The Van der Waals equation is a modified gas equation that explains the behaviour of which type of gases?

Introduction / Context:
This question belongs to the topic of gaseous state and equations of state. The familiar ideal gas equation PV = nRT assumes point like molecules with no intermolecular forces, which is only an approximation. To describe the actual behaviour of real gases more accurately, Van der Waals proposed a modified equation that corrects for molecular volume and attractive forces. You are asked to identify which type of gases this Van der Waals equation is intended to describe.

Given Data / Assumptions:

• The equation referred to is the Van der Waals equation of state.
• It introduces correction terms for pressure and volume compared with the ideal gas equation.
• The options mention ideal gases, real gases, mixtures of gases and diatomic gases only.
• Standard textbook meaning of ideal and real gases is assumed.

Concept / Approach:
An ideal gas obeys PV = nRT at all temperatures and pressures, with molecules treated as point particles that do not interact except through elastic collisions. Real gases deviate from this behaviour, especially at high pressure and low temperature, because their molecules occupy finite volume and experience intermolecular attractions and repulsions. The Van der Waals equation modifies the ideal gas equation by introducing a correction term a * n^2 / V^2 to account for intermolecular attraction and a volume correction term b * n to account for finite molecular size. This equation is specifically designed to approximate the behaviour of real gases, not truly ideal ones, and it works for many gases across a range of conditions.

Step-by-Step Solution:
Step 1: Recall the ideal gas equation PV = nRT, which is based on several simplifying assumptions about gas molecules. Step 2: Recognise that actual gases, such as carbon dioxide or ammonia, deviate from this ideal behaviour, especially at high pressure or low temperature. Step 3: Van der Waals introduced a corrected equation of the form (P + a * n^2 / V^2) * (V - n * b) = n * R * T. Step 4: The correction a * n^2 / V^2 reduces the effective pressure, compensating for attractive forces between molecules. Step 5: The correction V - n * b reduces the effective volume available to the gas, compensating for the finite size of molecules. Step 6: Because these corrections are specifically designed to handle deviations of actual gases from the ideal model, the Van der Waals equation is used for real gases.

Verification / Alternative check:
If gases truly behaved ideally, the simple PV = nRT equation would be sufficient and no corrections would be needed. In practice, however, measurements of pressure, volume and temperature for gases like carbon dioxide show deviations from ideal values, and the Van der Waals equation gives better agreement with experimental data. The constants a and b are different for different gases, which further confirms that the equation is tailored to describe real gases rather than an abstract ideal gas. Mixtures of gases can also be modelled, but the fundamental concept is still that they are real, not ideal.

Why Other Options Are Wrong:
Ideal gases are defined as obeying PV = nRT exactly, so there is no need to use the Van der Waals equation for a truly ideal gas. Mixtures of gases may still be treated as ideal or real; the equation in question does not specifically refer to mixtures only. Diatomic gases are not a special category in the context of the Van der Waals equation; they are simply real gases that can be described by it with appropriate constants. Therefore, the only correct and general description is that the Van der Waals equation applies to real gases.

Common Pitfalls:
One frequent confusion is to think that the Van der Waals equation defines a new ideal gas, whereas it actually corrects for non ideal behaviour. Another mistake is to associate the equation only with certain gases such as carbon dioxide or nitrogen, rather than understanding that it is a general model for many real gases. Some students also forget the physical meaning of constants a and b, which leads to weak conceptual understanding. Remember that the whole purpose of the Van der Waals equation is to improve the description of real gases, especially under conditions where ideal assumptions fail.

Final Answer:
The Van der Waals equation is used to explain and model the behaviour of real gases.