Question

What is common between the following molecules: $$ \mathrm{SO}_{3}, \mathrm{CO}_{3}^{2-}, \mathrm{NO}_{3}^{-} ? $$ (a) All have linear shape. (b) All have trigonal planar shape. (c) All have tetrahedral shape. (d) All have trigonal pyramidal shape.

Short answer

(b) All have trigonal planar shape.

Step-by-step solution

Analyze the Molecular Geometry

Examine the molecular geometry of each molecule to identify common features. Use VSEPR theory to infer the shapes based on the number of electron pairs (bonding and non-bonding) around the central atom.

Consider the Valence Shell Electron Pair Repulsion (VSEPR) Theory

For \(\mathrm{SO}_3\), the sulfur atom is surrounded by three oxygen atoms with no lone pairs, suggesting a trigonal planar shape. \(\mathrm{CO}_3^{2-}\) has a carbon atom surrounded by three oxygen atoms and no lone pairs, which also results in a trigonal planar shape. \(\mathrm{NO}_3^{-}\) has a nitrogen atom bonded to three oxygen atoms with no lone pairs, leading to the same trigonal planar shape.

Compare Molecular Shapes

Compare the shapes deduced in step 2 to find the commonality among the given molecules.

Key concepts

Understanding VSEPR Theory

To predict the 3-dimensional arrangement of atoms in a molecule, we utilize the Valence Shell Electron Pair Repulsion (VSEPR) theory. It operates on a simple premise — electron pairs around a central atom will position themselves as far apart as possible to minimize the repulsion between their negative charges.

This theory hinges on the fact that electrons are negatively charged and, just like magnets with the same poles facing each other, they will repel one another. The shape that a molecule takes is then a direct result of the electron groups around the central atom pushing away from each other.

The steps to predict molecular geometry using VSEPR theory usually involve counting the number of electron pairs (both bonding and nonbonding, also known as lone pairs) around the central atom and then applying the repulsion rules to determine the most favorable geometry.

As an exercise improvement tip, it's worthwhile to note that the count of electron pairs isn't limited to merely those involved in bonds. The presence of lone pairs of electrons can drastically alter the resultant molecular shape and must be considered in the analysis.

Identifying Trigonal Planar Shape

A trigonal planar shape is one of the fundamental molecular geometries in VSEPR theory. Characterized by 120-degree bond angles, this shape is flat, with all atoms and electron pairs lying in the same plane. The geometry is named 'trigonal planar' because it essentially forms a triangle on a plane.

Molecules such as \( \mathrm{SO}_{3} \), \( \mathrm{CO}_{3}^{2-} \), and \( \mathrm{NO}_{3}^{-} \) fall into this category due to the arrangement of three regions of electron density (in this case, bonding pairs) around their central atoms, resulting in a triangular arrangement. It's important to recognize that this shape occurs when there are no lone pairs on the central atom—a presence would alter the geometry due to increased repulsion.

For students looking to master the identification of molecular shapes, a great practice tip is to draw out the Lewis structures of molecules. This will make the number of bonding and nonbonding electron pairs visible and thereby facilitate a correct prediction of the molecule's geometry.

The Principle of Electron Pair Repulsion

Electron pair repulsion is a core concept that drives the predictions made by VSEPR theory. Since electrons carry the same negative charge, they naturally repel one another. This repulsion affects the spatial distribution of electrons and hence the overall shape of the molecule.

The repulsion strength varies depending on whether electron pairs are bonding or nonbonding. Nonbonding (lone) pairs exert greater repulsion than bonding pairs because they are held by only one nucleus, giving them a larger electron cloud that is closer to the central atom. This results in lone pairs pushing bonding pairs closer together, leading to a change in bond angles and ultimately the shape of the molecule.

To give an accurate depiction, the concept might be clearer if the electron pairs are visualized as balloons tied together at the center; given their buoyancy, the balloons try to float away from each other as far as the strings (or in the case of electrons, their atomic bonds) will allow. For a practical understanding, students should consider plotting the Lewis structures and applying the concept of repulsion to predict molecular shapes.