Problem 48 - A Complete Resource Book in Chemistry for JEE Main

Question

The values of van der Waals constant ' \(\alpha\) ' for the gases \(\mathrm{O}_{2}, \mathrm{~N}_{2}, \mathrm{NH}_{3}\) and \(\mathrm{CH}_{4}\) are \(1.360,1.390,4.170\) and \(2.253\) L atm. mol \(^{2}\) respectively. The gas which can most easily be liquefied is (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 (c) \(\mathrm{NH}_{3}\).

Step 1: Understanding Van der Waals 'a' Constant

The van der Waals constant \(a\) represents the magnitude of attractive forces between gas molecules. A larger \(a\) value indicates stronger intermolecular attractions, which makes the gas easier to liquefy.

Step 2: Identifying 'a' Constants

The \(a\) constants for the gases are as follows: \(\mathrm{O}_{2} = 1.360\) L atm mol\(^{2}\), \(\mathrm{N}_{2} = 1.390\) L atm mol\(^{2}\), \(\mathrm{NH}_{3} = 4.170\) L atm mol\(^{2}\), and \(\mathrm{CH}_{4} = 2.253\) L atm mol\(^{2}\).

Step 3: Comparing 'a' Constants

To determine which gas is easiest to liquefy, compare the \(a\) values. The highest \(a\) value corresponds to the gas with the strongest intermolecular forces.

Step 4: Determining the Most Easily Liquefied Gas

By analyzing the \(a\) constants, \(\mathrm{NH}_{3}\) has the highest value of 4.170 L atm mol\(^{2}\), suggesting it has the strongest intermolecular forces and is most easily liquefied.

Key Concepts

Intermolecular Forces

Intermolecular forces are the forces of attraction between molecules. These forces play a crucial role in determining the physical properties of substances, such as boiling point and solubility. The strength of these forces can vary, depending on the type of molecules involved. There are several types of intermolecular forces, including:

• London dispersion forces: These are the weakest forces that arise from temporary shifts in the electron cloud within molecules.
• Dipole-dipole interactions: Occur between molecules that have permanent dipole moments, leading to a positive end of one molecule being attracted to the negative end of another.
• Hydrogen bonding: A strong type of dipole-dipole interaction, occurring when hydrogen is bonded to electronegative atoms like oxygen, nitrogen, or fluorine.

In the context of gases, van der Waals constant 'a' helps to quantify these intermolecular forces. Gases with higher 'a' values have stronger intermolecular attractions, making them more likely to condense into liquids at lower pressures and/or temperatures.

Liquefaction of Gases

Gases can be turned into liquids through the process known as liquefaction. This involves cooling the gas or applying pressure to condense it into a liquid form. The ease with which a gas can be liquefied is often influenced by the strength of its intermolecular forces. When these forces are strong, molecules are already more inclined to stay closer together, making the task of liquefying them simpler.

• Temperature: Lowering the temperature reduces the kinetic energy of gas molecules, allowing intermolecular attractions to prevail and bringing molecules closer together.
• Pressure: Increasing pressure effectively forces molecules closer together, encouraging them to form a liquid phase.

Van der Waals constant 'a' specifically indicates the strength of these forces. A high 'a' value, like that of \( \mathrm{NH}_3 \), suggests strong molecular attractions, resulting in easier liquefaction. Therefore, when comparing gases, one with the largest 'a' value will generally be the easiest to liquefy.

Ammonia (NH3)

Ammonia, with the chemical formula \( \mathrm{NH}_3 \), is a common gas known for its pungent smell. Its molecules are composed of one nitrogen atom bonded to three hydrogen atoms, forming a trigonal pyramidal shape. This structure allows ammonia to engage in hydrogen bonding, a particularly strong form of intermolecular forces.
As one of the gases in the van der Waals equation context, ammonia has an exceptionally high 'a' constant of 4.170 L atm mol\(^2\). This high value indicates that ammonia molecules experience strong intermolecular attractions due to hydrogen bonding. As a result, it is much easier to liquefy compared to other gases like \( \mathrm{O}_2 \), \( \mathrm{N}_2 \), or \( \mathrm{CH}_4 \), which rely more heavily on weaker London dispersion forces.
Ammonia's ability to be easily liquefied makes it valuable in various applications, such as refrigerants and industrial processes where gaseous ammonia is required to be stored or handled in liquid form for ease of transport or reaction control.