Problem 102 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of van der Waals radius of \(\mathrm{F}, \mathrm{Cl}\) and \(\mathrm{Br}\) is (a) \(\mathrm{Cl}>\mathrm{F}>\mathrm{Br}\) (b) \(\mathrm{Br}>\mathrm{Cl}>\mathrm{F}\) (c) \(\mathrm{F}>\mathrm{Cl}>\mathrm{Br}\) (d) \(\mathrm{Br}>\mathrm{F}>\mathrm{Cl}\)

Step-by-Step Solution

Answer

(b) \( \mathrm{Br} > \mathrm{Cl} > \mathrm{F} \)

Step 1: Understand van der Waals Radii

Van der Waals radius is a measure of the size of an atom that forms only weak non-covalent bonds with neighboring atoms. Typically, as you move down a group in the periodic table, the van der Waals radius increases due to the additional electron shells.

Step 2: Identify the Periodic Trend

Fluorine (F), Chlorine (Cl), and Bromine (Br) are all halogens located in Group 17 of the periodic table. They descend in order as F, Cl, and Br, meaning F is at the top and Br is at the bottom.

Step 3: Apply the Trend to Determine Order

According to the periodic trend for halogens, the van der Waals radius increases as you move from top to bottom within the group. Hence, bromine has the largest radius, followed by chlorine, and then fluorine with the smallest.

Step 4: Choose the Correct Option

From the given options, (b) \( \mathrm{Br} > \mathrm{Cl} > \mathrm{F} \) correctly reflects the trend that the van der Waals radii increase from fluorine to bromine.

Key Concepts

Halogens

The halogens are a unique group of elements that include fluorine (F), chlorine (Cl), and bromine (Br), among others. They are located in Group 17 of the periodic table. Halogens are known for their ability to form salts and compounds through reactions with other elements. This group is fascinating due to its highly reactive nature, especially the elements found higher up the group, such as fluorine.
Despite being in the same group, halogens exhibit distinct characteristics as you move from the top to the bottom of the group. For example:

• Fluorine is the most reactive and electronegative of all elements.
• They generally exist as diatomic molecules in their elemental form, such as F extsubscript{2}, Cl extsubscript{2}, and Br extsubscript{2}.
• These elements display varying physical states; fluorine and chlorine are gases at room temperature, while bromine is a liquid.

Each halogen has a unique van der Waals radius, showing their size and interaction propensity with non-bonded atoms in space.

Periodic Trends

In chemistry, periodic trends are patterns that appear in the periodic table as you move in specific directions across the table. These trends help predict an element's properties based on its position. One of the most critical trends is the change in atomic and ionic radii as you move down a group or across a period.
When it comes to halogens like fluorine, chlorine, and bromine:

• As you descend a group, the additional electron shells increase the van der Waals radius.
• Moving from left to right across a period generally results in decreasing atomic size due to increased nuclear charge pulling at the electron cloud more tightly.

Understanding periodic trends, especially in terms of atomic size and reactivity, allows chemists to predict interaction strengths and possible compound formations.

Atomic Size

Atomic size or atomic radius refers to the distance from the nucleus of an atom to the outermost electron shell. As you study elements across the periodic table, changes in atomic size are apparent due to variations in electron shell number and nuclear charge.
For the halogens, these changes occur predictably:

• Fluorine, at the top of the halogen group, has the smallest atomic size because it has fewer electron shells.
• In contrast, bromine, at the bottom, has a larger atomic radius due to more electron shells despite the periodic increase in nuclear charge.

This results in bromine having a larger van der Waals radius than fluorine, reflecting its larger atomic and elemental size. Understanding these size differences is essential for grasping how atoms interact in different physical states and chemical reactions.

Non-Covalent Interactions

Non-covalent interactions are crucial to understanding many biological, chemical, and physical phenomena. These interactions occur between molecules without the sharing of electron pairs or covalent bonding. They primarily involve forces like van der Waals interactions, hydrogen bonding, and dipole-dipole interactions.
Specifically, van der Waals forces are weak, attractive forces that exist between all atoms and molecules. These forces include both attractive and repulsive interactions that are significant at short ranges. In the context of atomic size and halogens:

• Van der Waals radii are linked closely to atomic size since larger atoms or molecules exert stronger attractive forces at greater distances.
• For halogens, larger atoms like bromine tend to form larger van der Waals forces compared to smaller atoms like fluorine, affecting how they pack in solid states or interact in liquid forms.

Considering non-covalent interactions helps in understanding the physical properties of substances, such as boiling and melting points, solubility, and viscosity.