Understanding the Van der Waals Equation and Real Gas Behavior

The question asks what the Van der Waals equation explains the behaviour of. Let's look at the options and the concept behind this equation.

The ideal gas law, \(PV = nRT\), provides a simple model for gas behavior. However, this law relies on assumptions that are not entirely accurate for real gases:

• It assumes gas molecules have no volume.
• It assumes there are no attractive or repulsive forces between gas molecules (intermolecular forces).

These assumptions hold reasonably well for gases at low pressures and high temperatures, conditions under which real gases behave almost like ideal gases.

Why the Ideal Gas Law Fails for Real Gases

At high pressures, the volume occupied by the gas molecules themselves becomes significant compared to the total volume of the container. The "available" volume for movement is less than the container volume.

At low temperatures, the kinetic energy of the molecules is lower, making the attractive intermolecular forces more significant. These forces reduce the pressure exerted by the gas on the container walls.

Because of these deviations from ideal behavior, a more accurate equation is needed to describe real gas behavior.

The Van der Waals Equation for Real Gas Behavior

Johannes Diderik van der Waals modified the ideal gas equation to account for these non-ideal behaviors. His equation, known as the Van der Waals equation, is:

\(\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT\)

In this equation:

• The term \(\frac{an^2}{V^2}\) is added to the pressure \(P\). This term corrects for the attractive intermolecular forces between molecules, which effectively reduce the pressure. The constant \(a\) is related to the strength of these forces for a specific gas.
• The term \(nb\) is subtracted from the volume \(V\). This term accounts for the finite volume occupied by the gas molecules themselves (the excluded volume). The constant \(b\) is related to the size of the molecules for a specific gas.

By introducing these corrections, the Van der Waals equation provides a much better description of the pressure-volume-temperature relationship for real gases over a wider range of conditions compared to the simple ideal gas law. It specifically addresses the characteristics that distinguish real gases from ideal gases, like their finite size and the presence of intermolecular forces.

Therefore, the Van der Waals equation is specifically designed to explain the behavior of real gases.