Question

Identify the wrong relation for real gases:

• A. \( Z = \frac{V_{\text{ideal}}}{V_{\text{real}}} \)
• B. \( p_{\text{ideal}} = p_{\text{real}} + \frac{an^2}{V^2} \)
• C. \( V_{\text{real}} = V_{\text{ideal}} - nb \)
• D. \( \left( p + \frac{a}{V^2} \right) (V - b) = RT \)

Hint:

The compressibility factor Z measures deviations from ideal gas behavior, involving pressure, volume, and temperature, not the ratio of ideal to real volumes.

Answer 1

The Correct Option is A

The compressibility factor \( Z \) is a measure of deviation from ideal gas behavior and is defined as:
\[ Z = \frac{p_{\text{real}}V_{\text{real}}}{RT} \]
Option (A), which states \( Z = \frac{V_{\text{ideal}}}{V_{\text{real}}} \), is incorrect because \( Z \) is not defined in terms of the ratio of ideal to real volume. Instead, it involves pressure, volume, and temperature of the real gas relative to the ideal gas law.

Options (B), (C), and (D) are correct:

• (B) Adjusts pressure due to intermolecular forces (\( \frac{an^2}{V^2} \)).
• (C) Accounts for excluded volume (\( nb \)) in real gases.
• (D) Represents the van der Waals equation, which adjusts both pressure and volume.

Thus, the wrong relation is Option (A).