Bond Angles and the Shapes of Molecules

In the previous section a shared pair of electrons was presented as the fundamental unit of the covalent bond, and Lewis structures were drawn for several small molecules and ions containing various combinations of single, double, and triple bonds. In this section, we use the valence-shell electron-pair repulsion (VSEPR) model to predict the geometry of these and other covalently bonded molecules and ions. The VSEPR model can be explained in the following way. We know that an atom has an outer shell of valence electrons. These valence electrons may be involved in the formation of single, double, or triple bonds, or they may be unshared. Each set of electrons, whether unshared or in a bond, creates a negatively charged region of space. We have already learned that like charges repel each other. The VSEPR model states that the various regions containing electrons or electron clouds around an atom spread out so that each region is as far from the others as possible.

A. Linear Molecules
If a molecule contains only two atoms, those two atoms are in a straight line and thus form a linear molecule. Some three-atom molecules also have straight-line geometry. For example: Notice that, in the Lewis structure of these molecules, the central atom(s) bonds with only two other atoms and has no unshared electrons. Only two electron clouds emerge from that central atom. For these two clouds to be as far away from each other as possible, they must be on opposite sides of the central atom, forming a bond angle of 180° with each other. An angle of 180° gives a straight line. The VSEPR theory says, then, that the geometry around an atom that has only two bonds and no unshared electrons is a straight line. Figure 7.6 shows the linear nature of these molecules. FIGURE 7.6 Linear molecules: (a) carbon dioxide, CO2; (b) hydrogen cyanide, HCN; and (c) acetylene, C2H2.

B. Structures with Three Regions of High Electron Density around the Central Atom
Look at the following Lewis structures: In these molecules, each central atom has three electron clouds emanating from it. In sulfur dioxide, the sulfur atom is bonded to two oxygen atoms and has one unshared pair of electrons. In formaldehyde and ethylene, each carbon atom has two single bonds to hydrogen, a double bond to another atom, and no unshared pair. The sulfur atom in sulfur dioxide and the carbon atom in ethylene and formaldehyde is surrounded by three clouds of high electron density. For these clouds to be as far as possible from one another, they will form a plane containing the central atom and will emanate from the central atom at angles of 120° to each other. The structure will be trigonal planar. The central atom will be in the center of the triangle, and the ends of the electron clouds at the corners of the triangle. If you experiment with a marshmallow as the central atom and three toothpicks as electron clouds, you can prove to yourself that the toothpicks are farthest apart when using a trigonal planar structure. Figure 7.7 illustrates these structures. Note that the angles are not exactly 120° but are remarkably close to that predicted value. Although the electron clouds of these molecules give a trigonal planar shape around each carbon atom, one describes the geometry of a molecule only on the basis of the relationships between its atoms. A formaldehyde molecule is trigonal planar because it has an atom at the end of each electron cloud. The ethylene molecule has trigonal planar geometry around each of its carbon atoms. The whole molecule is planar, and its shape resembles two triangles joined point to point. In sulfur dioxide, there are three electron clouds around the sulfur. Only two of these connect two atoms. In the molecule, the oxygen-sulfur-oxygen atoms make a 120° angle. The molecule is bent.

A central atom surrounded by three clouds of high electron density will have trigonal planar geometry if it is bonded to three atoms. Its geometry will be called bent if it is bonded to two atoms and also has an unshared pair of electrons.

C. Structures with Four Regions of High Electron Density around the Central Atom
The following Lewis structures show three molecules whose central atom is surrounded by four clouds of high electron density: These molecules are alike in that each central atom is surrounded by four pairs of electrons, but they differ in the number of unshared electron pairs on the central atom. Remember that, although we have drawn them in a plane, the molecules are three-dimensional and atoms may be in front of or behind the plane of the paper. What geometry does the VSEPR theory predict for these molecules?

Let us predict the shape of methane, CH4. The Lewis structure of methane shows a central atom surrounded by four separate regions of high electron density. Each region consists of a pair of electrons bonding the carbon atom to a hydrogen atom. According to the VSEPR model, these regions of high electron density spread out from the central carbon atom in such a way that they are as far from one another as possible.

You can predict the resulting shape using a styrofoam ball or marshmallow and four toothpicks. Poke the toothpicks into the ball, making sure that the free ends of the toothpicks are as far from one another as possible. If you have positioned them correctly, the angle between any two toothpicks will be 109.5°. If you now cover this model with four triangular pieces of paper, you will have built a four-sided figure called a regular tetrahedron. Figure 7.8 shows (a) the Lewis structure for methane, (b) the tetrahedral arrangement of the four regions of high electron density around the central carbon atom, and (c) a space-filling model of methane. FIGURE 7.8 The shape of a methane molecule, CH4: (a) its Lewis structure; (b) its tetrahedral shape; (c) a space-filling model.

