CoreChem:7.2 The Shapes of Molecules

From ChemEd Collaborative

7.2 THE SHAPES OF MOLECULES

The location in three-dimensional space of the nucleus of each atom in a molecule defines the molecular shape or molecular geometry. Molecular shapes are important in determining macroscopic properties such as melting and boiling points, and in predicting the ways in which one molecule can react with another. A number of experimental methods are available for finding molecular geometries, but we will not describe them here. Instead we will concentrate on several rules based on Lewis diagrams which will allow you to predict molecular shapes.

To provide specific cases which illustrate these rules, “ball-and stick” models for the four molecules discussed in the previous section are shown in Fig. 7.1. In addition to BeCl₂, BCl₃, PF₅, and SF₆, we have included CCl₄, a molecule which does obey the octet rule. The atoms (spheres) in each ball-and-stick model are held together by bonds (sticks). These electron-pair bonds determine the positions of the atoms and hence the molecular geometry.

In each of the molecules shown in Fig. 7.1 the electron-pair bonds are arranged so that they avoid each other in space to the maximum possible extent. This may be understood in terms of the repulsion between electron clouds due to their like charges. During the 1950s the Australian R. S. Nyholm (1917 to 1971) and the Canadian R. J. Gillespie (1924 to ) summed up this behavior in terms of the valence-shell-electron-pair repulsion (VSEPR) theory. The VSEPR theory states that, because of their mutual repulsions, valence electron pairs surrounding an atom stay as far as possible from one another.

A simple model for demonstrating the behavior of electron pairs under the influence of their mutual repulsion is provided by a set of spherical balloons of equal size. It is a model that you can easily make for yourself. If, say, four balloons are tied together so that they squeeze each other fairly tightly, they inevitably adopt the tetrahedral arrangement shown for CCl₄ in col. f of Fig. 7.1 Although it is possible to flatten the balloons on a table until they are all in the same plane, they invariably spring back to the tetrahedral configuration as soon as the pressure is removed. A similar behavior is found if two, three, five, or six balloons are tightly tied together, except that in each case a different stable shape is adopted once the balloons are left to themselves. The overall appearance of the balloons is shown in, col. f of Fig. 7.1 In col. e a sketch of the geometrical figure to which these shapes correspond is also drawn.

Since all the shapes described in Fig. 7.1 constantly recur in chemical discussions, it is worth being able to recall them and their names without hesitation. To this end we will discuss the geometry of each of the five molecules. In BeCl₂ central Be atom has only two electron pairs in its valence shell. These are arranged on opposite sides of the Be atom in a straight line, and they bond the two atoms to the Be atom. Thus the three nuclei are all in a straight line, and the Cl―Be―Cl angle is 180°. A molecule such as BeCl₂, whose atoms all lie on the same straight line, is said to be linear. In BCl₃ the three valence electron pairs, and hence the three Cl nuclei, are arranged in an equilateral triangle around the B atom. Each Cl―B―Cl angle is 120° and all four nuclei (B included) lie in the same plane. The three Cl atoms are said to be trigonally arranged around B.

In CCl₄ the four Cl nuclei are at the four corners of a geometric figure called a tetrahedron. A tetrahedron has six equal edges, four equilateral triangular faces, and four identical corners (apices). The C nucleus lies in the exact center of the tetrahedron, equidistant from each corner. All the Cl—C—Cl angles are the same, namely, 109.5°. This important angle is called the tetrahedral angle. The four Cl atoms are said to be tetrahedrally arranged around the C atom. This tetrahedral arrangement is the most important of the five described in Fig. 7.1. In PF₅ the five F nuclei are arranged at the corners of a trigonal bi-pyramid. As drawn in the figure, one F atom lies directly above the P atom and one directly below. The remaining three F atoms are arranged in a triangle around the middle of the P. Some of the F―P―F angles are 90°, while others are 120°.

In SF₆ the six F atoms are arranged at the corners of an octahedron. An octahedron has twelve edges, eight equilateral triangular faces, and six identical corners. The name octahedron is derived from the eight faces, but it is usually the six corners of this figure which are of interest to chemists. Thus you will have to remember that an octahedral arrangement involves six atoms, not the eight that the name seems to imply. In SF₆ the six F atoms are octahedrally arranged around the S. All the F―S―F angles are 90°. Octahedral arrangements are quite common in chemistry. In crystals of LiH and NaCl, for instance (see Fig. 6.3), six anions are arranged octahedrally around each cation while six cations are arranged octahedrally around each anion.

