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).