \) increases, leading to an increase in the rate constant \( k \).
- This means that the reaction rate increases with an increase in temperature due to a greater number of molecules having energy greater than \( E_a \).

4. **Evaluating the Statements**:
- **Statement 1**: "High activation energy usually implies a fast reaction."
- This is **incorrect**. High activation energy implies a slow reaction.
- **Statement 2**: "Rate constant increases with increasing temperature."
- This is **correct**. As explained, increasing temperature increases \( k \).
- **Statement 3**: "Higher the magnitude of activation energy, stronger the temperature dependence of the rate constant."
- This is **correct**. A higher \( E_a \) means that the rate constant \( k \) is more sensitive to changes in temperature.
- **Statement 4**: "The pre-exponential factor is the measure of the rate at which collisions occur irrespective of their energy."
- This is **correct**. The pre-exponential factor \( A \) accounts for the frequency and proper orientation of collisions.

5. **Conclusion**:
- The correct statements are 2, 3, and 4. Statement 1 is incorrect.

### Final Answer:
The correct statements according to the Arrhenius equation are 2, 3, and 4.

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