Chemical Bonding II Molecular Geometry and Hybridization of Atomic Orbitals

CHAPTER 10 CHEMICAL BONDING II: MOLECULAR GEOMETRY AND HYBRIDIZATION OF ATOMIC ORBITALS 10.7 (a) The Lewis structure of PCl3 is shown below. Since in the VSEPR method the number of bonding pairs and lone pairs of electrons around the central atom (phosphorus, in this case) is important in determining the structure, the lone pairs of electrons around the chlorine atoms have been omitted for simplicity. There are three bonds and one lone electron pair around the central atom, phosphorus, which makes this an AB3E case. The information in Table 10.2 shows that the structure is a trigonal pyramid like ammonia. Cl P Cl Cl What would be the structure of the molecule if there were no lone pairs and only three bonds? (b) The Lewis structure of CHCl3 is shown below. There are four bonds and no lone pairs around carbon which makes this an AB4 case. The molecule should be tetrahedral like methane (Table 10.1). H Cl C Cl Cl (c) The Lewis structure of SiH4 is shown below. Like part (b), it is a tetrahedral AB4 molecule. H H Si H H (d) The Lewis structure of TeCl4 is shown below. There are four bonds and one lone pair which make this an AB4E case. Consulting Table 10.2 shows that the structure should be that of a distorted tetrahedron like SF4. Cl Cl Te Cl Cl Are TeCl4 and SF4 isoelectronic? Should isoelectronic molecules have similar VSEPR structures? 10.8 Strategy: The sequence of steps in determining molecular geometry is as follows: draw Lewis ⎯⎯ → find arrangement of ⎯⎯ → find arrangement ⎯⎯ → determine geometry structure electrons pairs of bonding pairs based on bonding pairs Solution: Lewis structure Electron pairs on central atom Electron arrangement Lone pairs Geometry 3 trigonal planar 0 trigonal planar, AB3 2 linear 0 linear, AB2 4 tetrahedral 0 tetrahedral, AB4 Cl (a) (b) Cl Al Cl Cl Zn Cl 2− Cl Cl (c) Zn Cl Cl 10.9 Lewis Structure − e pair arrangement geometry Br tetrahedral tetrahedral Cl trigonal planar trigonal planar tetrahedral trigonal pyramidal tetrahedral bent trigonal planar bent Br (a) Br C Br (b) Cl B Cl (c) F N F F (d) (e) 10.10 H Se O N H O − We use the following sequence of steps to determine the geometry of the molecules. draw Lewis ⎯⎯ → find arrangement of ⎯⎯ → find arrangement ⎯⎯ → determine geometry structure electrons pairs of bonding pairs based on bonding pairs (a) Looking at the Lewis structure we find 4 pairs of electrons around the central atom. The electron pair arrangement is tetrahedral. Since there are no lone pairs on the central atom, the geometry is also tetrahedral. H H C I H (b) Looking at the Lewis structure we find 5 pairs of electrons around the central atom. The electron pair arrangement is trigonal bipyramidal. There are two lone pairs on the central atom, which occupy positions in the trigonal plane. The geometry is t-shaped. F Cl F F (c) Looking at the Lewis structure we find 4 pairs of electrons around the central atom. The electron pair arrangement is tetrahedral. There are two lone pairs on the central atom. The geometry is bent. H (d) S H Looking at the Lewis structure, there are 3 VSEPR pairs of electrons around the central atom. Recall that a double bond counts as one VSEPR pair. The electron pair arrangement is trigonal planar. Since there are no lone pairs on the central atom, the geometry is also trigonal planar. O O (e) S O Looking at the Lewis structure, there are 4 pairs of electrons around the central atom. The electron pair arrangement is tetrahedral. Since there are no lone pairs on the central atom, the geometry is also tetrahedral. 2− O O S O O 10.11 The lone pairs of electrons on the bromine atoms have been omitted for simplicity. Br 10.12 Hg Br linear N + − N O linear S C N− linear (a) AB4 tetrahedral (f) AB4 tetrahedral (b) AB2E2 bent (g) AB5 trigonal bipyramidal (c) AB3 trigonal planar (h) AB3E trigonal pyramidal (d) AB2E3 linear (i) AB4 tetrahedral (e) AB4E2 square planar 10.13 The Lewis structure is: O H H C C O H H O H H C C AB 4 tetrahedral AB 3 trigonal planar H O 10.14 H AB 2 E 2 bent Only molecules with four bonds to the central atom and no lone pairs are tetrahedral (AB4). 2− Cl I Cl Cl Si Cl Cl I C I Cl I Cd Cl Cl What are the Lewis structures and shapes for XeF4 and SeF4? 10.19 All four molecules have two bonds and two lone pairs (AB2E2) and therefore the bond angles are not linear. Since electronegativity decreases going down a column (group) in the periodic table, the electronegativity differences between hydrogen and the other Group 6 element will increase in the order Te < Se < S < O. The dipole moments will increase in the same order. Would this conclusion be as easy if the elements were in different groups? 