Problem 14 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The values of van der Waals constant ' \(a\) ' for the gases \(\mathrm{O}_{2}, \mathrm{~N}_{2}, \mathrm{NH}_{3}\) and \(\mathrm{CH}_{4}\) are \(1.360,1.390,4.170\) and \(2.253 \mathrm{~L}^{2}\) atm \(\mathrm{mol}^{-2}\) respectively. The gas which can most easily be liquified is : [1989-1 Mark] (a) \(\mathrm{O}_{2}\) (b) \(\mathrm{N}_{2}\) (c) \(\mathrm{NH}_{3}\) (d) \(\mathrm{CH}_{4}\)

Step-by-Step Solution

Answer

The gas that can most easily be liquefied is NH3.

Step 1: Understanding the Problem

The problem involves determining which of the given gases can be most easily liquefied based on the van der Waals constant 'a'. This constant is related to the intermolecular forces within a gas, specifically focusing on the attraction between molecules.

Step 2: Analyze van der Waals Constant 'a'

The value of the van der Waals constant 'a' indicates the magnitude of intermolecular forces per mole-square volume. A higher value of 'a' suggests stronger intermolecular forces, which means the gas can be liquefied more easily.

Step 3: Compare Values of 'a'

The given values of 'a' for the gases are:- \(\mathrm{O}_2: 1.360\)- \(\mathrm{N}_2: 1.390\)- \(\mathrm{NH}_3: 4.170\)- \(\mathrm{CH}_4: 2.253\)Among these, \(\mathrm{NH}_3\) has the highest value of 4.170 \(\text{L}^2 \text{atm mol}^{-2}\).

Step 4: Conclusion on Ease of Liquefaction

Since \(\mathrm{NH}_3\) has the largest 'a' value, it means \(\mathrm{NH}_3\) has the strongest intermolecular forces compared to the other gases. Therefore, \(\mathrm{NH}_3\) can be liquefied the most easily.

Key Concepts

Intermolecular Forces

In order to understand why certain gases can be liquefied more easily than others, it is important to consider the role of intermolecular forces. Intermolecular forces refer to the attraction between molecules in a substance. These forces vary in strength and determine many properties of the substances, such as boiling point, melting point, and liquefaction.

For gases, the strength of intermolecular forces directly influences their ability to transition from a gaseous to a liquid state. Stronger intermolecular forces mean that molecules are drawn closer together, making it easier for the gas to condense into a liquid. In the context of the van der Waals constant 'a', a higher value indicates stronger intermolecular attractions. Therefore, when comparing gases with different 'a' values, the one with the highest value typically has the strongest intermolecular forces and is most easily liquefied.

Liquefaction of Gases

Liquefaction is the process of converting a gas into a liquid by cooling and/or compressing the gas. It is crucial for a variety of industrial and scientific applications, such as the transport and storage of gases, refrigeration, and air conditioning systems.

For a gas to liquefy with ease, it must have sufficient intermolecular forces that can overcome the kinetic energy of the gas molecules. High kinetic energy keeps molecules moving rapidly and far apart. When intermolecular forces are stronger, as indicated by a higher van der Waals 'a' constant, it becomes easier to bring the molecules close enough to form a liquid. In essence, gases with higher 'a' values require less extreme conditions (temperature or pressure) to transition to a liquid state.

Gas Properties

The properties of gases are mainly influenced by temperature, pressure, volume, and the nature of the gas itself, which is partly reflected by van der Waals constants. Apart from behaving ideally as described by the Ideal Gas Law, real gases exhibit deviations due to intermolecular attractions and the volume occupied by the gas particles. This is where van der Waals equation comes into play: \[ \left( P + \frac{a}{V^2} \right)(V-b)=nRT \]Where:

• \(P\) = pressure
• \(V\) = volume
• \(n\) = number of moles
• \(R\) = universal gas constant
• \(T\) = temperature
• \(a\) = measure of intermolecular forces
• \(b\) = volume occupied by gas particles

The constant 'a' adjusts for attractions between particles, while 'b' accounts for finite particle size, which is crucial in estimating non-ideal behavior in gases. Understanding these corrections provides a more accurate description of gas behavior, especially at high pressures and low temperatures where real gases deviate significantly from ideal behavior. By incorporating these factors, we gain a better understanding of the physical characteristics and reactivity of different gases.