Question

The van der Waals equation explains the behaviour of (a) ideal gas (b) real gases (c) vapours (d) non-real gases

Short answer

(b) real gases

Step-by-step solution

Analyze the choices

The first step is to understand each of the following options: (a) ideal gases, (b) real gases, (c) vapours, and (d) non-real gases. The ideal gas law is a hypothetical gas law that assumes gas particles do not interact and occupy no volume. Real gases are gases that do not follow the ideal gas laws exactly, due to interactions between particles and a finite volume of the particles. Vapours are a specific state of matter, not a category of gases. Non-real gases don't exist, there are only ideal and real gases in terms of behavior.

Match the choice with the concept of van der Waals equation

The van der Waals equation is used to understand the behavior of real gases, including their properties under different conditions. It includes terms to account for the finite volume of gas molecules and the intermolecular forces, things that ideal gases ignore. Hence, this equation doesn't apply to ideal gases, vapours, or 'non-real gases' (as such category does not exist), but precisely to real gases.

Key concepts

Ideal Gases

Ideal gases are a theoretical concept that simplifies our understanding of gas behavior. In reality, no gas perfectly fits this model, but it serves as a useful approximation for many purposes. The key assumption in the ideal gas model is that the gas molecules:

• Have no volume themselves — they're considered point particles.
• Do not interact with one another except through elastic collisions.
• Follow the ideal gas law, given by the equation: \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is the amount of substance in moles, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.

These simplifications mean that, across many conditions, ideal gases don't accurately describe real-world behavior. However, they offer a good approximation, especially at high temperatures and low pressures, where molecules are far apart.

Real Gases

Real gases differ notably from ideal gases due to interactions between gas molecules and the space they occupy. These differences become more pronounced under conditions of high pressure and low temperature. In these scenarios, ignoring the volume of the molecules and the forces between them is not sufficient.

The van der Waals equation describes the behavior of real gases more accurately by adjusting the ideal gas law to account for:

• The actual volume occupied by gas molecules, introducing the "volume correction" term \(b\).
• Attractive forces between molecules, introducing the "pressure correction" term \(a\), reducing actual pressure from the ideal level.

Applying the van der Waals equation helps us predict and understand the properties of real gases under various conditions, offering a more complete picture than the ideal gas law alone.

Intermolecular Forces

Intermolecular forces are forces of attraction or repulsion between molecules, distinct from the bonds within molecules. These forces have significant impacts on the behavior of gases, especially when real gases are considered.

• Types of intermolecular forces include van der Waals forces (such as dipole-dipole interactions and London dispersion forces) and hydrogen bonding.
• These forces become more evident under conditions like low temperatures or high pressures, where the molecules are closer together.

In the context of the van der Waals equation, intermolecular forces account for deviations from ideal behavior. The adjustment to the pressure-term within the equation accounts for these forces, altering the predicted pressure in real gases.

Non-Ideal Behavior

Non-ideal behavior in gases refers to deviations from the predictions of the ideal gas law. This occurs because real gas molecules have a finite volume and interact with one another, via intermolecular forces discussed earlier.

Non-ideal behavior is particularly significant in conditions of:

• High pressure, where the space between molecules decreases, amplifying the impact of intermolecular forces and molecular volume.
• Low temperature, which slows molecular movement, increasing interaction time and the effect of molecular forces.

The van der Waals equation offers a more reliable model of gas behavior by improving upon the ideal gas law. It includes additional parameters to account for these interactions and molecular volumes, allowing for a more realistic description of gas properties in varying conditions.