Question

Predict all bond angles for these molecules. (a) \(\mathrm{CH}_{3} \mathrm{OH}\) (b) \(\mathrm{PF}_{3}\) (c) \(\mathrm{H}_{2} \mathrm{CO}_{3}\)

Short answer

Answer: The bond angles in CH3OH are 109.5° (tetrahedral) and 104.5° (bent), in PF3 they are 107.0° (trigonal pyramidal), and in H2CO3 they are 120° (trigonal planar).

Step-by-step solution

Determine the Lewis structure of each molecule

First, we need to find out the Lewis structure of these molecules, as they give us the information about the arrangement of electrons in the molecule.

Determine electron geometry

After determining the Lewis structure, we will find the electron geometry of the molecule. Electron geometry describes the arrangement of electron pairs around the central atom, and it takes into account both bonding (shared) and lone (unshared) electron pairs.

Predict bond angles

With both the Lewis structure and electron geometry in mind, we can now predict bond angles for these molecules. (a) \(\mathrm{CH}_{3} \mathrm{OH}\): 1. Lewis structure: H-C-H, H-C-O-H 2. Electron geometry: Tetrahedral around the carbon atom (\(\mathrm{C}\)) and bent around the oxygen atom (\(\mathrm{O}\)) 3. Bond angles: \(\angle \mathrm{HCH}\) = 109.5° (tetrahedral) and \(\angle \mathrm{HCO}\) = 104.5° (bent) (b) \(\mathrm{PF}_{3}\): 1. Lewis structure: \(\mathrm{P}\) bonded to three \(\mathrm{F}\) atoms and has one lone pair 2. Electron geometry: Trigonal pyramidal 3. Bond angle: \(\angle \mathrm{FPF}\) = 107.0° (c) \(\mathrm{H}_{2} \mathrm{CO}_{3}\): 1. Lewis structure: \(\mathrm{O}\) double-bonded to \(\mathrm{C}\), \(\mathrm{C}\) single-bonded to \(\mathrm{H}\) and \(\mathrm{OH}\) 2. Electron geometry: Trigonal planar around \(\mathrm{C}\) 3. Bond angles: \(\angle \mathrm{HCO}\) and \(\angle \mathrm{OCO}\) are both = 120° To summarize, the bond angles for these molecules are as follows: - \(\mathrm{CH}_{3} \mathrm{OH}\): 109.5° (tetrahedral) and 104.5° (bent) - \(\mathrm{PF}_{3}\): 107.0° (trigonal pyramidal) - \(\mathrm{H}_{2} \mathrm{CO}_{3}\): 120° (trigonal planar)

Key concepts

Lewis Structures

When it comes to predicting bond angles, understanding Lewis structures is essential. These structures are diagrams that show the arrangement of valence electrons around atoms within a molecule. Each dot represents an electron and lines between atoms signify chemical bonds. Constructing a Lewis structure starts by counting valence electrons; these are used to form the bonds and lone pairs that determine the shape of the molecule.

To construct a Lewis structure for molecules like \textbf{CH}\(_3\)\textbf{OH}, \textbf{PF}\(_3\), and \textbf{H}\(_2\)\textbf{CO}\(_3\), follow these general steps:

• Determine the total number of valence electrons.
• Arrange atoms around a central atom, connecting them with single bonds.
• Place remaining electrons to satisfy the octet rule (or duet rule for hydrogen).
• Make double or triple bonds if necessary to account for all valence electrons.

This approach allows us to visualize the electron distribution and is the first step in predicting molecular shapes and bond angles.

Electron Geometry

Electron geometry, also known as electron-pair geometry, refers to the spatial arrangement of electron pairs (bonding and lone pairs) around a central atom. The arrangement is determined by the electrostatic repulsion between these pairs.

The basic electron geometries to consider are:

• Linear: 180° apart.
• Trigonal planar: 120° apart.
• Tetrahedral: 109.5° apart.
• Trigonal bipyramidal: 90°,120° apart.
• Octahedral: 90° apart.

If we consider \textbf{CH}\(_3\)\textbf{OH} as an example, the carbon atom exhibits a tetrahedral electron geometry with bond angles close to 109.5°. The oxygen atom, however, has two lone pairs which slightly reduces the bond angle to approximately 104.5°.

Molecular Geometries

Molecular geometry considers the positions of only the atoms in the molecules, not the nonbonding electron pairs. Hence, it's the three-dimensional layout of atoms dictated by the electron geometry but refined by the presence of lone electron pairs.

The common molecular geometries include:

• Linear: atoms are in a straight line.
• Bent: forms an angle less than 180°.
• Trigonal planar: atoms reside in a plane in a triangular shape.
• Tetrahedral: four faces on the molecule.
• Trigonal bipyramidal: five faces on the molecule.
• Octahedral: six faces on the molecule.

For instance, \textbf{PF}\(_3\) has a trigonal pyramidal molecular geometry because of one lone pair on the phosphorus atom affecting the arrangement of the bonding electron pairs.

Valence Shell Electron Pair Repulsion Theory

Valence Shell Electron Pair Repulsion (VSEPR) theory is the cornerstone concept for understanding molecular shapes and predicting bond angles. The premise is simple: electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion, thus determining the shape.

According to VSEPR theory, the molecules \textbf{CH}\(_3\)\textbf{OH}, \textbf{PF}\(_3\), and \textbf{H}\(_2\)\textbf{CO}\(_3\) have different shapes due to the arrangement and number of bonding and non-bonding electron pairs. \textbf{CH}\(_3\)\textbf{OH}'s central carbon is tetrahedral, while its oxygen atom has a bent shape. \textbf{PF}\(_3\) conforms to a trigonal pyramidal structure due to one lone pair at phosphorus. \textbf{H}\(_2\)\textbf{CO}\(_3\) displays a trigonal planar configuration around the central carbon with angles of 120°.

Each shape has an ideal bond angle, but the presence of lone pairs can alter these angles due to their larger repulsive force compared to bonding pairs. This is evident in the slight decrease in the bond angles of \textbf{CH}\(_3\)\textbf{OH} and \textbf{PF}\(_3\) compared to their ideal geometries.