Short Answer

Compressibility factor is a value that tells how much a real gas deviates from ideal gas behaviour. It compares the actual behavior of a gas with what is predicted by the ideal gas equation. The compressibility factor is usually written as Z.

If Z = 1, the gas behaves like an ideal gas.
If Z ≠ 1, the gas shows deviation. A value greater than 1 means the gas is less compressible, while a value less than 1 means the gas is more compressible than an ideal gas.

Detailed Explanation :

Compressibility factor

The compressibility factor, represented by the symbol Z, is a measure used to understand how real gases behave under different conditions of pressure and temperature. Ideal gases follow the equation  exactly. However, real gases do not always behave perfectly because of forces between molecules and because gas molecules have their own volume. The compressibility factor gives a clear numerical way to compare real gas behavior with ideal gas behavior.

The compressibility factor is defined as:

For an ideal gas, this equation gives Z = 1 because ideal gases strictly obey . But real gases show deviations from this rule, so their value of Z is not equal to 1.

Meaning of Z values

The value of Z gives important information:

• Z = 1 : Gas behaves ideally
• Z < 1 : Gas is more compressible than an ideal gas
• Z > 1 : Gas is less compressible than an ideal gas

These deviations depend on molecular attractions or repulsions.

1. When Z < 1

This happens when attractive forces between molecules dominate. Molecules pull each other closer, reducing the pressure slightly and making the gas more compressible.

Example:
Many gases at moderate pressures show Z < 1.

2. When Z > 1

This happens when repulsive forces dominate. Molecules push each other apart, increasing the pressure and making the gas harder to compress.

Example:
At very high pressure, most gases show Z > 1.

Why real gases deviate from ideal behavior

Real gases differ from ideal gases mainly because:

1. Real gas molecules have volume
   Ideal gases assume zero volume, but real molecules occupy space.
2. Intermolecular forces exist in real gases
   Ideal gases assume no attraction or repulsion, but real gases have van der Waals forces.

Due to these two reasons, the compressibility factor helps describe real gas behavior more accurately.

Behavior of Z at different conditions

Real gases behave differently depending on pressure and temperature:

1. At low pressure

Gas molecules are far apart. Intermolecular forces are negligible.
Therefore:

• Z ≈ 1 (almost ideal)

2. At high pressure

Molecules are very close. Repulsive forces become strong.
Therefore:

• Z > 1 (gas is less compressible)

3. At moderate pressure

Attractive forces may dominate.
Therefore:

• Z < 1 (gas is more compressible)

4. At high temperature

Gas molecules move faster. Forces between molecules become weaker.
Therefore:

• Z approaches 1 (gas behaves more ideally)

Importance of compressibility factor

The value of Z is extremely important in the study of gases for several reasons:

1. Helps understand real gas behavior

It shows how much real gases deviate from the ideal gas law, making calculations more accurate.

2. Used in engineering

In industries dealing with high-pressure gases—like natural gas processing, chemical plants, and petroleum refining—Z is necessary for designing safe systems.

3. Helps calculate real gas properties

The factor Z is used to find real volume, real pressure, and real temperature values of gases in scientific work.

4. Supports advanced equations

It helps improve equations like the van der Waals equation, Redlich–Kwong equation, and other real gas models.

Example of compressibility factor in practical use

Imagine a gas cylinder filled at high pressure. If ideal gas law is used for calculations, the result will not be accurate because the gas inside does not behave ideally. Engineers use the compressibility factor Z to correct the values and predict exact pressure and volume. This helps prevent accidents and ensures correct gas measurements.

Similarly, in natural gas pipelines, Z is used to calculate how much gas can be transported safely.

Relation with van der Waals forces

Since real gases have intermolecular forces, the compressibility factor indirectly represents these forces:

• Attraction lowers Z
• Repulsion increases Z

This links the compressibility factor with van der Waals constants ‘a’ and ‘b’, which correct for molecular attraction and molecular volume.

Conclusion

The compressibility factor is a numerical value that shows how much a real gas deviates from ideal gas behavior. It is defined as . A value of Z equal to 1 indicates ideal behavior, while values greater or less than 1 show deviations caused by molecular attractions or repulsions. The compressibility factor is important in physics, chemistry, and engineering because it helps predict real gas behavior accurately, especially under high pressure and low temperature.