Which of the following statements `(s)` are not correct?

Options

A. A plot of `log k` versus `1//T` is linear
B. A plot of `log k` versus `1//T` is nonlinear.
C. A plot of `log P` versus `1//T` is linear at constant volume.
D. A plot of `P` versus `1//V` is linear at constant temperature.

Answer

To determine which statements are not correct, we will analyze each statement based on the principles of chemical kinetics and gas laws.

### Step-by-Step Solution:

1. **Statement A: A plot of log k versus 1/T is linear.**
- According to the Arrhenius equation, \( k = A e^{-\frac{E_a}{RT}} \), taking the logarithm gives us:
\[ \log k = \log A - \frac{E_a}{R} \cdot \frac{1}{T} \]
- This is in the form of \( y = mx + c \), where \( y = \log k \), \( x = \frac{1}{T} \), and the slope \( m = -\frac{E_a}{R} \). Thus, this statement is **correct**.

2. **Statement B: A plot of log k versus 1/T is nonlinear.**
- Since we established that a plot of log k versus 1/T is linear (as shown in Statement A), this statement is **incorrect**.

3. **Statement C: A plot of log p versus 1/T is linear at constant volume.**
- From the ideal gas law, at constant volume:
\[ PV = nRT \implies P = \frac{nRT}{V} \]
- Rearranging gives \( P \propto T \). If we take logarithms:
\[ \log P = \log\left(\frac{nR}{V}\right) + \log T \]
- This indicates a linear relationship between log P and log T, not log P versus \( \frac{1}{T} \). Therefore, this statement is **incorrect**.

4. **Statement D: A plot of P versus 1/V is linear at constant temperature.**
- From the ideal gas law, we have:
\[ PV = nRT \implies P = \frac{nRT}{V} \]
- This indicates that \( P \) is inversely proportional to \( V \). If we plot \( P \) versus \( \frac{1}{V} \), it will yield a straight line through the origin. Thus, this statement is **correct**.

### Conclusion:
The statements that are **not correct** are:
- **Statement B**: A plot of log k versus 1/T is nonlinear.
- **Statement C**: A plot of log p versus 1/T is linear at constant volume.