Question

Identify the wrong relation for real gases

• A. \(z=\frac{V_{ideal}}{V_{real}}\)
• B. \(P_{ideal}=P_{real}+\frac{an^2}{V^2}\)
• C. \(V_{ideal}=V_{real}-nb\)
• D. \((p+\frac{a}{V^2})(V-b)=RT\)

Answer 1

The Correct Option is A, C

The question asks to identify the wrong relation for real gases. Let's evaluate each option:

Explanation of each option:

• (A) \( Z = \frac{V_{\text{ideal}}}{V_{\text{real}}} \): This is incorrect. The correct definition of compressibility factor \( Z \) involves pressure and volume relationships, not just the ratio of ideal and real volumes.
• (B) \( P_{\text{ideal}} = P_{\text{real}} + \frac{a n^2}{V^2} \): This is correct. This equation is part of the Van der Waals equation, where \( a \) is a constant related to intermolecular forces.
• (C) \( V_{\text{real}} = V_{\text{ideal}} - nb \): This is incorrect. The volume occupied by the gas molecules adds to the ideal gas volume, so the correct equation is \( V_{\text{real}} = V_{\text{ideal}} + nb \).
• (D) \( \left( p + \frac{a}{V^2} \right) (V - b) = RT \): This is correct. It is the Van der Waals equation for real gases.

Conclusion:

The incorrect relations are (A) and (C).

Answer 2

For real gases, the following are the correct relations:
Van der Waals equation: \[ \left( p + \frac{a}{V^2} \right) (V - b) = RT \] This is given in Option (D) and is valid for real gases.
Compressibility factor: \[ Z = \frac{V_{\text{real}}}{V_{\text{ideal}}} \] In Option (A), this is the correct expression, but it does not represent the right relation for real gases because \( Z \) is not simply the ratio of real and ideal volumes for real gases. The equation must account for non-ideal behavior and intermolecular forces.
Real gas volume correction: The correct relation for real gas volume is \( V_{\text{real}} = V_{\text{ideal}} - nb \), where \( n \) is the number of moles and \( b \) is the volume correction factor due to finite molecular size.
Option (C) is incorrect, as it should reflect the relationship where the actual volume is corrected for the finite size of molecules in the real gas.

Thus, Option (A) and Option (C) are wrong.