The number of correct statement/s from the following is __________
A. Larger the activation energy, smaller is the value of the rate constant.
B. The higher is the activation energy, higher is the value of the temperature coefficient.
C. At lower temperatures, increase in temperature causes more change in the value of k than at higher temperature
D. A plot of In k vs `1/T` is a straight line with slope equal `-(E_a)/R`

Answer

To determine the number of correct statements from the given options, we will analyze each statement one by one based on our understanding of chemical kinetics and the Arrhenius equation.

### Step-by-Step Solution:

1. **Statement A**: "Larger the activation energy, smaller is the value of the rate constant."
- **Analysis**: The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
Here, \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin. As the activation energy \( E_a \) increases, the exponential term \( e^{-\frac{E_a}{RT}} \) decreases, leading to a smaller value of \( k \). Therefore, this statement is **correct**.

2. **Statement B**: "The higher is the activation energy, higher is the value of the temperature coefficient."
- **Analysis**: The temperature coefficient (often denoted as \( Q \)) is related to how the rate constant \( k \) changes with temperature. The relationship can be derived from the Arrhenius equation. If \( E_a \) is higher, it means that the rate constant \( k \) will be more sensitive to changes in temperature. Thus, as \( E_a \) increases, the temperature coefficient also increases. Therefore, this statement is **correct**.

3. **Statement C**: "At lower temperatures, increase in temperature causes more change in the value of \( k \) than at higher temperature."
- **Analysis**: This statement is generally true. At lower temperatures, the rate constant \( k \) is more sensitive to changes in temperature because the exponential factor in the Arrhenius equation has a more significant effect. As temperature increases, the rate constant \( k \) increases, but the relative change in \( k \) tends to be larger at lower temperatures compared to higher temperatures. Therefore, this statement is **correct**.

4. **Statement D**: "A plot of \( \ln k \) vs \( \frac{1}{T} \) is a straight line with slope equal to \(-\frac{E_a}{R}\)."
- **Analysis**: From the Arrhenius equation, if we take the natural logarithm, we get:
\[ \ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T} \]
This equation is in the form of \( y = mx + c \), where \( y = \ln k \), \( m = -\frac{E_a}{R} \), and \( x = \frac{1}{T} \). Thus, the plot of \( \ln k \) versus \( \frac{1}{T} \) is indeed a straight line with a slope of \(-\frac{E_a}{R}\). Therefore, this statement is **correct**.

### Conclusion:
After analyzing all four statements, we find that statements A, B, C, and D are all correct. Therefore, the number of correct statements is **4**.