Question

Predict the electron pair geometry, the molecular shape, and the bond angle for a carbonate ion, \(\mathrm{CO}_{3}{ }^{2-},\) using VSEPR theory.

Short answer

Trigonal planar geometry and molecular shape with a bond angle of 120°.

Step-by-step solution

Draw the Lewis Structure

Begin by drawing the Lewis structure for the carbonate ion, \(\mathrm{CO}_{3}^{2-}\). Carbon is the central atom bonded to three oxygen atoms. Each oxygen atom shares a double bond with carbon, and the carbonate ion has a total charge of -2. Hence, a reasonable Lewis structure shows one carbon-oxygen double bond (a resonance structure), and two carbon-oxygen single bonds, each carrying a negative charge on the oxygen.

Count the Electron Domains

Using the Lewis structure, determine the number of electron domains around the central carbon atom. The central carbon atom is bonded to three oxygen atoms, resulting in three bonding domains. Since there are no lone pairs on the central carbon atom, the total number of electron domains is three.

Predict the Electron Pair Geometry

According to VSEPR theory, the electron pair geometry depends solely on the number of electron domains. With three electron domains, the electron pair geometry around the central carbon is trigonal planar.

Determine the Molecular Shape

Since there are no lone pairs affecting the molecular shape, the molecular shape remains the same as the electron pair geometry. Thus, the molecular shape of \(\mathrm{CO}_{3}^{2-}\) is also trigonal planar.

Calculate the Bond Angle

The ideal bond angle for a trigonal planar molecular shape is \(120^\circ\). This is due to the repulsion between the bonding pairs of electrons, which spread out to maintain equidistant spacing.

Key concepts

Electron Pair Geometry

The concept of electron pair geometry in VSEPR theory revolves around the spatial arrangement of all electron pairs—bonding and lone pairs—surrounding a central atom. It is crucial in determining the ultimate 3D orientation of a molecule. For the carbonate ion, \(\mathrm{CO}_{3}^{2-}\), understanding electron pair geometry begins by looking at the number of electron domains surrounding the central atom.
Carbon in \(\mathrm{CO}_{3}^{2-}\) is bonded to three oxygen atoms, providing us with a total of three bonding domains. Since there are no lone pairs on carbon, each of these domains corresponds to a bond.

• In VSEPR, the electron pairs repel each other and will arrange themselves to minimize this repulsion, thus determining the molecule's stable geometry.
• For three domains, the electron pairs align themselves in a plane equally 120 degrees apart, forming a trigonal planar geometry.

Knowing the electron pair geometry helps predict how the molecule will appear in space, which is pivotal for understanding molecular shapes.

Molecular Shape

Molecular shape explains the arrangement of just the bonding atoms around the central atom, without considering the lone pairs directly, although their presence can influence the shape indirectly. In the carbonate ion, \(\mathrm{CO}_{3}^{2-}\), there aren't any lone pairs on the central carbon atom, meaning the molecular shape is determined solely by the bonding atoms.
The molecular shape and electron pair geometry for \(\mathrm{CO}_{3}^{2-}\) coincide because the electron domains all contribute to bonding, yielding a trigonal planar shape.

• The shape is determined by the symmetry and arrangement of the three oxygen atoms within the same plane around the carbon atom.
• This symmetry leads to a balanced distribution of charge and minimizes electron repulsion, crucial for stabilizing the molecule.

The understanding of molecular shapes is fundamental for predicting not just physical properties but also chemical reactivity.

Bond Angle

Bond angles are the angles formed between adjacent bonds at an atom, and they are essential for defining the geometry and potential reactions of the molecule. In the context of the carbonate ion, \(\mathrm{CO}_{3}^{2-}\), the bond angles are a direct consequence of its trigonal planar shape.
With a trigonal planar structure, the ideal bond angle is \(120^\circ\), a result of even spacing and repulsion minimization between the bonding pairs of electrons.

• The consistent \(120^\circ\) angles ensure that the oxygen atoms are equidistant from each other when viewed in the plane they occupy.
• This uniformity is essential for molecular symmetry and can affect how molecules interact, particularly in polar interactions or in aligning within larger lattice structures.

Bond angles not only influence the spatial arrangement but also play a vital role in dictating how molecules engage in chemical processes.