For a reaction, activation energy (E_a ) =0 and rate constant, `k = 1.5 x 10^4 s^(-1)` at 300 K. What is the value of rate constant at 320 K'?

Options

A. `3.2 x 10^6 s^(-1)`
B. `3.2 x 10^4 s^(-1)`
C. `1.5 x 10^4 s^(-1)`
D. `6.4 x 10^8 s^(-1)`

Answer

To find the value of the rate constant at 320 K given that the activation energy (E_a) is 0 and the rate constant (k) at 300 K is \(1.5 \times 10^4 \, s^{-1}\), we can use the Arrhenius equation. Here's how to solve it step by step:

### Step 1: Write down the Arrhenius equation
The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \(k\) = rate constant
- \(A\) = pre-exponential factor
- \(E_a\) = activation energy
- \(R\) = universal gas constant (8.314 J/(mol·K))
- \(T\) = temperature in Kelvin

### Step 2: Substitute the known values
In this case, we know:
- \(E_a = 0\)
- \(k_1 = 1.5 \times 10^4 \, s^{-1}\) at \(T_1 = 300 \, K\)

Substituting \(E_a = 0\) into the Arrhenius equation simplifies it to:
\[ k = A \]
This means that the rate constant \(k\) is equal to the pre-exponential factor \(A\).

### Step 3: Determine the pre-exponential factor
Since \(k_1 = A\) at \(T_1\), we have:
\[ A = 1.5 \times 10^4 \, s^{-1} \]

### Step 4: Find the rate constant at 320 K
Now we need to find \(k_2\) at \(T_2 = 320 \, K\). Since \(E_a = 0\), the pre-exponential factor remains constant:
\[ k_2 = A = 1.5 \times 10^4 \, s^{-1} \]

### Conclusion
Thus, the rate constant at 320 K is:
\[ k_2 = 1.5 \times 10^4 \, s^{-1} \]

### Final Answer
The value of the rate constant at 320 K is \(1.5 \times 10^4 \, s^{-1}\).

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