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 con- stant.
D. The pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy

Answer

### Step-by-Step Solution

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

2. **Analyzing Activation Energy**:
- Higher activation energy (\( E_a \)) indicates that more energy is required for the reactants to reach the transition state.
- Therefore, a high activation energy does not imply a fast reaction; rather, it implies a slow reaction because fewer molecules will have enough energy to overcome the barrier.

3. **Effect of Temperature on Rate Constant**:
- As temperature (\( T \)) increases, the term \( \frac{E_a}{RT} \) decreases, leading to an increase in the rate constant (\( k \)).
- This is because higher temperatures increase the number of collisions with sufficient energy to overcome the activation energy.

4. **Understanding the Pre-exponential Factor**:
- The pre-exponential factor (\( A \)) is related to the frequency of collisions and the orientation of reactants during collisions.
- It can be divided into two components: \( Z \) (collision frequency) and \( P \) (steric or probability factor).

5. **Conclusion on Statements**:
- **Statement 1**: High activation energy implies a fast reaction. **(False)**
- **Statement 2**: Rate constant increases with an increase in temperature. **(True)**
- **Statement 3**: Higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant. **(True)**
- **Statement 4**: The pre-exponential factor is a measure of the rate at which collisions occur irrespective of their energy. **(True)**

6. **Final Answer**:
According to the Arrhenius equation, statements 2, 3, and 4 are correct, while statement 1 is incorrect.