In Arrhenius equation , `k=Ae^(E_a/(RT))` , A may be termed as rate constant .

Options

A. When 100% reactant will convert into the product
B. When the temperature becomes high
C. When the fraction of molecule crossing over the energy barrier becomes unity
D. At very low temperature

Answer

To solve the question regarding the Arrhenius equation \( k = Ae^{-\frac{E_a}{RT}} \), where \( A \) is termed as the rate constant, we will analyze the components of the equation and their implications.

### Step-by-Step Solution:

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

2. **Identifying the Role of \( A \)**:
In the context of the Arrhenius equation, \( A \) represents the frequency factor, which is a measure of the frequency of collisions between reactant molecules. It is a constant that depends on the specific reaction and is influenced by factors such as molecular orientation and the probability of successful collisions.

3. **Behavior of \( k \) with Temperature**:
As the temperature \( T \) increases, the term \( \frac{E_a}{RT} \) decreases, leading to an increase in the exponential term \( e^{-\frac{E_a}{RT}} \). This results in an increase in the rate constant \( k \). Therefore, we can conclude that:
- At very high temperatures, the value of \( k \) approaches \( A \) because the exponential term approaches 1.

4. **Effect of Activation Energy**:
The activation energy \( E_a \) plays a crucial role in determining how sensitive the rate constant \( k \) is to changes in temperature. A higher \( E_a \) means that the reaction is more sensitive to temperature changes, while a lower \( E_a \) means that the reaction rate becomes less dependent on temperature.

5. **Conclusion**:
In summary, the Arrhenius equation indicates that the rate constant \( k \) becomes equal to the frequency factor \( A \) at very high temperatures or when the activation energy \( E_a \) approaches zero. Thus, we can conclude that:
- The rate constant \( k \) can be termed as equal to \( A \) under conditions of high temperature or low activation energy.