Short Answer

Van der Waals constants a and b are correction terms used in the van der Waals equation for real gases. The constant a corrects for intermolecular forces, while b corrects for the finite volume of gas molecules. These constants help make the ideal gas equation more accurate for real gases.

Different gases have different values of a and b because each gas has unique intermolecular forces and molecular sizes. These constants help predict real gas behaviour more correctly at high pressure and low temperature.

Detailed Explanation

Van der Waals Constants a and b

Van der Waals constants, represented by a and b, are two important parameters introduced in the van der Waals equation to correct the ideal gas equation for real gas behaviour. The ideal gas equation PV = nRT assumes that gas molecules have no intermolecular forces and no volume. However, real gases do not behave ideally, especially at high pressures and low temperatures. To make gas calculations more accurate, Johannes van der Waals introduced two correction constants that modify pressure and volume in the ideal gas equation.

The van der Waals equation for real gases is:

In this equation, a and b are constants that depend on the type of gas and correct the behaviour of real gases by accounting for attractive forces and molecular volume.

Meaning of Constant a

The constant a corrects for intermolecular forces of attraction between gas molecules.
In real gases, molecules attract each other slightly. This reduces the pressure exerted by the gas on the walls of the container. The ideal gas equation does not consider this attraction, so it predicts a higher pressure than real gases actually exert.

The constant a increases the pressure term in the equation to account for the attraction.

• High value of a means strong intermolecular forces.
  Example: Ammonia (NH₃) and carbon dioxide (CO₂).
• Low value of a means weak intermolecular forces.
  Example: Helium (He) and hydrogen (H₂).

Thus, a represents how strongly the molecules attract each other. Gases with strong attractions require a larger correction.

Meaning of Constant b

The constant b corrects for the finite volume of gas molecules.
In the ideal gas equation, gas molecules are considered point-sized with no actual volume. But real gas molecules occupy space. When gases are compressed to high pressures, this molecular volume cannot be ignored.

The constant b subtracts the volume occupied by the gas molecules from the total volume of the container. It represents the space that gas molecules themselves take up and cannot be used for movement.

• High value of b means larger molecules.
  Example: Bigger gas molecules like CO₂.
• Low value of b means smaller molecules.
  Example: Small molecules like He and H₂.

Thus, b measures the effective volume of one mole of gas molecules.

Why a and b Are Needed

The ideal gas law works well only at low pressure and high temperature. At high pressure or low temperature, real gases deviate from ideal behaviour. The reasons for deviation are:

1. Gas molecules attract each other (pressure becomes lower than ideal).
2. Gas molecules occupy space (volume becomes less than ideal).

The van der Waals constants correct these deviations:

• a increases the calculated pressure to correct the effect of attractions.
• b decreases the available volume to correct for molecular size.

These corrections allow the equation to describe real gases more accurately.

Effect of Constant a on Gas Behaviour

The constant a varies for different gases depending on the strength of attraction.

• Gases with high attraction (like NH₃) have larger a values.
• Gases with weak attraction (like He, H₂) have small a values.

This means gases with strong attractions are more compressible and show negative deviations from ideal behaviour at moderate pressures.

Effect of Constant b on Gas Behaviour

The size of gas molecules affects the value of b.

• Larger molecules push each other more when compressed, so the available volume becomes significantly reduced.
• Smaller molecules are compact and need only a small correction.

Thus, b is directly proportional to molecular size.

Van der Waals Equation and Its Importance

The van der Waals equation:

This equation is widely used because:

• It predicts gas behaviour correctly at high pressures.
• It helps understand liquefaction of gases.
• It explains compressibility factor deviations.
• It is used in chemical engineering, thermodynamics, and industry.

It improves upon the ideal gas equation by including real-world corrections.

Examples of Gases and Their Constants

Some gases and their approximate values (not exact) show how different gases vary:

• Helium: very small a and b
• Hydrogen: small a and b
• Carbon dioxide: large a and moderate b
• Ammonia: very large a due to hydrogen bonding

This shows how intermolecular forces and molecular sizes differ among gases.

Conclusion

Van der Waals constants a and b are correction terms used to adjust the ideal gas equation for real gas behaviour. Constant a accounts for intermolecular attractions, while constant b represents the finite volume of gas molecules. These constants vary for different gases and help predict gas behaviour more accurately under real conditions such as high pressure and low temperature. They make the van der Waals equation an important tool in understanding and working with real gases.