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 follow these steps:

### Step 1: Understand 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 (Arrhenius factor),
- \( E_a \) is the activation energy,
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin.

### Step 2: Analyze the Relationship
From the Arrhenius equation, we can see that as the temperature \( T \) increases, the exponential term \( e^{-\frac{E_a}{RT}} \) increases, leading to an increase in the rate constant \( k \). This indicates that \( k \) increases with increasing temperature.

### Step 3: Identify the Nature of the Plot
The relationship between \( k \) and \( T \) is not linear; instead, it is exponential. This means that the plot of \( k \) versus \( T \) should show a curve that rises steeply as \( T \) increases.

### Step 4: Examine the Given Plots
Now, we need to examine the provided plots (options) to identify which one shows this exponential increase in \( k \) with respect to \( T \).

- **Option A**: If this plot shows a curve that rises steeply as temperature increases, it is likely the correct answer.
- **Option B, C, D**: If these plots show a linear increase or a decrease in \( k \) with respect to \( T \), they do not follow the Arrhenius equation.

### Step 5: Conclusion
After examining the plots, we conclude that the plot that shows an exponential increase in the rate constant \( k \) with increasing temperature \( T \) is the one that follows the Arrhenius equation.

Thus, the answer is:
**Option A**.

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