Chemistry · Class 11 · States of Matter: Gases and Liquids · Term 3

Deviation from Ideal Behaviour and Liquefaction of Gases

Investigate why real gases deviate from ideal behavior, particularly at high pressures and low temperatures. Learn about the van der Waals equation and the concept of critical temperature.

TL;DR:Ever wondered why the gas in your LPG cylinder is a liquid, or how an AC cools your room? This topic uncovers the real behaviour of gases that makes these technologies possible.

• CBSE Learning Outcomes
• NCERT Class 11 Chemistry: Unit 5 - States of Matter

About This Topic

This topic, a crucial part of the 'States of Matter' chapter for Class 11, moves students beyond the simplified model of the ideal gas law. In the Indian curriculum, it serves as the first deep dive into the limitations of scientific models and the need for refinement. The overview should begin by revisiting the two faulty assumptions of the Kinetic Theory of Gases: that gas molecules have negligible volume and that there are no intermolecular forces of attraction. These assumptions hold true only at low pressures and high temperatures.

The core of the topic is the van der Waals equation, presented as a logical correction to the ideal gas equation. Teachers should emphasise the physical significance of the constants 'a' (a measure of intermolecular attraction) and 'b' (the excluded volume per mole), linking them to the properties of real gases. The second major concept is the liquefaction of gases, contextualised through Andrews' experiments on carbon dioxide isotherms. This section is vital for explaining the concept of critical temperature, pressure, and volume, which has immense practical applications in industries ranging from cryogenics to the storage of household LPG.

Key Questions

1. Explain the significance of the 'a' and 'b' constants in the van der Waals equation.
2. Analyze the conditions required for the liquefaction of a gas, including the role of critical temperature.
3. Compare the pressure-volume isotherms of a real gas with those of an ideal gas.

Learning Objectives

• Identify the two incorrect postulates of the kinetic theory of gases that lead to deviations from ideal behaviour.
• Explain the physical significance of the van der Waals constants 'a' and 'b' and apply the van der Waals equation to simple problems.
• Analyse the pressure-volume isotherms of a real gas to define critical temperature, critical pressure, and critical volume.
• Predict the conditions of temperature and pressure under which a real gas will behave most ideally.
• Interpret graphs of compressibility factor (Z) versus pressure to compare the deviation of different real gases.

Key Vocabulary

Real Gas	A gas that does not obey the ideal gas law under all conditions of temperature and pressure because its molecules have finite volume and exert intermolecular forces.
Van der Waals Equation	An equation of state for real gases that modifies the ideal gas law to account for molecular volume and intermolecular attractive forces.
Compressibility Factor (Z)	A factor that quantifies the deviation of a real gas from ideal gas behaviour. It is the ratio of the actual molar volume of the gas to the molar volume it would occupy if it were an ideal gas at the same temperature and pressure.
Critical Temperature (Tc)	The highest temperature at which a gas can be converted into a liquid by the application of pressure. Above this temperature, liquefaction is impossible.
Boyle Temperature (Tb)	The temperature at which a real gas behaves like an ideal gas over an appreciable range of pressures.

Watch Out for These Misconceptions

Common Misconception

Any gas can be liquefied just by applying enough pressure.

What to Teach Instead

A gas can only be liquefied below a specific temperature called its critical temperature (Tc). Above this temperature, it exists as a gas and cannot be turned into a liquid, no matter how high the pressure.

Common Misconception

The van der Waals constants 'a' and 'b' are just mathematical 'fudge factors' without any real meaning.

What to Teach Instead

These constants have clear physical significance. 'a' is a measure of the magnitude of intermolecular attractive forces, and 'b' is related to the effective volume occupied by the gas molecules themselves.

Common Misconception

Ideal gas behaviour is a rare, special case.

What to Teach Instead

All real gases approach ideal behaviour at sufficiently high temperatures and low pressures. Under these conditions, the kinetic energy of molecules overcomes attractive forces and the molecular volume becomes negligible compared to the container volume.

Active Learning Ideas

Collaborative Problem-Solving

Plotting Z vs P

Provide students with data for the compressibility factor (Z) versus pressure (P) for different gases like H₂, He, CH₄, and CO₂. Students plot these on a graph to visually compare their deviation from the ideal gas line (Z=1).

30 min·Pairs

Jigsaw

Van der Waals Constants Jigsaw

Divide the class into 'expert' groups for constant 'a' and constant 'b'. Each group researches its constant's significance and then re-groups to teach their peers what they learned.

40 min·Small Groups

Collaborative Problem-Solving

Critical Temperature Analogy

Use an analogy of trying to pack unruly children (gas molecules) into a room. At high energy (high temp), they run around too much to be packed. Only below a certain energy level (critical temp) can they be forced together (liquefied) by pushing the walls in (pressure).

15 min·Whole Class

Real-World Connections

• The storage of LPG (Liquefied Petroleum Gas) in household cylinders is a direct application of gas liquefaction under pressure.
• Air conditioners and refrigerators work on the principle of compressing a refrigerant gas to liquefy it, which releases heat, and then allowing it to expand and vaporise, which absorbs heat.
• Aerosol cans, like deodorants and insect repellents, contain a product mixed with a liquefied propellant gas under pressure.
• Cryosurgery and cryopreservation use liquefied gases like liquid nitrogen, which is produced by cooling and compressing nitrogen gas below its critical temperature.
• The transport and storage of industrial gases like oxygen, nitrogen, and argon in liquid form in tankers is more efficient than transporting them as compressed gases.

Assessment Ideas

Exit Ticket

Use an exit ticket asking students to rank three gases (e.g., NH₃, N₂, H₂) in order of their expected deviation from ideal behaviour and to justify their ranking based on intermolecular forces.

Quick Check

A set of numerical problems where students must use the van der Waals equation to calculate P, V, or T for a given real gas, and compare the result with the value obtained from the ideal gas law.

Quick Check

Provide students with unlabelled P-V isotherms for a real gas and ask them to identify the critical point, the gaseous phase, the liquid phase, and the liquid-vapour equilibrium region.

Frequently Asked Questions

Why do we still use the ideal gas law if it's not accurate for real gases?

The ideal gas law is a very useful approximation that works well under common conditions of low pressure and high temperature. It provides a simple, foundational model for understanding gas behaviour before introducing more complex corrections.

What is the state of a substance above its critical temperature and pressure?

It is called a supercritical fluid. This state has unique properties, with the density of a liquid but the flow and diffusion properties of a gas. It's used as a solvent in processes like decaffeinating coffee.

Why do hydrogen and helium show positive deviation from ideal behaviour almost always?

Being very small molecules with extremely weak intermolecular forces, the repulsive forces due to their molecular volume (the 'b' factor) dominate over the weak attractive forces (the 'a' factor) even at relatively low pressures. This makes their compressibility factor Z greater than 1.