Problem 71 - A Complete Resource Book in Chemistry for JEE Main

Question

The van der Waals forces in halogen decrease in the order (a) \(\mathrm{I}_{2}>\mathrm{Br}_{2}>\mathrm{Cl}_{2}>\mathrm{F}_{2}\) (b) \(\mathrm{F}_{2}>\mathrm{Cl}_{2}>\mathrm{Br}_{2}>\mathrm{I}_{2}\) (c) \(\mathrm{I}_{2}>\mathrm{F}_{2}>\mathrm{Br}_{2}>\mathrm{Cl}_{2}\) (d) \(\mathrm{Cl}_{2}>\mathrm{I}_{2}>\mathrm{Br}_{2}>\mathrm{F}_{2}^{2}\)

Step-by-Step Solution

Answer

The correct answer is (a) \( \mathrm{I}_2 > \mathrm{Br}_2 > \mathrm{Cl}_2 > \mathrm{F}_2 \).

Step 1: Understand van der Waals Forces

Van der Waals forces are weak intermolecular forces that occur between molecules. In the case of halogens, these forces depend on the size and shape of the molecules, and larger atoms or molecules typically experience stronger van der Waals forces due to their increased number of electrons.

Step 2: Consider Atomic Size of Halogens

The size of halogen molecules increases down the group in the periodic table. Therefore, the order of size from largest to smallest for the diatomic molecules is: \( \mathrm{I}_2 > \mathrm{Br}_2 > \mathrm{Cl}_2 > \mathrm{F}_2 \). Larger halogen molecules have stronger van der Waals forces.

Step 3: Analyze the Given Options

Compare the general rule about molecular size and van der Waals forces to the given options. Since larger molecules have stronger van der Waals forces, the correct order is \( \mathrm{I}_2 > \mathrm{Br}_2 > \mathrm{Cl}_2 > \mathrm{F}_2 \).

Step 4: Identify the Correct Option

Based on the analysis, option (a) \( \mathrm{I}_2 > \mathrm{Br}_2 > \mathrm{Cl}_2 > \mathrm{F}_2 \) correctly represents the order of decreasing van der Waals forces based on molecular size.

Key Concepts

Halogens

Halogens are a unique group of elements located in Group 17 of the periodic table. They include fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At). Each of these elements forms diatomic molecules, meaning they exist naturally as pairs, such as \(\text{F}_2, \text{Cl}_2, \text{Br}_2, \text{I}_2,\) and \(\text{At}_2\). One of their defining characteristics is their high reactivity, which decreases as you move down the group.
Halogens also exhibit a range of physical properties that are useful in understanding their behavior in various chemical reactions. For instance, they transition smoothly from gases (fluorine and chlorine) to liquids (bromine) to solids (iodine and astatine) at room temperature.
Understanding these trends in reactivity and physical states can help us predict how halogens will interact with other substances and explain why their van der Waals forces change in the sequence seen in inter-atomic interactions.

Molecular Size

Molecular size refers to the overall dimensions of a molecule. For diatomic molecules like halogens, it is directly influenced by the atomic size of the elements involved. In the context of halogen molecules, the size affects how these molecules interact through van der Waals forces. Larger molecules typically have a higher number of electrons, leading to increased polarizability and stronger intermolecular forces.
This increase in force strength is because larger electron clouds can become more distorted more easily, leading to temporary dipoles that attract neighboring molecules. Therefore, in the family of halogens, iodine, being the largest, will have stronger van der Waals forces compared to smaller halogens like fluorine.
This principle is crucial for predicting the strength of intermolecular forces as size increases, thereby influencing the halogens' physical states and boiling points.

Atomic Size

Atomic size is the distance from the nucleus of an atom to the outer boundary of the surrounding cloud of electrons. It plays a central role in determining the behavior and characteristics of elements, including the halogens.
As you move down the periodic table from fluorine to astatine, the atomic size increases. This trend is due to the addition of extra electron shells as the atomic number increases. Consequently, elements with a larger atomic size have a larger molecular size when they form diatomic molecules.
The increased atomic size directly impacts the van der Waals forces. Larger atoms like iodine have extensive electron clouds that can induce stronger intermolecular attractions compared to smaller atoms like fluorine. Therefore, understanding atomic size trends helps explain variations in physical properties and the corresponding strengths of van der Waals forces as you move down the halogen group.

Intermolecular Forces

Intermolecular forces are the forces that mediate interaction between molecules, including van der Waals forces. They are crucial for determining the physical properties of substances such as boiling and melting points.
Van der Waals forces in halogens are primarily influenced by molecular size. Larger halogen molecules, like \(\text{I}_2\) and \(\text{Br}_2\), have more dispersed electron clouds, which enhance polarizability and thus result in stronger intermolecular attractions. This is why these molecules require more energy to disrupt their structure, leading to higher boiling points compared to smaller molecules.
Moreover, understanding these forces provides insights into the behaviors of halogens in chemical reactions. Even though these forces are weaker than covalent or ionic bonds, they play a significant role in the directional nature of reactions and help explain trends across the halogen group.