Problem 123 - A Complete Resource Book in Chemistry for JEE Main

Question

Which bond angle \(\theta\), would result in the maximum dipole moment for the triatomic molecule \(\mathrm{XY}_{2}\) shown below? (a) \(\theta=120^{\circ}\) (b) \(\theta=90^{\circ}\) (c) \(\theta=145^{\circ}\) (d) \(\theta=175^{\circ}\)

Step-by-Step Solution

Answer

The bond angle \( \theta \) of 90° would result in the maximum dipole moment.

Step 1: Understanding Dipole Moment

The dipole moment is a measure of the polarity of a molecule. In a triatomic molecule like \( \mathrm{XY}_2 \), the dipole moment depends on the vector sum of the individual bond dipoles. The greater the vector sum, the higher the dipole moment.

Step 2: Analyzing Bond Configurations

Consider how the angle \( \theta \) affects the vector sum of the dipole moments. When \( \theta \) is 180°, the dipoles cancel each other out, resulting in no net dipole moment. As \( \theta \) decreases, the dipoles don't completely cancel, and the net dipole moment increases.

Step 3: Calculating Maximum Dipole Effect

The maximum dipole moment occurs when the angle \( \theta \) enables the greatest effective combination of the individual dipole moments. Generally, when \( \theta \) is around 90°, the dipoles are most effectively combined in the same direction, increasing the net dipole moment.

Step 4: Selecting the Best Option

Given the options, 90° (option b) is closest to this effective combination angle where the dipoles would be combined to achieve maximum net dipole moment.

Key Concepts

Bond Angle

In the context of molecular geometry, the bond angle refers to the geometric angle formed between two adjacent bonds that converge at an atom. This angle is crucial in determining the overall shape of the molecule and can have a significant impact on its properties. For a triatomic molecule like \( \mathrm{XY}_2 \), different bond angles can lead to different distributions of electronic charge across the molecule. As a result, the bond angle plays a direct role in the dipole moment of the molecule.

To give an example, if the bond angle is 180°, the molecule is linear, and the bond dipoles cancel each other out, leading to no net dipole moment. However, as this angle changes to a lesser value, say 90°, the dipoles do not align in a straight line. Instead, they partially align in the same direction, enhancing the dipole moment. Therefore, the bond angle is key to studying and predicting molecular polarity, especially in molecules like \( \mathrm{XY}_2 \) where the angle directly affects the molecule's net dipole moment.

Triatomic Molecule

Triatomic molecules, as the name suggests, consist of three atoms. These molecules can be linear or bent, depending on the bond angle between their atoms. For instance, a classic example of a triatomic molecule is water (\( \mathrm{H}_2\mathrm{O} \)), which has a bent shape. Similarly, in a molecule like \( \mathrm{XY}_2 \), the arrangement of the atoms and the bond angle leads to particular molecular shapes that influence various properties.

This shape is not merely about the physical arrangement of atoms, but it also influences chemical properties like reactivity and polarity. By analyzing the bond angles and resulting shape of a triatomic molecule, chemists can make educated guesses about its behavior in different chemical reactions. For example, in our problem, altering the angle \( \theta \) in a triatomic structure impacts how the individual atomic charges add together, affecting the dipole moment.

Molecular Polarity

Understanding molecular polarity is essential for grasping how molecules interact with each other and their environment. Polarity occurs when there is an uneven distribution of electron density, resulting in a molecule having a positive and a negative side. In molecules like \( \mathrm{XY}_2 \), the shape significantly affects its polarity.

Bond angles alter how individual dipole moments from each bond can add or cancel each other out. A molecule with an angular shape and asymmetrical charge distribution is typically polar. For instance, a \( \theta \) close to 90° in a \( \mathrm{XY}_2 \) molecule often yields maximum dipole moments, creating a strongly polar molecule. This is because this angular configuration enhances the alignment of dipole moments into a common direction, further creating a distinct positive and negative pole within the molecule. Such polar molecules are crucial in various applications like solvents, as they can dissolve ionic compounds and facilitate reactions.