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 question regarding the Arrhenius equation, we will break it down step by step.

### Step-by-Step Solution:

1. **Understand the Arrhenius Equation**:
The Arrhenius equation describes how the rate constant (k) of a reaction depends on temperature (T). The general form of the equation is:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) = rate constant
- \( A \) = pre-exponential factor (frequency factor)
- \( E_a \) = activation energy (the minimum energy required for a reaction to occur)
- \( R \) = universal gas constant (8.314 J/mol·K)
- \( T \) = absolute temperature in Kelvin

2. **Identify the Components**:
- The rate constant \( k \) is what we are trying to express in relation to temperature.
- The pre-exponential factor \( A \) is a constant that represents the frequency of collisions and the orientation of reactants.
- The activation energy \( E_a \) is crucial as it determines the sensitivity of the reaction rate to temperature changes.

3. **Rearranging the Equation**:
If we want to express the effect of temperature on the rate constant, we can focus on how \( k \) changes with \( T \):
\[ k = A e^{-\frac{E_a}{RT}} \]
This shows that as the temperature \( T \) increases, the term \( -\frac{E_a}{RT} \) becomes less negative, which increases the value of \( k \).

4. **Conclusion**:
The Arrhenius equation effectively demonstrates that the rate constant increases with an increase in temperature, reflecting the increased kinetic energy of the molecules involved in the reaction.

### Final Expression:
The Arrhenius equation is given as:
\[ k = A e^{-\frac{E_a}{RT}} \]