Plots showing the variation of the rate constant `(k)` with temperature `(T)` are given below. The plot that follows the Arrhenius equation is

Options

A.
B.
C.
D.

Explanation

To determine which plot shows the variation of the rate constant \( k \) with temperature \( T \) that follows the Arrhenius equation, we can analyze the relationship described by the equation and how it translates into a graphical representation.

### Step-by-Step Solution:

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

2. **Taking the Natural Logarithm**:
To analyze the equation, we can take the natural logarithm of both sides:
\[ \ln k = \ln A - \frac{E_a}{RT} \]
This shows that \( \ln k \) is a linear function of \( \frac{1}{T} \).

3. **Identifying the Relationship**:
From the equation, we see that as the temperature \( T \) increases, the term \( \frac{E_a}{RT} \) decreases, leading to an increase in \( k \). Therefore, \( k \) increases exponentially with increasing \( T \).

4. **Graphical Representation**:
- If we plot \( k \) versus \( T \), we expect to see an exponential increase in \( k \) as \( T \) increases.
- This means the graph should show a steep upward curve, indicating that \( k \) increases rapidly with temperature.

5. **Analyzing Given Plots**:
- Look for a plot that shows \( k \) increasing sharply as \( T \) increases.
- The correct plot will not be linear or show a gradual increase; instead, it will exhibit an exponential rise.

6. **Conclusion**:
After analyzing the provided plots, the one that shows an exponential increase in \( k \) with increasing \( T \) is the plot that follows the Arrhenius equation.

### Final Answer:
The plot that follows the Arrhenius equation is **option A**.