The temperature dependence of the rate of a chemical reaction can be explained by Arrhenius equaiton which is

Options

A. `k = Ae^(Ea//RT)`
B. `k = Ae^(-Ea//RT)`
C. `k = Ae xx (E_(a))/(RT)`
D. `k = Ae xx (RT)/(E_(a))`

Answer

To solve the question regarding the temperature dependence of the rate of a chemical reaction as explained by the Arrhenius equation, we can follow these steps:

### 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) and activation energy (Ea). It is mathematically represented as:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) = rate constant
- \( A \) = pre-exponential factor (frequency factor)
- \( E_a \) = activation energy (in joules per mole)
- \( R \) = universal gas constant (8.314 J/(mol·K))
- \( T \) = temperature (in Kelvin)

2. **Identify the Components**: In the equation:
- The term \( A \) represents the frequency of collisions and the orientation of reactants.
- The exponential term \( e^{-\frac{E_a}{RT}} \) indicates how the rate constant decreases with increasing activation energy and how it increases with temperature.

3. **Analyze Temperature Dependence**:
- As temperature (T) increases, the term \( \frac{E_a}{RT} \) decreases, leading to an increase in the value of \( k \).
- This means that higher temperatures generally lead to faster reaction rates, as more molecules have sufficient energy to overcome the activation energy barrier.

4. **Conclusion**: The Arrhenius equation effectively shows that the rate of a chemical reaction increases with an increase in temperature due to the exponential relationship between temperature and the activation energy.

### Final Answer:
The Arrhenius equation that explains the temperature dependence of the rate of a chemical reaction is:
\[ k = A e^{-\frac{E_a}{RT}} \]