For a reaction, the energy of activation is zero. What is the value of rate constant at 300 K, if `k= 1.6 xx 10^6 s^(-1)` at 280 K?

Explanation

To solve the problem, we need to analyze the situation given that the activation energy (Ea) is zero. We can use the Arrhenius equation to determine the rate constant (k) at the new temperature.

### 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
- \( A \) = frequency factor (pre-exponential factor)
- \( E_a \) = activation energy
- \( R \) = universal gas constant (8.314 J/(mol·K))
- \( T \) = temperature in Kelvin

2. **Substituting the Given Values**:
Since the activation energy \( E_a \) is zero, we can substitute it into the equation:
\[ k = A e^{-\frac{0}{RT}} = A e^{0} = A \]
This means that the rate constant \( k \) is equal to the frequency factor \( A \) when \( E_a = 0 \).

3. **Temperature Independence**:
The frequency factor \( A \) is independent of temperature. Therefore, if \( k \) is \( 1.6 \times 10^6 \, \text{s}^{-1} \) at 280 K, it will remain the same at any other temperature, including 300 K.

4. **Conclusion**:
Thus, the value of the rate constant \( k \) at 300 K is:
\[ k = 1.6 \times 10^6 \, \text{s}^{-1} \]

### Final Answer:
The value of the rate constant at 300 K is \( 1.6 \times 10^6 \, \text{s}^{-1} \).

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