Question

Which species has the smaller bond angle, \(\mathrm{ClO}_{4}^{-}\) or \(\mathrm{ClO}_{3}^{-}\) or ? Explain.

Short answer

\(\mathrm{ClO}_{3}^{-}\) has the smaller bond angle because it has one lone pair on the central atom, causing greater electron pair repulsion and thus reducing the bond angle compared to the tetrahedral \(\mathrm{ClO}_{4}^{-}\).

Step-by-step solution

Analyze Lewis Structures

First, draw the Lewis structures for each molecule. For \(\mathrm{ClO}_{4}^{-}\), chlorine (Cl) is the central atom surrounded by four oxygen (O) atoms with double bonds, and one extra electron due to the negative charge. All oxygens have a full octet and there are no lone pairs on chlorine. For \(\mathrm{ClO}_{3}^{-}\), Cl is again the central atom, surrounded by three oxygens. Two oxygens are double-bonded and one is single-bonded to Cl. The central Cl atom also accommodates one lone pair of electrons to account for the negative charge.

Consider Electronic Repulsion

The bond angles are, in principle, determined by the repulsion between electron pairs around the central atom, described by the VSEPR theory. In \(\mathrm{ClO}_{4}^{-}\), there are no lone pairs on the central atom, while in \(\mathrm{ClO}_{3}^{-}\) there is a lone pair. Lone pairs repel more strongly than bonding pairs, which causes the bond angles to deviate from the idealized angles.

Identify Molecular Geometry

Due to the differing numbers of electron regions (steric number), the molecular geometry of \(\mathrm{ClO}_{4}^{-}\) is tetrahedral, which has bond angles of approximately 109.5 degrees. However, for \(\mathrm{ClO}_{3}^{-}\), the presence of a lone pair means the geometry resembles trigonal pyramidal, which usually has bond angles less than 109.5 degrees.

Compare Bond Angles

Since the electronic repulsion from the lone pair in \(\mathrm{ClO}_{3}^{-}\) causes the bond angles to be smaller than in a regular tetrahedral structure, \(\mathrm{ClO}_{3}^{-}\) has the smaller bond angle compared to \(\mathrm{ClO}_{4}^{-}\).

Key concepts

Molecular Geometry

Understanding the shape of molecules is a fundamental aspect of chemistry, and molecular geometry is the term we use to describe the three-dimensional arrangement of atoms within a molecule. Different molecular geometries arise from the way electron pairs, both bonding and nonbonding, are arranged around a central atom, which minimizes the repulsion between them.

Common molecular shapes include linear, bent, trigonal planar, tetrahedral, and trigonal pyramidal. These shapes are predictable by applying Valence Shell Electron Pair Repulsion (VSEPR) theory to the molecule's Lewis structure. For example, a molecule with four electron domains—such as \(\mathrm{ClO}_{4}^{-}\) which has no lone electron pairs—will adopt a tetrahedral geometry to maximize the distance between electron domains. This symmetry allows for uniform bond angles.

Lewis Structures

Lewis structures represent the arrangement of electrons in a molecule, showcasing how atoms are bonded together and the occurrence of any lone electron pairs. Drawing a correct Lewis structure is essential for predicting molecular geometry and understanding the behavior of a molecule.

When creating a Lewis structure, we first distribute the valence electrons so that each atom, ideally, has an octet (or duet for hydrogen) - except in cases of expanded octets or less-than-octet structures. In a Lewis structure, lines represent bonded electron pairs, while dots signify lone pairs. Determining the correct number of bonds and lone pairs allows us to then use VSEPR theory to predict the molecular shape, as seen in the textbook exercise where we draw the structures for \(\mathrm{ClO}_{4}^{-}\) and \(\mathrm{ClO}_{3}^{-}\).

Electron Pair Repulsion

Electron pair repulsion is a fundamental principle in VSEPR theory which posits that electron pairs around a central atom will assume a geometry that minimizes their mutual repulsion. This interaction governs the molecular shape and bond angles in a molecule.

Bonding pairs of electrons are attracted to two nuclei and therefore occupy more space, while lone pairs are only attracted to one nucleus and are closer to the central atom, taking up more space. The greater repulsion between lone pairs can significantly alter molecular geometry and decrease bond angles, as seen with \(\mathrm{ClO}_{3}^{-}\), where a lone pair on the central chlorine atom forces bonding pairs closer together, leading to smaller bond angles compared to molecules without lone pairs.

Bond Angles

Bond angles are the angles between adjacent lines representing bonds that come off a central atom in a molecule. They are critical for understanding the spatial arrangement of atoms and can significantly influence the molecule's physical and chemical properties.

VSEPR theory helps in predicting the bond angles in a molecule based on the premise that electron pairs, whether bonding or non-bonding, will arrange themselves as far apart as possible to minimize repulsion. Idealized bond angles are based on specific molecular geometries—such as 109.5° for a tetrahedral shape. Real-world deviations from these ideal angles occur due to differences in electron pair repulsion, leading to the conclusion, as demonstrated in the given exercise, that \(\mathrm{ClO}_{3}^{-}\) has a smaller bond angle than \(\mathrm{ClO}_{4}^{-}\) due to the presence of a lone pair on the central atom.