Problem 14 - Chemistry The Central Science

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?

Step-by-Step Solution

Answer

The bond angles in methane and perchlorate ion are close to or exactly 109.5°. The BF3 molecule is flat.

Step 1: Determine the shape and hybridization of the molecules

Methane (CH4) has a central carbon attached to four hydrogen atoms. The central carbon atom forms four sigma bonds with these hydrogen atoms and is sp3 hybridized. The perchlorate ion (ClO4-) has a central chlorine atom attached to four oxygen atoms. The central chlorine atom forms one sigma bond and three double bonds (one each with the oxygen atoms) and is also sp3 hybridized. Both CH4 and ClO4- have tetrahedral geometry because they have four electron domains around the central atom.

Step 2: Determine the bond angles in a tetrahedral molecule

In a tetrahedral molecule, the angles between the bonds are determined by the equal repulsion between the four electron domains. This results in an ideal bond angle of 109.5°. In both the CH4 and ClO4- molecules, there should be bond angles close to, if not exactly, 109.5°. #a) Answer#: The bond angles in methane and perchlorate ion are close to or exactly 109.5°. #b) Flat molecule: NH3 or BF3#

Step 3: Determine the shapes of NH3 and BF3

Ammonia (NH3) is composed of a nitrogen atom connected to three hydrogen atoms. It exhibits sp3 hybridization but with a lone pair of electrons on the central nitrogen atom results in a trigonal pyramidal geometry. Boron trifluoride (BF3) is composed of a boron atom connected to three fluorine atoms. It exhibits sp2 hybridization, and since there are no lone pairs of electrons on the boron atom, it results in a trigonal planar geometry.

Step 4: Identify the flat molecule

The trigonal pyramidal geometry of NH3 means that it is not flat. On the other hand, BF3 has a trigonal planar geometry, which lacks a third dimension making it a flat molecule. #b) Answer#: The BF3 molecule is flat.

Key Concepts

Tetrahedral Geometry

The concept of tetrahedral geometry is fundamental in understanding molecular shapes in chemistry. It refers to a molecule consisting of a central atom surrounded by four other atoms or groups that are equidistant from each other. This arrangement is analogous to a pyramid with a triangular base, hence the term 'tetrahedral'. Imagine placing a central atom in the middle of a ball, and then pushing four additional atoms towards the surface; they will naturally position themselves as far away from each other as possible.

In this configuration, the angles between any two bonds, which we call 'bond angles', are always approximately 109.5 degrees. This occurs because the electron pairs around the central atom tend to repel each other equally, creating a uniform distribution. Substances like methane \(\mathrm{CH}_{4}\) and the perchlorate ion \(\mathrm{ClO}_{4}^{-}\) adopt this geometry, signifying that all bond angles are nearly the same across these molecules.

Bond Angles

Bond angles are a pivotal aspect of molecular geometry, revealing the spatial arrangement of atoms within a molecule. The term specifically refers to the angle formed between two covalent bonds that share a common atom. For example, in tetrahedral molecules such as methane \(\mathrm{CH}_{4}\), the bond angles are crucial as they are indicative of the molecule's three-dimensional shape.

The ideal bond angle in a perfectly symmetrical tetrahedral molecule is 109.5 degrees, as seen in both methane and the perchlorate ion. However, it's important to understand that the presence of double bonds, lone pairs, or other factors can cause deviations from this ideal angle in other types of molecules.

Hybridization

Hybridization is the concept of merging atomic orbitals into new hybrid orbitals that can accommodate bonding pairs of electrons in molecules. It's an integral part of understanding how atoms bond in different geometric arrangements. For instance, a carbon atom in methane forms four equivalent sp3 hybrid orbitals from mixing one 's' and three 'p' orbitals. This hybridization results in four mutually perpendicular orbitals, shaping the tetrahedral geometry of methane.

Similarly, when a boron atom in boron trifluoride (BF3) hybridizes its one 's' and two 'p' orbitals, it forms three sp2 hybrid orbitals that lie in the same plane, which leads to the trigonal planar geometry of BF3.

Trigonal Planar

Molecules with trigonal planar geometry have three atoms bonded to a central atom—and this forms a plane. There are no atoms or lone pairs of electrons above or below this plane, making the molecule flat. Each bond angle in a perfectly trigonal planar molecule is 120 degrees. The central atom in such molecules is sp2 hybridized, which indicates the merging of three atomic orbitals (one 's' and two 'p' orbitals) to create three new equal sp2 hybrid orbitals.

An example of such a molecule is boron trifluoride (BF3), where the boron is at the center, and the three fluorine atoms are arranged equidistantly around it, creating a flat molecule with 120 degree bond angles.

Trigonal Pyramidal

Trigonal pyramidal geometry occurs in molecules with a central atom bonded to three other atoms, plus one lone pair of electrons. The presence of the lone pair affects the geometry, making it different from tetrahedral despite having similar sp3 hybridization. This lone pair exerts repulsive forces on the bonded electron pairs, causing them to move closer together and altering the bond angles slightly.

In ammonia (NH3), for instance, the nitrogen atom is the central atom, with three hydrogen atoms bonded to it and one lone pair of electrons. This setup results in bond angles slightly less than 109.5 degrees, making NH3 a molecule that is not flat but rather has a three-dimensional pyramidal shape.