Absolutely Small - Michael D. Fayer [98]
FIGURE 14.14. Ethane, single bond, carbon tetrahedral bonds. Ethylene, double bond, carbon trigonal bonds. Acetylene, triple bond, carbon linear bonds.
TABLE 14.1. Single, Double, and Triple C-C Bonds.
Carbon-Carbon Double Bond—Ethylene
First let’s look at the bonding in ethylene. As can be seen in Figure 14.15, the carbon centers are trigonal. As discussed, to have trigonal bonding, a carbon atom will use three sp2 hybrid atomic orbitals to form bonding MOs (see Figure 14.7). Carbon has four valence atomic orbitals to use for bonding, 2s, 2px, 2py, and 2pz. In the top part of the figure, the ethylene molecule is in the xy plane. So the carbons and the hydrogens are in the plane of the page, which is xy. To form the trigonal sp2 hybrids to make three bonds, each carbon will use the 2s, 2px, and 2py orbitals. With the three sp2 hybrids, each carbon will make three σ bonds, one to the other carbon and two to hydrogens. The σ bonding is shown in the top portion of Figure 14.15.
When a carbon forms three sp2 hybrids with the 2s, 2px, and 2py orbitals, it has its 2pz orbital left over that does no participate in the σ bonding. In the top part of Figure 14.15, the 2pz orbitals stick out of and into the page. Each carbon has one unpaired electron in its 2pz orbital. The bottom portion of the figure shows the ethylene molecule rotated. The σ bonds are shown as the lines connecting the atoms. The positive lobes of the 2pz orbitals overlap constructively as do the negative lobes. The two 2pz orbitals combine to make a π bonding molecular orbital, as shown in Figure 13.3. This is a π bond because there is no electron density along the line connecting the carbon atomic centers. The net result is that the two carbon atoms have a double bond composed of a σ bond formed from a sp2 orbital on each carbon and a π bond formed from a 2pz orbital on each orbital.
FIGURE 14.15. Ethylene double bond orbitals. Top: Each carbon uses three sp2hybrids to make three σ bonds in a trigonal configuration. The page is the xy plane, with z out of the plane. Bottom: Each carbon has a 2pzorbital not used to form the sp2hybrids. The 2pzorbitals combine to make a π bonding molecular orbital to give a second bond between the carbons.
It is not possible for rotation to occur around the carbon-carbon double bond. Rotation around the bond would require the overlap of the two 2pz orbitals to get worse and worse as the angle got bigger and bigger. For a 90° rotation, the two 2p orbitals would be pointing perpendicular to each other, and have no overlap. Such a rotation would break the π bond, which takes a great deal of energy. As mentioned, measurements and theory have been used to determine that the time for butane in liquid solution to rotate about the C-C single bond is about 50 ps. For ethane the time is about 12 ps. Butane rotates slower than ethane about the single C-C bond because it has two additional methyl groups (CH3), one on each end of the central two carbons. If you put ethylene in the same liquid at room temperature, it can be roughly estimated that it will take about one hundred billion years to rotate about the double bond because of the large amount of energy required to break the π bond. Therefore, for all practical purposes, a double bond (and a triple bond) prevents rotational isomerization between conformers that differ by the configuration about the double bond.
Carbon-Carbon Triple Bond—Acetylene
Acetylene forms a triple bond between the carbons in a manor analogous to the double bond formation in ethylene. Each carbon has four atomic orbitals, 2s, 2px, 2py, and 2pz, to use in bonding. Acetylene is linear (see Figure 14.14). Take the line of the molecule to be the x axis. Then, each carbon will form two sp hybrids from its 2s and 2px orbitals. The two sp hybrids on