In the ideal gas model used in kinetic theory, an ideal gas is a purely theoretical substance. According to this model, which of the following phase changes can an ideal gas not undergo?

Introduction / Context:
The ideal gas is a useful abstraction in physics and chemistry that obeys the simple relation p * V = n * R * T without deviations. This model helps to understand gas behaviour at moderate pressures and temperatures and simplifies many calculations. However, it does not include real world effects such as intermolecular attractions that cause gases to liquefy or solidify. This question asks you to identify which phase changes are not represented in the simple ideal gas model.

Given Data / Assumptions:

• The ideal gas equation p * V = n * R * T assumes non interacting point particles.
• There are no attractive forces or finite molecular volumes in the ideal gas model.
• Real gases deviate from ideal behaviour at high pressures and low temperatures and can condense into liquids or solids.
• The question asks what an ideal gas cannot do within the idealised model.

Concept / Approach:
In the ideal gas model, molecules are treated as point particles that move randomly and do not attract each other. This means that no matter how much you cool or compress an ideal gas within the mathematical model, it continues to obey the ideal gas equation without condensing into a liquid or solid. Real gases, however, have intermolecular forces and finite sizes, and under sufficient pressure and low temperature, they undergo phase transitions to liquid and then to solid. Since the ideal gas is defined by assumptions that exclude such interactions, phase changes like liquefaction and solidification fall outside the model. Thus, in the strict ideal gas model, the gas cannot be liquefied or solidified.

Step-by-Step Solution:
Step 1: Recall the core assumptions of the ideal gas model: molecules have negligible volume and no intermolecular attractions.Step 2: Recognise that phase transitions to liquid or solid require significant intermolecular attractions to hold molecules close together.Step 3: Understand that because the ideal gas model ignores these attractions, it cannot describe condensation phenomena.Step 4: Note that in the ideal model, gas behaviour is described for all temperatures and pressures by p * V = n * R * T.Step 5: Compare this with real gas behaviour, where deviations and liquefaction appear, which are handled by more complex equations of state such as the van der Waals equation.Step 6: Conclude that an ideal gas cannot be liquefied or solidified within the simple model.

Verification / Alternative check:
When plotting p V T relationships for real gases, you see curves that deviate from the straight hyperbolic plots expected from the ideal gas law, particularly near phase change regions. During liquefaction, pressure can remain nearly constant while volume decreases, behaviour that cannot be described by p * V = n * R * T for a single phase ideal gas. Engineers use real gas equations for such regions. In contrast, ideal gas calculations are confined to conditions where the gas remains in the gaseous state. This confirms that liquefaction and solidification are outside the ideal gas description.

Why Other Options Are Wrong:
Option A focuses only on liquefaction, but the question asks more generally about phase changes; the deeper point is that any condensation into liquid is not included in the ideal gas model. Option B mentions solidification alone, which is also excluded but again does not capture the full range of condensation processes. Option D states that an ideal gas can be heated and expanded, which it certainly can in the model; the ideal gas law works for higher temperatures and volumes. The most complete and accurate statement is that the ideal gas model does not describe liquefaction or solidification into condensed phases.

Common Pitfalls:
Students may confuse the ideal gas model with real gas behaviour and think that if you cool any gas enough it must liquefy, forgetting that the question is about the mathematical ideal, not real substances. Others may incorrectly believe that the ideal gas law can describe all states of matter if used with the right constants. To avoid these misunderstandings, remember that the ideal gas model is an approximation valid when intermolecular forces are negligible and no phase changes occur.

Final Answer:
Within the simple ideal gas model, an ideal gas cannot be liquefied or solidified into condensed phases; such phase changes lie outside the model assumptions.