What is compressibility factor (Z)?

Short Answer

The compressibility factor (Z) is a value that shows how much a real gas differs from ideal gas behaviour. It is calculated using the formula Z = PV / nRT. If Z = 1, the gas behaves ideally. If Z is greater or less than 1, the gas shows deviation from ideal behaviour.

This factor helps scientists understand how real gases behave under different temperatures and pressures. High pressure or low temperature usually cause gases to deviate more from ideal behaviour, which is reflected in the compressibility factor.

Detailed Explanation

Compressibility Factor Z

The compressibility factor, represented by Z, is an important quantity in the study of real gases. It tells us how much a real gas differs from the behaviour predicted by the ideal gas equation PV = nRT. In simple words, Z helps measure how “compressible” a real gas is compared to an ideal gas.

For an ideal gas, the equation PV = nRT is always perfectly true, so the value of Z = 1. But real gases do not follow this equation exactly because they have intermolecular forces and finite molecular volume. As a result, real gases often show values of Z either greater than 1 or less than 1. These deviations help us understand the actual behaviour of gases under different conditions.

The compressibility factor is useful because it brings together pressure, volume, temperature, and amount of gas into one number that shows deviation clearly and simply. It plays an important role in industries, chemical engineering, thermodynamics, and the study of gas behaviour in real-life situations.

Definition and Formula of Z

The compressibility factor is defined as:

Z = PV / nRT

Where:

  • P = pressure of the gas
  • V = volume
  • n = number of moles
  • R = universal gas constant
  • T = temperature

If Z = 1, the gas behaves ideally.
If Z ≠ 1, the gas deviates from ideal behaviour.

This equation compares the actual behaviour of a gas (PV) with the expected ideal behaviour (nRT).

Meaning of Z = 1, Z > 1, and Z < 1

The value of Z helps identify the type of deviation:

  1. Z = 1 → Ideal Gas Behaviour

When Z equals 1, the gas perfectly obeys the ideal gas equation. This usually happens at low pressure and high temperature, where real gases behave almost ideally.

  1. Z > 1 → Gas Is Less Compressible

When Z is greater than 1, the gas shows positive deviation.
This means:

  • Gas is harder to compress.
  • Repulsive forces dominate.
  • Molecules are very close due to high pressure.

Examples:

  • Helium and hydrogen show Z > 1 at high pressure.
  1. Z < 1 → Gas Is More Compressible

When Z is less than 1, the gas shows negative deviation.
This means:

  • Gas can be compressed more easily.
  • Attractive forces dominate.
  • Molecules are drawn closer at low temperature or moderate pressure.

Examples:

  • Carbon dioxide and ammonia often show Z < 1 due to stronger attractions.

Why Real Gases Deviate (Role of Z)

Real gases do not behave ideally because of:

  1. Intermolecular forces
    Attractive or repulsive forces affect pressure and volume.
  2. Finite molecular volume
    Gas molecules occupy space, which affects behaviour at high pressure.

These real-world factors change the values of P, V, and T in such a way that PV is no longer equal to nRT, causing Z to differ from 1.

Conditions Affecting Compressibility Factor

The compressibility factor changes depending on temperature and pressure.

  1. High Pressure
  • Molecules are forced close.
  • Volume of particles becomes important.
  • Repulsive forces increase.
  • Z > 1
  1. Low Temperature
  • Molecules move slowly.
  • Attractive forces become strong.
  • Pressure becomes lower than expected.
  • Z < 1
  1. Low Pressure and High Temperature
  • Molecules are far apart.
  • Intermolecular forces become negligible.
  • Behaviour approaches ideal.
  • Z ≈ 1

These conditions help predict when real gases deviate strongly or behave almost ideally.

Use of Compressibility Factor in Real Life

The compressibility factor is widely used in:

  1. Gas storage
    Industries storing gases like oxygen, nitrogen, hydrogen, and LPG use Z to estimate correct gas volume and pressure.
  2. Chemical engineering
    Z helps design reactors, compressors, and pipelines by predicting gas behaviour.
  3. Thermodynamics
    Z is used to calculate real gas properties such as internal energy and enthalpy.
  4. Petroleum industry
    Natural gas in reservoirs behaves differently from ideal gases; Z helps estimate gas extraction rates.
  5. High-pressure experiments
    Scientists use Z to understand behaviour of gases under extreme conditions.

Van der Waals Equation and Z

The van der Waals equation adjusts the ideal gas equation for real gases by correcting:

  • intermolecular attraction (a)
  • molecular volume (b)

Using Z with van der Waals corrections gives accurate gas predictions across temperature and pressure ranges.

Conclusion

The compressibility factor (Z) shows how much a real gas deviates from ideal gas behaviour. It is calculated using Z = PV / nRT, where Z = 1 indicates ideal behaviour, while values greater or less than 1 show deviation. Z helps explain the real behaviour of gases under different conditions of temperature and pressure and is widely used in industry and science to understand and predict gas properties accurately.