Question

(a) Methane \(\left(\mathrm{CH}_{4}\right)\) and the perchlorate ion \(\left(\mathrm{ClO}_{4}{ }^{-}\right)\)are both described as tetrahedral. What does this indicate about their bond angles? (b) The \(\mathrm{NH}_{3}\) molecule is trigonal pyramidal, while \(\mathrm{BF}_{3}\) is trigonal planar. Which of these molecules is flat?

Short answer

(a) For tetrahedral species, such as Methane \(\left(\mathrm{CH}_{4}\right)\) and the perchlorate ion \(\left(\mathrm{ClO}_{4}{ }^{-}\right)\), the bond angles are equal to \(109.5^\circ\). (b) \(\mathrm{NH}_{3}\) has a trigonal pyramidal geometry and \(\mathrm{BF}_{3}\) has a trigonal planar geometry. Since the trigonal planar geometry represents a flat configuration, \(\mathrm{BF}_{3}\) is the flat molecule.

Step-by-step solution

Understanding Tetrahedral Geometry

Tetrahedral geometry is a commonly encountered molecular geometry, and it occurs when a central atom is surrounded by four bonded atoms. The bond angles of a tetrahedral species are equal and can be determined using VSEPR (Valence Shell Electron Pair Repulsion) theory, which states that electron pairs in a molecule will repel each other and position themselves as far apart as possible.

Calculating Bond Angles in a Tetrahedral Species

In a tetrahedral species, the bond angle is equal to \(109.5^\circ\). This angle is a consequence of the repulsion between the four bonding electron pairs surrounding the central atom. To minimize the repulsion, these electron pairs will arrange themselves as far apart as possible in a three-dimensional geometry.

Understanding Trigonal Pyramidal and Trigonal Planar Geometries

Trigonal pyramidal and trigonal planar geometries are two other molecular shapes encountered in covalent species. Trigonal pyramidal molecules have a central atom bonded to three other atoms, with one lone pair of electrons, while trigonal planar molecules have a central atom bonded to three other atoms, with no lone pairs of electrons. The difference between these two geometries is essential in determining which molecule is flat.

Determining Flat Molecule

To determine which of the given molecules is flat, we need to consider their molecular geometries: \(\mathrm{NH}_{3}\) has a trigonal pyramidal geometry because it has three atoms bonded to one central nitrogen atom, and one lone pair of electrons. On the other hand, \(\mathrm{BF}_{3}\) is trigonal planar, with three atoms bonded to a central boron atom and no lone pairs of electrons. Since the trigonal planar geometry represents a flat configuration, \(\mathrm{BF}_{3}\) is the flat molecule.

Key concepts

VSEPR Theory

The VSEPR (Valence Shell Electron Pair Repulsion) theory is central to understanding the shape of molecules. According to this theory, the three-dimensional arrangement of atoms around a central atom in a molecule is largely determined by the repulsions between electron pairs in the valence shell of the central atom. Electron pairs, including both bonding pairs and lone pairs, repel each other and tend to occupy positions in space where they are as far apart as possible. This minimizes repulsive forces and helps to determine the geometry of the molecule.

Leaning on this concept ensures a strong foundation when predicting molecular shapes and the resulting bond angles, making it easier to grasp how complex molecules, like organic compounds or transition metal coordination complexes, are structured.

Tetrahedral Geometry

Tetrahedral geometry is a common shape for molecules where a central atom is bonded to four other atoms, positioned at the corners of an imaginary tetrahedron. When we say that both methane (\(\mathrm{CH}_{4}\)) and the perchlorate ion (\(\mathrm{ClO}_{4}^{-}\)) have tetrahedral geometry, we underline that they have similar spatial arrangements regarding their bond angles and shape. Each of the four atoms is bonded to the central atom with angles of about \(109.5^\circ\) between them.

This bond angle is key to maximizing the distance between bonding electron pairs, thus reducing their mutual repulsion in accordance with the VSEPR theory. Such geometry leads to an even distribution of charge and a molecular shape that is symmetrical, which often contributes to the nonpolar nature of tetrahedral molecules.

Bond Angles

Bond angles are the angles between adjacent lines representing bonds that emanate from a central atom to its bonded counterparts. In a perfect tetrahedral molecule, these angles are exactly \(109.5^\circ\). However, bond angles can vary slightly in real-life molecules depending on factors such as the size of the bonded atoms or the presence of lone pairs, which occupy more space and push bonding pairs closer together, reducing the bond angle.

For instance, while both methane and the perchlorate ion are described as tetrahedral with ideal bond angles of \(109.5^\circ\), actual deviations can occur due to differences in the central atoms or the substituent effects on electron pair repulsion. Nonetheless, the approximate \(109.5^\circ\) bond angle is a very useful starting point for predicting and visualizing the three-dimensional shape of most tetrahedral molecules.

Trigonal Pyramidal Geometry

With trigonal pyramidal geometry, the molecules take a form akin to a pyramid with a triangular base. The central atom is located at the apex of the pyramid and is bonded to three other atoms at the corners of the triangular base, with a lone pair of electrons at the central atom creating the pyramid shape. Ammonia (\(\mathrm{NH}_{3}\)) is a classic example of this.

In trigonal pyramidal molecules, the bond angles tend to be slightly less than \(109.5^\circ\) due to the presence of a lone pair which, according to VSEPR theory, exerts more repulsion than bonded pairs. This characteristic shape results in a lack of planarity; thereby, these molecules are not flat and have a distinct three-dimensional form.

Trigonal Planar Geometry

Trigonal planar geometry occurs in molecules with a central atom bonded to three other atoms—all in the same plane, forming a perfect triangle. This shape is characterized by bond angles of \(120^\circ\), resulting from the three bonding pairs spreading out as far apart as possible in a planar, or flat, configuration. Boron trifluoride (\(\mathrm{BF}_{3}\)) is an example known for its trigonal planar geometry as it does not have lone pairs on the central atom to distort this shape.

The planarity and the equal bond angles give trigonal planar molecules their characteristic flat appearance, distinguishing them from the non-planar, trigonal pyramidal molecules. This explanation leads to the conclusion that among the given examples, \(\mathrm{BF}_{3}\) is the flat molecule, directly tied to its trigonal planar geometry.