Chemical Bonding II: Molecular Shapes, Valence Bond Theory, and Molecular Orbital Theory Review Questions 10.1 J The properties of molecules are directly related to their shape. The sensation of taste, immune response, the sense of smell, and many types of drug action all depend on shape-specific interactions between molecules and proteins. According to VSEPR theory, the repulsion between electron groups on interior atoms of a molecule determines the geometry of the molecule. The five basic electron geometries are (1) Linear, which has two electron groups. (2) Trigonal planar, which has three electron groups. (3) Tetrahedral, which has four electron groups. (4) Trigonal bipyramid, which has five electron groups. (5) Octahedral, which has six electron groups. An electron group is defined as a lone pair of electrons, a single bond, a multiple bond, or even a single electron. H—C—H 109.5= ijj^^jl (a) Linear geometry \ \ (b) Trigonal planar geometry I Tetrahedral geometry I Equatorial chlorine Axial chlorine "P—Cl: \ Trigonal bipyramidal geometry 1 I Octahedral geometry I 369 370 Chapter 10 Chemical Bonding II The electron geometry is the geometrical arrangement of the electron groups around the central atom. The molecular geometry is the geometrical arrangement of the atoms around the central atom. The electron geometry and the molecular geometry are the same when every electron group bonds two atoms together. The presence of unbonded lone-pair electrons gives a different molecular geometry and electron geometry. (a) Four electron groups give tetrahedral electron geometry, while three bonding groups and one lone pair give a trigonal pyramidal molecular geometry. (b) Four electron groups give a tetrahedral electron geometry, while two bonding groups and two lone pairs give a bent molecular geometry. (c) Five electron groups give a trigonal bipyramidal electron geometry, while four bonding groups and one lone pair give a seesaw molecular geometry. (d) Five electron groups give a trigonal bipyramidal electron geometry, while three bonding groups and two lone pairs give a T-shaped molecular geometry. (e) Five electron groups gives a trigonal bipyramidal electron geometry, while two bonding groups and three lone pair give a linear geometry. (f) Six electron groups give an octahedral electron geometry, while five bonding groups and one lone pair give a square pyramidal molecular geometry. (g) Six electron groups give an octahedral electron geometry, while four bonding groups and two lone pairs gives a square planar molecular geometry. Larger molecules may have two or more interior atoms. When predicting the shapes of these molecules, determine the geometry about each interior atom and use these geometries to determine the entire three- dimensional shape of the molecules. To determine if a molecule is polar, do the following: 1. Draw the Lewis structure for the molecule and determine the molecular geometry. 2. Determine whether the molecule contains polar bonds. 3. Determine whether the polar bonds add together to form a net dipole moment. Polarity is important because polar and nonpolar molecules have different properties. Polar molecules inter- act strongly with other polar molecules, but do not interact with nonpolar molecules, and vice versa. 10.8 According to valence bond theory a chemical bond results from the overlap of two half-filled orbitals with spin-pairing of the two valence electrons. 10.9 According to valence bond theory, the shape of the molecule is determined by the geometry of the overlap- ping orbitals. 10.10 In valence bond theory, the interaction energy is usually negative (or stabilizing) when the interacting atomic orbitals contain a total of two electrons that can spin-pair. 10.11 Hybridization is a mathematical procedure in which the standard atomic orbitals are combined to form new atomic orbitals called hybrid orbitals. Hybrid orbitals are still localized on individual atoms, but they have different shapes and energies from those of standard atomic orbitals. They are necessary in valence bond theory because they correspond more closely to the actual distribution of electrons in chemically- bonded atoms. 10.12 Hybrid orbitals minimize the energy of the molecule by maximizing the orbital overlap in a bond. Chapter 10 Chemical Bonding II 373 10.29 Nonbonding orbitals are atomic orbitals not involved in a bond and will remain localized on the atom. 10.30 In Lewis theory, a chemical bond is the transfer or sharing of electrons represented as dots. Lewis theory allows us to predict the combination of atoms that form stable molecules, and the general shape of a molecule. Lewis theory is a quick way to predict the stability and shapes of molecules based on the number of valence electrons. However, it does not deal at all with how the bonds that we make are formed. Valence bond theory is a more advanced bonding theory that treats electrons in a quantum-mechanical manner. A quantitative