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, we will follow the steps outlined below:

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

### Step 2: Substitute Activation Energy
According to the problem, the activation energy \( E_a \) is equal to \( RT \). Therefore, we substitute \( E_a \) with \( RT \):
\[ k = A e^{-\frac{RT}{RT}} \]

### Step 3: Simplify the Exponential Term
The exponential term simplifies as follows:
\[ e^{-\frac{RT}{RT}} = e^{-1} \]
Thus, we can rewrite the equation:
\[ k = A e^{-1} \]

### Step 4: Use the Given Value of \( \frac{1}{e} \)
We know from the problem statement that:
\[ \frac{1}{e} \approx 0.3679 \]
Therefore, we can express \( k \) as:
\[ k = A \cdot \frac{1}{e} \]
This implies:
\[ k \approx 0.3679 A \]

### Step 5: Convert to Percentage
To express \( k \) as a percentage of \( A \):
\[ k = 0.3679 A \]
This can be converted to percentage:
\[ k \approx 36.79\% \text{ of } A \]

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

### Summary of Options
1. The rate of reaction doesn't depend on initial concentration - Incorrect
2. The rate constant becomes about 37% of the Arrhenius constant \( A \) - Correct
3. The rate constant becomes equal to 73% of the Arrhenius constant \( A \) - Incorrect
4. The rate of the reaction becomes infinite or zero - Incorrect

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

---