Arrhenius equation `k=Ae^(-E_(a)//RT)` If the activation energy of the reaction is found to be equal to RT, then [given : `(1)/(e )=0.3679`]

Options

A. the rate of reactions does not depend upon initial concentration
B. the rate constant becomes about `37%` of the Arrhenius constant A
C. the rate constant becomes equal to `73%` of the Arrhenius constant A
D. the rate of the reaction becomes infinite of zero

Answer

To solve the problem using the Arrhenius equation, we will follow these steps:

### Step 1: Write down the Arrhenius equation
The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]

### Step 2: Substitute the condition given in the problem
We are given that the activation energy \( E_a \) is equal to \( RT \). Therefore, we can substitute \( E_a \) in the equation:
\[ k = A e^{-\frac{RT}{RT}} \]

### Step 3: Simplify the exponent
The exponent simplifies as follows:
\[ k = A e^{-1} \]

### Step 4: Use the value of \( \frac{1}{e} \)
We know from the problem statement that:
\[ \frac{1}{e} = 0.3679 \]
Thus, we can rewrite the equation as:
\[ k = A \cdot \frac{1}{e} = A \cdot 0.3679 \]

### Step 5: Calculate the percentage of \( A \)
To express \( k \) as a percentage of \( A \):
\[ k = 0.3679 A \]
This can be expressed as:
\[ k = 36.79\% \text{ of } A \]

### Conclusion
Therefore, the rate constant \( k \) becomes approximately 37% of the Arrhenius constant \( A \).

### Final Answer
The correct option is that the rate constant becomes 37% of the Arrhenius constant \( A \).

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