The Arrhenius equation expressing the effect of temperature on the rate constant of a reaction is given as

Options

A. `k=E_a/RT`
B. `k=e^(-E_a/RT)`
C. `k=Ae^(-E_a/RT)`
D. `k=In (E_a)/RT`

Answer

To solve the problem regarding the Arrhenius equation, we need to understand the components of the equation and how they relate to the rate constant of a reaction.

### Step-by-Step Solution:

1. **Understand the Arrhenius Equation**:
The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) = rate constant
- \( A \) = frequency factor (also known as the pre-exponential factor)
- \( E_a \) = activation energy (in joules per mole)
- \( R \) = universal gas constant (8.31 J/(K·mol))
- \( T \) = absolute temperature (in Kelvin)

2. **Identify the Components**:
- The equation shows that the rate constant \( k \) is dependent on the temperature \( T \) and the activation energy \( E_a \).
- As the temperature increases, the term \( e^{-\frac{E_a}{RT}} \) increases, leading to an increase in \( k \).

3. **Analyze the Options**:
The question likely presents multiple-choice options regarding the components of the Arrhenius equation. Based on the transcript, the correct option is the third one, which correctly represents the negative exponent in the equation.

4. **Conclusion**:
The correct representation of the Arrhenius equation indicates that the rate constant \( k \) is proportional to the frequency factor \( A \) and inversely related to the exponential term \( e^{-\frac{E_a}{RT}} \). Thus, the correct option is the one that includes the negative exponent.

### Final Answer:
The correct option regarding the Arrhenius equation is the third option.