The basis theory behind Arrhenius' equation is that

Options

A. The number of effective colliisons is proportional to the number of molecules above a certain threshold energy.
B. As the temperature increases, so does the number of molecules with energies exceeding the threshold energy.
C. The rate constant is a function of temeperature.
D. The activation energy and pre-exponential factor are always temperature inedpendent.

Answer

### Step-by-Step Solution:

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

2. **Analyzing the First Statement**:
The first statement claims that the number of active collisions is proportional to the number of molecules with energy above a certain threshold energy (activation energy). This is true because only those molecules that have energy equal to or greater than the activation energy can effectively collide and lead to a reaction.

**Hint**: Consider how energy distribution among molecules relates to collision effectiveness.

3. **Analyzing the Second Statement**:
The second statement mentions that as temperature increases, the number of molecules with energy exceeding the threshold energy also increases. This is correct because increasing temperature increases the kinetic energy of the molecules, allowing more of them to surpass the activation energy.

**Hint**: Think about the relationship between temperature and molecular energy distribution.

4. **Analyzing the Third Statement**:
The third statement indicates that the rate constant \( k \) is a function of temperature. This is indeed true, as seen in the Arrhenius equation where \( k \) varies with \( T \).

**Hint**: Reflect on how the rate constant changes with temperature in the context of reaction kinetics.

5. **Analyzing the Fourth Statement**:
The fourth statement claims that activation energy and the pre-exponential factor are temperature independent. This is correct; for a given reaction, these values remain constant regardless of temperature changes.

**Hint**: Consider the definitions of activation energy and the pre-exponential factor in the context of a specific reaction.

6. **Conclusion**:
All four statements (A, B, C, and D) are correct regarding the basis theory behind the Arrhenius equation. Therefore, the answer is that all options are correct.

### Final Answer:
All options (A, B, C, and D) are correct regarding the basis theory behind Arrhenius' equation.