The activation energy of a reaction is zero. The rate constant of this reaction

Options

A. Increases with increase of temperature
B. Decreases with an increase of temperature
C. Decreases with decrease of temperature
D. Is nearly independent of temperature

Answer

To solve the question regarding the rate constant of a reaction with zero activation energy, we can follow these steps:

### Step-by-Step Solution:

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

2. **Substitute Activation Energy**:
In this case, the problem states that the activation energy \( E_a \) is zero. We substitute \( E_a = 0 \) into the Arrhenius equation:
\[ k = A e^{-\frac{0}{RT}} \]

3. **Simplify the Equation**:
Since \( e^{0} = 1 \), the equation simplifies to:
\[ k = A \cdot 1 = A \]
Thus, the rate constant \( k \) is equal to the frequency factor \( A \).

4. **Analyze the Temperature Dependence**:
The expression \( k = A \) indicates that the rate constant is independent of temperature because there is no temperature term in the final expression.

5. **Conclusion**:
Therefore, the rate constant of the reaction with zero activation energy is equal to the frequency factor \( A \) and is independent of temperature.

### Final Answer:
The rate constant of this reaction is equal to the frequency factor \( A \) and is independent of temperature.

---