In a closed vessel of 5 litres capacity, 1 g of `O_(2)` is heated from `300` to `600 K`. Which statement is not correct ?

Options

A. Pressure of the gas increases
B. The rate of collision increases
C. The number of moles of gas increases
D. The energy of gaseous molecules increases

Explanation

To solve the problem, we need to analyze the statements regarding the behavior of oxygen gas (O₂) in a closed vessel when it is heated from 300 K to 600 K.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a closed vessel with a capacity of 5 liters.
- The amount of O₂ present is 1 g.
- The initial temperature is 300 K and the final temperature is 600 K.

2. **Calculating Moles of O₂**:
- To find the number of moles of O₂, we use the formula:
\[ \text{Number of moles} (n) = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
- The molar mass of O₂ is approximately 32 g/mol.
- Therefore, the number of moles of O₂ is:
\[ n = \frac{1 \text{ g}}{32 \text{ g/mol}} = 0.03125 \text{ moles} \]

3. **Applying Gay-Lussac's Law**:
- According to Gay-Lussac's law, at constant volume, the pressure of a gas is directly proportional to its absolute temperature:
\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]
- Since the volume is constant (closed vessel), as the temperature increases from 300 K to 600 K, the pressure will also increase.

4. **Analyzing the Statements**:
- **Statement A**: "Pressure of the gas increases."
- This is correct because as temperature increases, pressure increases at constant volume.

- **Statement B**: "The rate of collision increases."
- This is also correct because higher temperature means higher kinetic energy, leading to more frequent collisions between gas molecules.

- **Statement C**: "The number of moles of gas increases."
- This statement is incorrect. The number of moles remains constant in a closed vessel since no gas is added or removed.

- **Statement D**: "The energy of gaseous molecules increases."
- This is correct because the kinetic energy of gas molecules is proportional to temperature. As temperature increases, the kinetic energy also increases.

5. **Conclusion**:
- The statement that is not correct is **Statement C**: "The number of moles of gas increases."

### Summary of the Solution:
- The correct answer is that **Statement C** is not correct.