Absolutely Small - Michael D. Fayer [90]
MOLECULAR SHAPES—TETRAHEDRAL METHANE
To examine the shapes of molecules and how chemical bonding can give rise to different shapes, we need to introduce some new ideas about atomic orbitals. We will use methane as an example of a relatively simple polyatomic molecule to bring out the important issues.
Methane (natural gas) is CH4. Now, look again at carbon’s position in the Periodic Table (Figure 11.4). Note that carbon needed to make four electron pair sharing covalent bonds to achieve the neon closed shell configuration. In methane, carbon makes four bonds with four hydrogen atoms. The connectivity of the atoms can be shown in a simple diagram, which is the left portion of Figure 14.1. Each line represents an electron pair covalent bond. However, this diagram does not tell much about methane’s shape. Methane is not flat. The right side of the figure shows a ball-and-stick model of the three-dimensional shape of methane. (See the end of Chapter 13 for a discussion of ball-and-stick and space-filling models.) Methane is a perfect tetrahedron. Imagine having a model like the right side of Figure 14.1 and gluing a triangular piece of paper with sides of equal length that just covered three of the hydrogen atoms. You can glue on four such triangles, three sides and the bottom. These four triangles form a perfect triangular pyramid with the hydrogens at the four apices and the carbon in the middle. The angle formed by the line from a hydrogen to the carbon and then a line from the carbon to another hydrogen is exactly 109.5°. This is true of all four angles. They are identical. The angle for a perfect tetrahedral molecule is 109.5°.
FIGURE 14.1. Left: diagram showing the bond connectivity of methane, but not its three-dimensional shape. Right: a three-dimensional ball-and-stick model of methane that shows the tetrahedral shape of the molecule.
Minimizing Repulsion Between Bonds Determines the Shape
Why does methane have a tetrahedral shape? In Chapter 13, we saw that bonding molecular orbitals concentrate electron density between the atomic nuclei. The concentration of electron density between the nuclei is shown in Figures 13.2 and 13.3 for σ and π bonds. Chapter 13 discussed diatomic molecules in which only two atoms are bonded. We did not have to worry about how multiple atoms with some set of bonds connecting them would be arranged. While quantum theory can calculate the details of the shapes of molecules, the basic reason why a molecule will have a particular shape, such as tetrahedral, is quite simple. In polyatomic molecules, sharing electrons between two atomic nuclei to form a bond concentrates electron density between the nuclei, just as it does with diatomic molecules. However, in polyatomics, we have a number of bonds, each of which has a high density of negatively charged electrons. The negatively charged regions, the bonds, repel each other. Basically, the bonds want to stay as far away from each other as possible. These regions of high negatively charged electron density want to overlap as little as possible. Forming bonds lowers the energy of the system relative to the separated atoms. If the energy is not lowered, bonds will not be formed. But to make the energy as low as possible, the system of atoms assumes a configuration that minimizes the electron repulsions by keeping the bonds away from each other.
In methane, the tetrahedral shape minimizes the repulsions between the bonds. Look at the left-hand drawing in Figure 14.1. The four hydrogens are in a plane. If I keep them in the plane, they are as well separated as possible. The angle formed by two adjacent bonds is 90°. With the atoms in the plane, if I make one of the angles larger than 90° to further separate two of the hydrogen-carbon bonds, these bonds get closer to the other two bonds. So if the four hydrogen atoms are kept in