What conditions cause maximum deviation?

Short Answer

Maximum deviation from ideal gas behaviour occurs when gases are at high pressure and low temperature. Under these conditions, gas molecules come very close to each other, and intermolecular forces become strong. As a result, gases no longer follow the ideal gas equation accurately.

At high pressure, the volume of gas molecules becomes significant, and at low temperature, attractive forces strongly affect gas behaviour. These combined effects cause real gases to show the largest deviation from ideal behaviour.

Detailed Explanation

Conditions Causing Maximum Deviation

Ideal gases follow the equation PV = nRT exactly, assuming that gas molecules have no intermolecular forces and no volume. Real gases, however, do not fully satisfy these assumptions. The difference between real gas behaviour and ideal gas behaviour is called deviation.
This deviation becomes very noticeable under certain conditions. The conditions that cause the maximum deviation from ideal behaviour are high pressure and low temperature.

Under these extreme conditions, real gas molecules behave very differently from ideal gases because the effects of molecular forces and molecular volume become highly significant.

Deviation at High Pressure

At high pressure:

  • Gas molecules are pushed very close to each other.
  • The distance between particles becomes very small.
  • Intermolecular forces (attractive or repulsive) become strong.
  • The actual volume of gas molecules becomes important.

Under such conditions, the ideal gas assumption that molecules have negligible volume no longer holds true. In fact, when the gas is compressed, the size of molecules occupies a noticeable portion of the container, reducing the free space available for movement.

This causes real gases to show positive deviation, where the gas pressure becomes greater than what the ideal gas equation predicts. Repulsive forces dominate when the molecules are too close, pushing them apart and increasing the pressure more than expected.

Deviation at Low Temperature

Low temperature causes another major deviation. At low temperature:

  • Gas molecules move slowly because kinetic energy decreases.
  • Attractive forces between molecules become stronger.
  • Molecules stick closer together.
  • Gas pressure becomes lower than predicted by the ideal gas equation.

The ideal gas equation assumes that molecules move fast enough so that attractions do not matter. But at low temperature, the slow-moving molecules feel strong attractions, causing them to collide with the container walls less forcefully. This reduces pressure and leads to negative deviation.

Low temperature also pushes gases closer to the point of liquefaction. Real gases begin to behave more like liquids than gases under such conditions, making the deviation very large.

Combined Effect of High Pressure and Low Temperature

When both conditions occur together:

  • Molecules are extremely close due to high pressure.
  • They move slowly due to low temperature.
  • Attractive and repulsive forces become very strong.
  • The ideal gas equation fails badly.

This is the situation where real gases show maximum deviation from ideal behaviour.
Examples include gases stored in cylinders, LPG containers, and CO₂ under cooling and compression.

Why These Conditions Cause Maximum Deviation

The main reasons these conditions cause large deviations are:

  1. Intermolecular Forces Become Significant

Ideal gas model assumes no attractions, but real gases have attractions and repulsions.
At low temperature, attractions dominate.
At high pressure, repulsions dominate.

Both types of forces interfere with ideal behaviour.

  1. Molecular Volume Cannot Be Ignored

At high pressure, the volume available for gas movement becomes much smaller.
The actual size of gas particles starts to matter.

Therefore, the ideal assumption of zero molecular volume becomes false.

  1. Behaviour Approaches Liquefaction

A gas becomes more like a liquid at low temperature and high pressure.
Liquids never follow the ideal gas equation, so deviation becomes maximum.

  1. High Pressure Increases Collisions

Frequent collisions increase the impact of repulsive forces, making pressure higher than predicted.

All these factors create maximum differences between ideal predictions and real gas behaviour.

Examples of Maximum Deviation

Some gases that show large deviations under high pressure and low temperature are:

  • Carbon dioxide (CO₂) → liquefies easily and shows strong deviation.
  • Ammonia (NH₃) → strong hydrogen bonding causes large deviation.
  • Sulphur dioxide (SO₂) → has strong intermolecular forces.
  • Water vapour → deviates strongly as it approaches condensation.

Gases like helium and hydrogen show less deviation because they have weak forces and very small molecular size.

Van der Waals Explanation

The van der Waals equation explains maximum deviation through two constants:

  • a corrects for attraction
  • b corrects for molecular volume

Under high pressure, the correction for b becomes large.
Under low temperature, the correction for a becomes large.
Together, these corrections show why deviation increases greatly under extreme conditions.

Conclusion

Maximum deviation from ideal gas behaviour occurs under high pressure and low temperature. These conditions force gas molecules close together and reduce their kinetic energy, increasing the effects of intermolecular forces and molecular volume. As a result, real gases no longer follow the ideal gas equation accurately. Understanding these conditions helps predict gas behaviour in industrial processes, storage, and scientific studies.