Consider the following statements :
The mean free path of gas molecules
I. decreases with increase in concentration
II. increases with decrease in pressure at constant temperature
III. decreases with increase in molecular size
Which of the above statements are correct?

Options

A. I , II
B. I, III
C. II, III
D. I, II, III

Explanation

To solve the question regarding the mean free path of gas molecules and the correctness of the given statements, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding Mean Free Path**:
- The mean free path is defined as the average distance a molecule travels between successive collisions. It is influenced by factors such as concentration, pressure, and molecular size.

2. **Analyzing Statement I**:
- **Statement I**: The mean free path of gas molecules decreases with an increase in concentration.
- **Explanation**: When concentration increases, the number of gas molecules in a given volume increases. This leads to more frequent collisions among the molecules, which reduces the average distance traveled between collisions. Therefore, this statement is **correct**.

3. **Analyzing Statement II**:
- **Statement II**: The mean free path increases with a decrease in pressure at constant temperature.
- **Explanation**: According to Boyle's Law, at constant temperature, a decrease in pressure results in an increase in volume. As the volume increases, the space available for gas molecules to move also increases, leading to fewer collisions. Hence, the mean free path increases. Therefore, this statement is **correct**.

4. **Analyzing Statement III**:
- **Statement III**: The mean free path decreases with an increase in molecular size.
- **Explanation**: When the size of the molecules increases, the effective volume occupied by the molecules increases, which reduces the available space for movement. This leads to more collisions and a shorter mean free path. Therefore, this statement is **correct**.

5. **Conclusion**:
- All three statements (I, II, and III) are correct regarding the mean free path of gas molecules.

### Final Answer:
All statements (I, II, and III) are correct.