Short Answer

The van der Waals constants a and b represent two important corrections for real gases. The constant a corrects for the intermolecular attractive forces that reduce gas pressure. The constant b corrects for the finite volume of gas molecules, which reduces the available space for movement.

These corrections help modify the ideal gas equation so that it more accurately describes the behaviour of real gases at high pressure and low temperature, where deviations from ideal behaviour become significant.

Detailed Explanation

Corrections Represented by a and b

In the study of gases, the ideal gas equation PV = nRT assumes that gas molecules have no intermolecular forces and no volume. This makes calculations simple, but real gases do not follow these assumptions perfectly. Real gases have weak attractions between particles and occupy a definite amount of space. To correct these limitations, van der Waals introduced two constants, a and b, which modify the ideal gas equation.

The corrected equation, known as the van der Waals equation, is:

In this equation, a and b represent corrections for pressure and volume so that the behaviour of real gases can be accurately predicted, especially under conditions where deviations from ideal behaviour are large.

Correction Represented by Constant a

The constant a represents a correction for intermolecular attraction between gas molecules. In real gases, molecules attract each other slightly. This weak attraction reduces the pressure exerted by the gas because particles are pulled inward and hit the container walls with less force.

The ideal gas equation does not consider this attraction. It assumes molecules never pull on each other and always hit the container walls with full strength. Therefore, the pressure calculated by the ideal gas equation is usually higher than the actual pressure of the real gas.

The constant a corrects this error by adding a term to pressure in the van der Waals equation:

• High value of a: strong attraction, gas deviates more (e.g., NH₃, CO₂).
• Low value of a: weak attraction, gas is close to ideal (e.g., He, H₂).

Thus, a corrects the pressure drop caused by intermolecular forces.

Correction Represented by Constant b

The constant b represents a correction for the finite volume of gas molecules. In the ideal gas equation, molecules are treated as point-sized particles that occupy no space. But in reality, gas molecules have size and take up some space in the container.

At high pressure, when the gas is compressed, the actual volume of gas molecules becomes important. The ideal gas equation assumes that the entire container volume is available for molecular movement, which is not true.

The constant b corrects this by subtracting the space occupied by gas molecules:

• High value of b: larger molecules need more correction (e.g., CO₂).
• Low value of b: smaller molecules need less correction (e.g., He).

Thus, b corrects the volume overestimation of the ideal gas equation.

Why These Corrections Are Needed

Real gases deviate from ideal behaviour mostly under two conditions:

1. High Pressure

• Molecules are very close.
• Molecular volume cannot be ignored → corrected by b.
• Repulsive forces become important.
• Pressure becomes higher than predicted by PV = nRT.

2. Low Temperature

• Molecules move slowly.
• Attractive forces increase → corrected by a.
• Pressure becomes lower than predicted by the ideal gas equation.

Under normal conditions (low pressure and high temperature), corrections are small, and real gases behave almost ideally.

Combined Effect of a and b

The constants work together in the van der Waals equation:

• a modifies pressure by correcting for attraction.
• b modifies volume by correcting for molecular size.

These corrections make real gas calculations more accurate. Without a and b, the predictions of gas behaviour would be inaccurate, especially when gases are compressed or cooled.

Industries and Applications Using These Corrections

The corrections represented by a and b are used in:

• Gas liquefaction industries
• Refrigeration systems
• Chemical manufacturing
• Petroleum and natural gas processing
• High-pressure gas storage
• Thermodynamic studies

Understanding these corrections helps in designing safer equipment, predicting gas compressibility, and studying the behaviour of gases under extreme conditions.

Examples Showing Need for Corrections

• CO₂ forms dry ice at low temperature because attractions are strong (high a).
• NH₃ liquefies easily due to hydrogen bonding, requiring large correction for a.
• Helium behaves almost ideally at room temperature because it has small a and b values.

These examples show that real gases need corrections to match actual behaviour.

Conclusion

The van der Waals constants a and b represent essential corrections for real gases. Constant a corrects for intermolecular attractions that reduce pressure, while constant b corrects for the finite volume of gas molecules. Together, these corrections make the van der Waals equation more accurate than the ideal gas equation, especially under high pressure and low temperature. They help us understand and predict real gas behaviour more reliably in science and industry.