Problem 15 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

In van der Waals equation of state for a non-ideal gas, the term that accounts for intermolecular forces is [1988-1 Mark] (a) \((V-b)\) (b) \(R T\) (c) \(\left(P+\frac{a}{V^{2}}\right)\) (d) \((R T)^{-1}\)

Step-by-Step Solution

Answer

(c) \( \left( P + \frac{a}{V^2} \right) \) accounts for intermolecular forces.

Step 1: Understanding the van der Waals Equation

The van der Waals equation is given by \[ \left( P + \frac{a}{V^2} \right) (V-b) = RT \], where \( P \) is the pressure, \( V \) is the volume, \( a \) is a constant that corrects for intermolecular forces, \( b \) is a constant that corrects for molecular size, \( R \) is the ideal gas constant, and \( T \) is the temperature.

Step 2: Identifying Intermolecular Forces Term

In the van der Waals equation, the term \( \frac{a}{V^2} \) accounts for the intermolecular forces. This is because intermolecular forces tend to reduce the pressure exerted by the gas on the container walls, and the term \( \frac{a}{V^2} \) is added to the pressure \( P \) to correct for these forces.

Step 3: Selecting the Correct Option

Reviewing the choices, (c) \( \left( P + \frac{a}{V^2} \right) \) clearly includes the term \( \frac{a}{V^2} \), which adjusts \( P \) to account for intermolecular forces. None of the other options contain the \( \frac{a}{V^2} \) term.

Key Concepts

Intermolecular Forces

Intermolecular forces are the forces of attraction or repulsion that act between neighboring molecules. These forces are weaker than the chemical bonds that hold individual molecules together, but they can significantly influence the properties of substances, especially gases. The van der Waals equation accounts for these forces, which are absent in the ideal gas law. Intermolecular forces cause molecules in a gas to attract each other, reducing the pressure that the gas particles exert on the walls of their container. This reduction is corrected by the term \( \frac{a}{V^2} \) in the van der Waals equation, where \( a \) is a constant specific to each gas, representing the magnitude of these forces.

• For gases with strong intermolecular forces, a larger \( a \) value is used.
• For gases with weaker forces, \( a \) is smaller.

Ultimately, the presence of intermolecular forces means that gases do not behave ideally, which leads us to the concept of non-ideal gases.

Non-Ideal Gas

In contrast to ideal gases, non-ideal gases do not perfectly follow the ideal gas law due to the existence of intermolecular forces and the finite size of gas molecules. The ideal gas law presumes that gas particles have no size and do not interact with one another. However, in reality, molecules occupy space and exert forces on each other.
The van der Waals equation modifies the ideal gas law to better reflect the behavior of real gases. By introducing the constants \( a \) and \( b \), it accounts for the two main factors:

• \( a \) corrects for the pressure reduction due to intermolecular forces.
• \( b \) adjusts for the volume occupied by the gas molecules.

This equation is crucial for understanding and predicting the behavior of gases under non-ideal conditions, such as high pressures or low temperatures.

Pressure Correction

The pressure correction term in the van der Waals equation is essential for adjusting the pressure in non-ideal gas scenarios. In the ideal gas law, \( PV = nRT \), pressure is thought to be solely due to particles colliding with the walls of the container. However, in non-ideal gases, intermolecular attractions reduce this pressure.
The correction is quantified by the term \( \frac{a}{V^2} \). This term is added to the observed pressure \( P \) to compute the corrected pressure that conforms to the actual behavior of the gas.

• This reflects a more realistic scenario where gas particles are affected by each other.
• It allows for better prediction and understanding of gas behavior in environments where non-ideal conditions prevail.

By understanding the pressure correction concept, we can appreciate the nuances of gas behavior beyond the ideal models.