Molecules with Lone Pairs

The VSEPR theory is also able to explain and predict the shapes of molecules which contain lone pairs. In such a case the lone pairs as well as the bonding pairs are considered to repel and avoid each other. For example, since there are two bonds in the SnCl₂ molecule, one might expect it to be linear like BeCl₂. If we draw the Lewis diagram, though, we find a lone pair as well as two bonding pairs in the valence shell of the Sn atom:

Ideally the three pairs of electrons should arrange themselves trigonally around the Sn atom, giving an angle of 120° between electron pairs, and hence between the two Cl atoms. Experimental measurements on SnCl₂ reveal that the molecule is angular or V-shaped, as shown, but the Cl—Sn—Cl angle is significantly less than the predicted 120°. This smaller angle occurs because a lone pair of electrons is always “fatter” than a bonding pair. That is, a lone pair is like a bigger balloon which takes up more room and squeezes the bonding pairs closer together. This decreases the angle between bonding pairs in SnCl₂, and hence between the bonded Cl atoms, from the expected value of 120°. The “fatness” of a lone pair compared with a bonding pair is shown in Fig. 7.2.

A lone pair also affects the structure of ammonia, NH₃. Since this molecule obeys the octet rule, the N atom is surrounded by four electron pairs:

If these pairs were all equivalent, we would expect the angle between them to be the regular tetrahedral angle of 109.5°. Experimentally, the angle is found to he somewhat less, namely, 107°. Again this is because the lone pair is “fatter” than the bonding pairs and able to squeeze them closer together.

The electronic structure of the H₂O molecule is similar to that of NH₃ except that one bonding pair has been replaced by a lone pair:

Here there are two “fat” lone pairs, and so the bonding pairs are squeezed even closer together than in NH₃. The H―O―H angle is found to be 104.5°. The structures of BeCl₂, BCl₃, SnCl₂, CCl₄, NH₃ and H₂O include all the combinations of lone pairs and bonding pairs and all molecular shapes which are possible for two, three, and four pairs of electrons. These shapes, together with details of their geometries, are summarized in Fig. 7.3. Again, because of their frequent occurrence, it is wise to commit these to memory. Note in particular that the shape of a molecule is described in terms of the geometry of the nuclei and not of the electron clouds. For example, the shape of the NH₃ molecule is described as a trigonal pyramid since the N nucleus forms the apex of a pyramid, slightly above an equilateral triangle of H nuclei. Although the electron-pair clouds are arranged in an approximate tetrahedron around the N nucleus, it is incorrect to describe the molecular shape as tetrahedral. The atomic nuclei are not at the corners of a tetrahedron.

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EXAMPLE 7.1 Sketch and describe the geometry of the following molecules: (a) GaCl₃, (b) AsCl₃, and (c) AsOCl₃.

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Solution

a) Since the element gallium belongs to group III, it has three valence electrons. The Lewis diagram for GaCl₃ is thus

Since there are three bonding pairs and no lone pairs around the Ga atom, we conclude that the three Cl atoms are arranged trigonally and that all four atoms are in the same plane.

b) Arsenic belongs to group V and therefore has five valence electrons. The Lewis structure for AsCl₃ is thus

Since a lone pair is present, the shape of this molecule is a trigonal pyramid, with the As nucleus a little above an equilateral triangle of Cl nuclei.

c) The Lewis diagram for AsOCl₃ is similar to that of AsCl₃.

Since there are four bonding pairs, the molecule is tetrahedral. Sketches of each of these molecules are

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The VSEPR theory can also be applied to molecules which contain five and six pairs of valence electrons, some of which are lone pairs. We have not included such species here because the majority of compounds fall into the categories we have described.

Multiple Bonds and Molecular Shapes

In a double bond, two electron pairs are shared between a pair of atomic nuclei. Despite the fact that the two electron pairs repel each other, they must remain between the nuclei, and so they cannot avoid each other. Therefore, for purposes of predicting molecular geometry, the two electron pairs in a double bond behave as one. They will, however, be somewhat “fatter” than a single electron-pair bond. For the same reason the three electron pairs in a triple bond behave as an “extra-fat” bond.

As an example of the multiple-bond rules, consider hydrogen cyanide, HCN. The Lewis structure is

Treating the triple bond as if it were a single “fat” electron pair, we predict a linear molecule with an H―C―H angle of 180°. This is confirmed experimentally. Another example is formaldehyde, CH₂O, whose Lewis structure is

Since no lone pairs are present on C, the two H’s and the O should be arranged trigonally, with all four atoms in the same plane. Also, because of the “fatness” of the double bond, squeezing the C—H bond pairs together, we expect the H―C―H angle to be slightly less than 120°. Experimentally it is found to have the value of 117°.

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EXAMPLE 7.2 Predict the shape of the two molecules (a) nitrosyl chloride, NOCl, and (b) carbon dioxide, CO₂.

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Solution

a) We must first construct a skeleton structure and then a Lewis diagram. Since N has a valence of 3, O a valence of 2, and Cl is monovalent, a probable structure for NOCl is

Completing the Lewis diagram, we find

Since N has two bonds and one lone pair, the molecule must be angular. The O—N—Cl angle should be about 120°. Since the “fat” lone pair would act to reduce this angle while the “fat” double bond would tend to increase it, it is impossible to predict at this level of argument whether the angle will be slightly larger or smaller than 120°.

b) The Lewis structure of CO₂ was considered in the previous chapter and found to be

Since C has no lone pairs in its valence shell and each double bond acts as a fat bond pair, we conclude that the two O atoms are separated by 180° and that the molecule is linear.