According to the VSEPR model, the H - C - H bond angle in methane should be 109.5°. This angle has been measured experimentally and found to be 109.5°. Thus, the bond angle predicted by the VSEPR model is identical to that observed. We say that methane is a tetrahedral molecule. The carbon atom is at the center of a tetrahedron. Each hydrogen is at one of the corners of the tetrahedron.

We can predict the shape of the ammonia molecule in exactly the same manner. The Lewis structure of NH3 (see Figure 7.9) shows a central nitrogen atom surrounded by four separate regions of high electron density. Three of these regions consist of a single pair of electrons forming a covalent bond with a hydrogen atom; the fourth region contains an unshared pair of electrons. According to the VSEPR model, the four regions of high electron density around the nitrogen are arranged in a tetrahedral manner, so we predict that each H - N - H bond angle should be 109.5°. The observed bond angle is 107.3°. This small difference between the predicted angle and the observed angle can be explained by proposing that the unshared pair of electrons on nitrogen repels the adjacent bonding pairs more strongly than the bonding pairs repel each other. FIGURE 7.9 The shape of an ammonia molecule, NH3: (a) its Lewis structure; (b) its geometry; (c) a space filling mdel. Notice how the unshared electrons serve to create its shape.

Ammonia is not a tetrahedral molecule. The atoms of ammonia form a pyramidal molecule with nitrogen at the peak and the hydrogen atoms at the corners of a triangular base. Just as the unshared pair of electrons in sulfur dioxide contribute to the geometry of the molecule but are not included in the description of its geometry, the unshared pair of electrons in ammonia gives it a tetrahedral shape but its geometry is based only on the arrangement of atoms, which is pyramidal. Figure 7.10 shows the Lewis structure of the water molecule. In H2O, a central oxygen atom is surrounded by four separate regions of high electron density. Two of these regions contain a pair of electrons forming a covalent bond between oxygen and hydrogen; the other two regions contain an unshared electron pair. The four regions of high electron density in water are arranged in a tetrahedral manner around oxygen. Based on the VSEPR model, we predict an H - O - H bond angle of 109.5°. Experimental measurements show that the actual bond angle is 104.5°. The difference between the predicted and observed bond angles can be explained by proposing, as we did for NH3, that unshared pairs of electrons repel adjacent bonding pairs more strongly than the bonding pairs repel each other. Note that the variation from 109.5° is greatest in H2O, which has two unshared pairs of electrons; it is smaller in NH3, which has one unshared pair; and there is no variation in CH4.

To describe the geometry of the water molecule, remember that the geometry of a molecule describes only the geometric relationships between its atoms. The three atoms of a water molecule are in a bent line like those of sulfur dioxide. We say the water molecule is bent. FIGURE 7.10 The shape of a water molecule, H2O: (a) its Lewis structure; (b) its geometry; (c) a space- filling model. Notice how the unshared pairs of electrons affect the tetrahedral geometry.

A general prediction emerges from our discussions of the shapes of methane, ammonia, and water: Whenever four separate regions of high electron density surround a central atom, we can accurately predict a tetrahedral distribution of electron clouds and bond angles of approximately 109.5°.

The geometry of molecules can be predicted. A molecule whose central atom is bonded to four other atoms is tetrahedral. One in which the central atom has one unshared pair of electrons and bonds to three other atoms will be pyramidal, and one in which the central atom has two unshared pairs of electrons and bonds to two other atoms will be bent. Table 7.2 summarizes this geometry.

TABLE 7.2 Molecular shapes and bond angles
Number of regions
of high electron
density around
central atom
Arrangement of
regions of high
electron density
in space
Predicted
bond
angles
Example Geometry of
molecule
4 tetrahedral 109.5° CH4, methane tetrahedral
NH3, ammonia pyramidal
H2O, water bent
3 trigonal planar 120° H2CO, formaldehyde trigonal planar
C2H4, ethylene planar
SO2, sulfur dioxide bent
2 linear 180° CO2, carbon dioxide linear
C2H2, acetylene linear

 Example Predict all bond angles in the following molecules. a. CH3Cl   b. CH3CNl     c. CH3COOH Solution a. The Lewis structure of methyl chloride is: In the Lewis structure of CH3Cl carbon is surrounded by four regions of high electron density, each of which forms a single bond. Based on the VSEPR model, we predict a tetrahedral distribution of electron clouds around carbon, H - C - H and H - C - Cl bond angles of 109.5°, and a tetrahedral shape for the molecule. Note the use of doted lines to represent a bond projecting behind the plane of the paper and a solid wedge to represent a bond projecting forward from the plane of the paper. b. The Lewis structure of acetonitrile, CH3CN is: The methyl group, CH3-, is tetrahedral. The carbon of the -CN group is in the middle of a straight line stretching from the carbon of the methyl group through the nitrogen. c. The Lewis structure of acetic acid is: Both the carbon bonded to three hydrogens and the oxygen bonded to carbon and hydrogen are centers of tetrahedral structures. The central carbon will have 120 7deg bond angles. The geometry around the first carbon is tetrahedral, around the second carbon atom is trigonal planar, and around the oxygen is bent.