Two van der waal's gases have same value of a but different value of b which of the following statement is correct ?

Options

A. The smaller the value of b larger will be compressibility
B. The larger the value of b larger will be compressibility
C. Both have same compressibility
D. All the with smaller value of b will occupy larger volume

Answer

To solve the question regarding the two van der Waals gases that have the same value of 'a' but different values of 'b', we need to analyze the implications of the van der Waals equation and the meanings of the constants involved.

### Step-by-Step Solution:

1. **Understanding the van der Waals Equation**:
The van der Waals equation is given by:
\[ P + \frac{aN^2}{V^2} (V - Nb) = RT \]
where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( T \) = temperature
- \( R \) = universal gas constant
- \( a \) = measure of attraction between particles
- \( b \) = volume occupied by one mole of gas particles (effective size of gas)

2. **Identifying the Variables**:
In this case, we have two gases (let's call them gas X and gas Y) with:
- Same value of \( a \) (indicating similar intermolecular attractions)
- Different values of \( b \) (indicating different effective sizes of gas molecules)

3. **Interpreting the Value of 'b'**:
The value of \( b \) represents the volume occupied by the gas molecules themselves. A smaller value of \( b \) means that the gas molecules are smaller or occupy less volume, while a larger value of \( b \) means the gas molecules are larger or occupy more volume.

4. **Compressibility**:
- Compressibility is defined as the ability of a substance to decrease in volume under pressure.
- If \( b \) is smaller, the gas can be compressed more easily because there is less volume occupied by the gas particles themselves, allowing for more space for the gas to be compressed into.

5. **Analyzing the Statements**:
- **Statement 1**: "Smaller the value of B, larger will be the compressibility."
- This is **correct** because smaller \( b \) means more space available for compression.
- **Statement 2**: "Larger the value of B, larger will be the compressibility."
- This is **incorrect**; larger \( b \) means less compressibility.
- **Statement 3**: "Both have same compressibility."
- This is **incorrect**; different \( b \) values imply different compressibilities.
- **Statement 4**: "All the smaller value of B will occupy larger volume."
- This is **incorrect**; smaller \( b \) means less volume occupied.

6. **Conclusion**:
The correct statement is that the smaller the value of \( b \), the larger will be the compressibility.

### Final Answer:
The correct statement is: **Smaller the value of B, larger will be the compressibility.**