Predicting the Shapes of Molecules
There is no direct relationship between the formula of a compound and the shape of its molecules. The shapes of these molecules can be predicted from their Lewis structures, however, with a model developed about 30 years ago, known as the valence-shell electron-pair repulsion (VSEPR) theory. The VSEPR theory assumes that each atom in a molecule will achieve a geometry that minimizes the repulsion between electrons in the valence shell of that atom. The five compounds shown in the figure below can be used to demonstrate how the VSEPR theory can be applied to simple molecules.
There are only two places in the valence shell of the central atom in BeF2 where electrons can be found. Repulsion between these pairs of electrons can be minimized by arranging them so that they point in opposite directions. Thus, the VSEPR theory predicts that BeF2 should be a linear molecule, with a 180o angle between the two Be-F bonds.
There are three places on the central atom in boron trifluoride (BF3) where valence electrons can be found. Repulsion between these electrons can be minimized by arranging them toward the corners of an equilateral triangle. The VSEPR theory therefore predicts a trigonal planar geometry for the BF3 molecule, with a F-B-F bond angle of 120o.
BeF2 and BF3 are both two-dimensional molecules, in which the atoms lie in the same plane. If we place the same restriction on methane (CH4), we would get a square-planar geometry in which the H-C-H bond angle is 90o. If we let this system expand into three dimensions, however, we end up with a tetrahedral molecule in which the H-C-H bond angle is 109o28'.
Repulsion between the five pairs of valence electrons on the phosphorus atom in PF5 can be minimized by distributing these electrons toward the corners of a trigonal bipyramid. Three of the positions in a trigonal bipyramid are labeled equatorial because they lie along the equator of the molecule. The other two are axial because they lie along an axis perpendicular to the equatorial plane. The angle between the three equatorial positions is 120o, while the angle between an axial and an equatorial position is 90o.
There are six places on the central atom in SF6 where valence electrons can be found. The repulsion between these electrons can be minimized by distributing them toward the corners of an octahedron. The term octahedron literally means "eight sides," but it is the six corners, or vertices, that interest us. To imagine the geometry of an SF6 molecule, locate fluorine atoms on opposite sides of the sulfur atom along the X, Y, and Z axes of an XYZ coordinate system.
Incorporating Double and Triple Bonds Into the VSEPR Theory
Compounds that contain double and triple bonds raise an important point: The geometry around an atom is determined by the number of places in the valence shell of an atom where electrons can be found, not the number of pairs of valence electrons. Consider the Lewis structures of carbon dioxide (CO2) and the carbonate (CO32-) ion, for example.
There are four pairs of bonding electrons on the carbon atom in CO2, but only two places where these electrons can be found. (There are electrons in the C=O double bond on the left and electrons in the double bond on the right.) The force of repulsion between these electrons is minimized when the two C=O double bonds are placed on opposite sides of the carbon atom. The VSEPR theory therefore predicts that CO2 will be a linear molecule, just like BeF2, with a bond angle of 180o. The Lewis structure of the carbonate ion also suggests a total of four pairs of valence electrons on the central atom. But these electrons are concentrated in three places: The two C-O single bonds and the C=O double bond. Repulsions between these electrons are minimized when the three oxygen atoms are arranged toward the corners of an equilateral triangle. The CO32- ion...