Limitations of the Ideal Gas Model and Deviations of Real Gases
- You're inflating a balloon on a chilly winter day.
- You notice that the balloon doesn’t expand as much as it would on a warm day, even though you’ve filled it with the same amount of air. Why is this?
The answer lies in the behavior of gases under different conditions.
Why Do Real Gases Deviate from Ideal Gas Behavior?
The ideal gas model is based on several simplifying assumptions, as explored in the previous section:
- Gas particles have negligible volume compared to the volume of their container.
- There are no intermolecular forces between gas particles.
- Collisions between gas particles are perfectly elastic.
- The kinetic energy of gas particles is directly proportional to their temperature in kelvin.
While these assumptions work well for many gases under standard conditions, they break down under specific circumstances.
Real gases deviate from ideal behavior primarily due to:
- Intermolecular Forces: At low temperatures, attractive forces between particles become significant.
- Finite Particle Volume: At high pressures, the volume occupied by gas particles themselves is no longer negligible.
1. Low Temperatures: The Role of Intermolecular Forces
At low temperatures, gas particles move more slowly because their kinetic energy decreases.
This reduced motion allows intermolecular forces—such as van der Waals forces—to become more pronounced.
These forces cause gas particles to attract each other, reducing the pressure exerted by the gas compared to what the ideal gas law predicts.
Example
Consider a gas like ammonia
Analogy
- Imagine a group of people walking quickly in a crowded room.
- If they’re moving fast, they’re less likely to stop and interact with each other.
- This is similar to gas particles at high temperatures—they move too quickly for intermolecular forces to take effect.
- Now imagine the same group walking slowly.
- They’re more likely to stop and interact, just as gas particles are more likely to experience intermolecular attractions at low temperatures.
Tip
To minimize deviations from ideal behavior, gases should be studied athigh temperatures, where the kinetic energy of particles overcomes intermolecular forces.
Self review
Can you think of other examples where slowing down movement increases interactions? How does this relate to gas behavior?
2. High Pressures: The Significance of Particle Volume
At high pressures, gas particles are compressed into a smaller space.
Under these conditions, the volume of the gas particles themselves becomes significant compared to the total volume of the gas.
- This means that the space available for the particles to move is less than the container’s volume, violating the ideal gas assumption that particle volume is negligible.
- As a result, the gas occupies more volume than predicted by the ideal gas law.
- This effect is particularly noticeable in gases with larger molecules, such as butane
Analogy
- Think of a jar filled with marbles.
- If the jar is large, the marbles take up only a small fraction of the total volume, leaving plenty of empty space.
- Now imagine squeezing the marbles into a much smaller jar.
- The volume occupied by the marbles themselves becomes a significant fraction of the total volume, just as the particle volume becomes significant for gases at high pressures.
Tip
To minimize deviations from ideal behavior, gases should be studied atlow pressures, where particles are far apart and their individual volumes are negligible.
Self review
How does the size of gas particles influence their behavior at high pressures?
Factors Affecting Deviations: The Nature of the Gas
Not all gases deviate from ideal behavior to the same extent. The degree of deviation depends on the nature of the gas, particularly:
- Intermolecular Forces: Polar gases with strong intermolecular forces (e.g., hydrogen fluoride, HF) deviate more than nonpolar gases (e.g., helium, He).
- Molecular Size: Larger gas molecules occupy more volume and deviate more than smaller molecules.
Common Mistake
Many students assume that all gases deviate from ideal behavior equally. Remember that factors like polarity and molecular size play a crucial role in determining the extent of deviation.
Real vs. Ideal Gases: A Summary of Conditions
| Condition | Ideal Gas Behavior | Real Gas Behavior |
|---|---|---|
| Low Temperature | Negligible intermolecular forces | Significant intermolecular attractions |
| High Pressure | Negligible particle volume | Particle volume becomes significant |
| High Temperature | Particles move too fast for interactions | Deviations are minimal |
| Low Pressure | Particles are far apart | Deviations are minimal |
Self review
Under what conditions do real gases behave most like ideal gases? Why?
Van der Waals Equation: A More Realistic Model (HL Only)
To account for the deviations of real gases, the van der Waals equation modifies the ideal gas law:
Here:
Note
The van der Waals equation provides a more accurate representation of real gas behavior but is more complex to use than the ideal gas law.
Reflection and Practice
Self review
- Why do gases deviate from ideal behavior at low temperatures and high pressures?
- Compare the behavior of helium
- How does the van der Waals equation improve upon the ideal gas law?
Theory of Knowledge
How do the assumptions of the ideal gas model influence our understanding of real-world phenomena? What are the risks of relying too heavily on simplified models?