approach is extremely complicated but a qualitative approach allows an understanding of how the bonds are formed. In valence bond theory, electrons reside in quantum-mechanical orbitals local- ized on individual atoms. When two atoms approach each other, the electrons and nucleus of one atom interact with the electron and nucleus of the other atom. If the energy of the system is lowered, a chemi- cal bond forms. So, valence bond theory portrays a chemical bond as the overlap of two half-filled atomic orbitals. The shape of the molecule can be predicted from the geometry of the overlapping orbitals. Also, valence bond theory explains the rigidity of the double bond. However, valence bond theory falls short in explaining certain phenomenon such as magnetism and certain bond properties. Valence bond theory treats the electrons as if they reside in the quantum-mechanical orbitals that we calculate for an atom. This is an oversimplification that is partially compensated for by introducing the concept of hybridization. An even more complex quantum-mechanical model is molecular orbital theory. In molecular orbital theory, a chemical bond occurs when the electrons in the atoms can lower their energy by occupying the molecu- lar orbitals of the resultant molecule. The chemical bonds in MO theory are not localized between atoms, but spread throughout the entire molecule. Molecular orbital theory uses trial functions to solve the Schrodinger equation for the molecules. In order to determine how well the trial function works, you cal- culate the energy, trying to minimize the energy. However, no matter how "good" your guess, you can never do better than nature at minimizing energy. These minimum-energy calculations for orbitals must be done by computer. All three of these models have strengths and weaknesses, none is "correct." What information you need, depends on which approach you use. Problems by Topic VSEPR Theory and Molecular Geometry 10.31 Four electron groups: A trigonal pyramidal molecular geometry has three bonding groups and one lone pair of electrons, so there are four electron pairs on atom A. 10.32 Three electron groups: A trigonal planar molecular geometry has three bonding groups and no lone pairs of ~N. electrons so there are three electron pairs on atom A. / • 10.33 1I (a) 4 total electron groups, 4 bonding groups, 0 lone pairs / A tetrahedral molecular geometry has four bonding groups and no lone pairs. So, there are four total V / electron groups, four bonding groups, and pairs. (b) 5 total electron groups, 3 bonding groups, 2 lone pairs A T-shaped molecular geometry has three bonding groups and two lone pairs. So, there are five total electron groups, three bonding groups, and two lone pairs. (c) 6 total electron groups, 5 bonding groups, 1 lone pairs A square pyramidal molecular geometry has five bonding groups and one lone pair. So, there are six total electron groups, five bonding groups, and one lone pairs. 10.34 (a) 6 total electron groups, 6 bonding groups, 0 lone pairs An octahedral molecular geometry has six bonding groups and no lone pairs. So, there are six total electron groups, six bonding groups, and no lone pairs. (b) 6 electron groups, 4 bonding groups, 2 lone pairs A square planar molecular geometry has four bonding groups and two lone pairs. So, there are six total electron groups, four bonding groups, and two lone pairs. 374 Chapter 10 Chemical Bonding II (c) 5 electron groups, 4 bonding groups, 1 lone pair A seesaw molecular geometry has four bonding groups and one lone pair. So, there are five total elec- tron groups, four bonding groups, and one lone pair. PF3: Electron geometry-tetrahedral; molecular geometry-trigonal pyramidal; bond angle = 109.5° Because of the lone pair, the bond angle will be less than 109.5°. Draw a Lewis structure for the molecule: PF3 has 26 valence electrons. • rc • -p -F •• • • Determine the total number of electron groups around the central atom: There are four electron groups on P. Determine the number of bonding groups and the number of lone pairs around the central atom: There are three bonding groups and one lone pair. Use Table 10.1 to determine the electron geometry, molecular geometry, and bond angles: Four electron groups give a tetrahedral electron geometry; three bonding groups and one lone pair give a trigonal pyramidal molecular geometry; the idealized bond angles for tetrahedral geometry are 109.5°. The lone pair will make the bond angle less than idealized. (b) SBr2: Electron geometry-tetrahedral; molecular geometry-bent; bond angle = 109.5° Because of the lone pairs, the bond angle will be less than 109.5°. Draw a Lewis structure for the molecule: has 20 valence electrons. Determine the total number of electron groups around the central atom: There are four electron groups on S. Determine the number of bonding groups and the number of lone pairs around the central atom: There are two bonding groups and two lone pairs.