Short Answer:

The van der Waals equation is a modified form of the ideal gas law that takes into account the volume of gas molecules and the intermolecular forces between them. It gives a more accurate prediction of real gas behavior, especially at high pressure and low temperature, where the ideal gas law fails.

While the ideal gas law assumes that gas molecules have no size and do not attract or repel each other, the van der Waals equation includes two correction factors: one for molecular volume and another for molecular attraction. This makes it better for studying real gases in practical situations.

Detailed Explanation:

Van der Waals equation and its difference from ideal gas law

In thermodynamics, the ideal gas law (PV = nRT) is widely used to describe the behavior of gases. It works well under normal conditions—that is, low pressure and high temperature. But when gases are exposed to high pressure or low temperature, they deviate from ideal behavior. This is because real gas molecules have finite size and experience intermolecular forces, which the ideal gas law ignores.

To make gas behavior more realistic, Dutch scientist Johannes Diderik van der Waals introduced a corrected version of the ideal gas law, known as the van der Waals equation.

Van der Waals Equation

The van der Waals equation is written as:

(P + a/v²)(v – b) = RT

Where:

• P = Pressure of the gas
• v = Molar volume (volume per mole of gas)
• T = Temperature in Kelvin
• R = Universal gas constant
• a = Constant to correct intermolecular attraction
• b = Constant to correct molecular volume

These two constants (a and b) are different for each gas and are determined experimentally.

Main Differences Between Ideal Gas Law and Van der Waals Equation

1. Molecular Volume Correction (b)

• Ideal gas law assumes gas molecules have no volume.
• Van der Waals equation subtracts a value b from volume to account for the finite size of molecules.
  → It means gases cannot be compressed beyond a limit.

2. Intermolecular Attraction Correction (a)

• Ideal gas law assumes no attraction or repulsion between molecules.
• Van der Waals equation adds a pressure correction term a/v² to account for molecular attraction.
  → Real gases attract each other, so actual pressure is lower than ideal.

3. Applicability

• Ideal gas law is good for theoretical calculations under normal conditions.
• Van der Waals equation is used for accurate predictions at high pressure, low temperature, or near phase changes (like liquefaction).

Why These Differences Matter

At high pressures:

• Gas molecules are closer together, so intermolecular forces and molecular sizes become significant.
• The volume available to move freely is reduced, and molecules interact more, causing deviations.

At low temperatures:

• Molecules move slower, so attractive forces between them have a larger effect.

In these situations, the ideal gas law fails, but the van der Waals equation provides better results by including real gas behavior.

Applications in Engineering

• Chemical processing: Used to design equipment that handles gases under non-ideal conditions.
• Refrigeration and liquefaction: Helps predict how gases behave during phase changes.
• Aerospace and high-pressure systems: Necessary for analyzing high-altitude or deep-sea environments where ideal gas law is not accurate.
• Thermodynamic cycle design: More precise gas property prediction improves engine and turbine performance.

Conclusion

The van der Waals equation improves upon the ideal gas law by accounting for real gas behavior through corrections for molecular volume and intermolecular forces. While the ideal gas law is simpler and useful for many cases, it does not work well at high pressures or low temperatures. The van der Waals equation fills this gap, providing a more accurate way to study and design systems involving real gases in engineering and science.