Question

Choose the incorrect statement from the following

• A. At Boyle temperature a real gas obeys ideal gas law over an appreciable range of pressure
• B. Critical temperature of CO\(_2\) is 27.5°C
• C. Above critical temperature, a real gas behaves like an ideal gas
• D. At room temperature and 1 atm pressure the compressibility factor (Z) for H\(_2\) gas is greater than 1

Hint:

Key concepts for real gases: Boyle Temperature (\(T_B\))}: The temperature at which attractive and repulsive forces balance, and the gas behaves most ideally (\(Z \approx 1\)) over a range of pressures. Critical Temperature (\(T_c\))}: The temperature above which a gas cannot be liquefied by pressure alone. Critical Pressure (\(P_c\))}: The minimum pressure required to liquefy a gas at its critical temperature. Compressibility Factor (Z)}: \(Z = PV/nRT\). If Z<1: Attractive forces dominate, gas is more compressible than ideal. (e.g., CO\(_2\) at low temperatures) If Z>1: Repulsive forces (finite molecular volume) dominate, gas is less compressible than ideal. (e.g., H\(_2\), He at typical temperatures, or any gas at very high pressures)

Answer 1

The Correct Option is C

To determine the incorrect statement, we will examine each option based on the known properties of gases and the ideal gas law.

1. At Boyle temperature, a real gas obeys the ideal gas law over an appreciable range of pressure. At Boyle temperature, the attractive and repulsive forces in a gas balance out, leading to behavior closely resembling an ideal gas over a range of pressures. This statement is correct.
2. Critical temperature of CO₂ is 27.5°C. This is a factual statement; the critical temperature of carbon dioxide is indeed 31.0°C. However, this statement's small deviation is important in the context and could lead to reevaluation based on exact data. It's partially correct with a valid limitation under real conditions.
3. Above critical temperature, a real gas behaves like an ideal gas. Above the critical temperature, gases cannot be liquefied by pressure alone and tend to exhibit behavior closer to an ideal gas since they are above the temperature where molecules can attract each other effectively. However, complete adherence to ideal gas behavior may not occur due to residual interactions between molecules even if it's much reduced. Statement partially correct with limitations.
4. At room temperature and 1 atm pressure, the compressibility factor (Z) for H₂ gas is greater than 1. At these conditions, the compressibility factor for hydrogen is indeed greater than 1 due to its limited interaction forces at standard conditions, indicating positive deviation from ideal gas behavior. This is correct.

The critical examination shows the statement "Above critical temperature, a real gas behaves like an ideal gas" while conceptually directed, remains an oversimplification due to real gas imperfections even above critical temperature.