Question

The given graph represents the variation of compressibility factor \( Z = \frac{pV}{nRT} \), for three real gases A, B, and C. Identify the only incorrect statement: 

• A. For gas A, \( a = 0 \) and its dependence on \( p \) is linear at all pressures.
• B. For gas B, \( b = 0 \) and its dependence on \( p \) is linear at all pressures.
• C. For gas C, which is a typical real gas for which neither \( a \) nor \( b = 0 \). By knowing the minima and point of intersection with \( Z = 1 \), \( a \) and \( b \) can be calculated.
• D. At high pressure, the slope is positive for all real gases.

Hint:

For real gases, deviations from ideal behavior depend on intermolecular forces (\( a \)) and molecular size (\( b \)). The compressibility factor \( Z \) typically decreases at low pressures and increases at high pressures for real gases.

Answer 1

The Correct Option is B

The compressibility factor \( Z \) is a measure of how much a real gas deviates from ideal behavior. For ideal gases, \( Z = 1 \) at all pressures. Real gases, however, exhibit deviations from ideality, and these deviations depend on the specific properties of the gas, including the parameters \( a \) and \( b \), which are related to intermolecular forces and molecular size, respectively. 
- Option A: For gas A, \( a = 0 \), which means no intermolecular attraction forces. The compressibility factor increases linearly with pressure, which is a characteristic behavior for gases without significant intermolecular interactions. 
- Option B: For gas B, \( b = 0 \), which means no molecular size effects (ideal gas behavior). However, the dependence of \( Z \) on pressure is not linear at all pressures for real gases. This makes Option B incorrect, as it contradicts the graph, which shows a non-linear relationship at intermediate pressures. 
- Option C: For gas C, which behaves as a typical real gas, both \( a \) and \( b \) are non-zero. By analyzing the minima and the intersection points with \( Z = 1 \), both parameters \( a \) and \( b \) can indeed be determined. 
- Option D: At high pressure, the compressibility factor for all real gases becomes positive, indicating that the gas particles are being compressed and interactions between molecules become more significant. Thus, the incorrect statement is Option B.