10.20 The electronegativity of the halogens decreases from F to I. Thus, the polarity of the H−X bond (where X denotes a halogen atom) also decreases from HF to HI. This difference in electronegativity accounts for the decrease in dipole moment. 10.21 CO2 = CBr4 (μ = 0 for both) < H2S < NH3 < H2O < HF 10.22 Draw the Lewis structures. Both molecules are linear (AB2). In CS2, the two C−S bond moments are equal in magnitude and opposite in direction. The sum or resultant dipole moment will be zero. Hence, CS2 is a nonpolar molecule. Even though OCS is linear, the C−O and C−S bond moments are not exactly equal, and there will be a small net dipole moment. Hence, OCS has a larger dipole moment than CS2 (zero). 10.23 Molecule (b) will have a higher dipole moment. In molecule (a), the trans arrangement cancels the bond dipoles and the molecule is nonpolar. 10.24 Strategy: Keep in mind that the dipole moment of a molecule depends on both the difference in electronegativities of the elements present and its geometry. A molecule can have polar bonds (if the bonded atoms have different electronegativities), but it may not possess a dipole moment if it has a highly symmetrical geometry. Solution: Each vertex of the hexagonal structure of benzene represents the location of a C atom. Around the ring, there is no difference in electronegativity between C atoms, so the only bonds we need to consider are the polar C−Cl bonds. The molecules shown in (b) and (d) are nonpolar. Due to the high symmetry of the molecules and the equal magnitude of the bond moments, the bond moments in each molecule cancel one another. The resultant dipole moment will be zero. For the molecules shown in (a) and (c), the bond moments do not cancel and there will be net dipole moments. The dipole moment of the molecule in (a) is larger than that in (c), because in (a) all the bond moments point in the same relative direction, reinforcing each other (see Lewis structure below). Therefore, the order of increasing dipole moments is: (b) = (d) < (c) < (a). Cl Cl Cl (a) 10.33 AsH3 has the Lewis structure shown below. There are three bond pairs and one lone pair. The four electron pairs have a tetrahedral arrangement, and the molecular geometry is trigonal pyramidal (AB3E) like ammonia 3 (See Table 10.2). The As (arsenic) atom is in an sp hybridization state. H H As H 3 Three of the sp hybrid orbitals form bonds to the hydrogen atoms by overlapping with the hydrogen 1s 3 orbitals. The fourth sp hybrid orbital holds the lone pair. 10.34 Strategy: The steps for determining the hybridization of the central atom in a molecule are: draw Lewis Structure of the molecule use VSEPR to determine the electron pair arrangement surrounding the central atom (Table 10.1 of the text) Solution: (a) Write the Lewis structure of the molecule. H H Si H H use Table 10.4 of the text to determine the hybridization state of the central atom Count the number of electron pairs around the central atom. Since there are four electron pairs around Si, the electron arrangement that minimizes electron-pair repulsion is tetrahedral. 3 3 We conclude that Si is sp hybridized because it has the electron arrangement of four sp hybrid orbitals. (b) Write the Lewis structure of the molecule. H H H Si Si H H H Count the number of electron pairs around the “central atoms”. Since there are four electron pairs around each Si, the electron arrangement that minimizes electron-pair repulsion for each Si is tetrahedral. 3 3 We conclude that each Si is sp hybridized because it has the electron arrangement of four sp hybrid orbitals. 10.35 − The Lewis structures of AlCl3 and AlCl4 are shown below. By the reasoning of the two problems above, 2 3 the hybridization changes from sp to sp . − Cl Cl Al Cl Cl Al Cl Cl Cl What are the geometries of these molecules? 2 10.36 Draw the Lewis structures. Before the reaction, boron is sp hybridized (trigonal planar electron 3 arrangement) in BF3 and nitrogen is sp hybridized (tetrahedral electron arrangement) in NH3. After the 3 reaction, boron and nitrogen are both sp hybridized (tetrahedral electron arrangement). 10.37 (a) NH3 is an AB3E type molecule just as AsH3 in Problem 10.33. Referring to Table 10.4 of the text, the 3 nitrogen is sp hybridized. (b) N2H4 has two equivalent nitrogen atoms. Centering attention on just one nitrogen atom shows that it is 3 an AB3E molecule, so the nitrogen atoms are sp hybridized. From structural considerations, how can N2H4 be considered to be a derivative of NH3? (c) The nitrate anion NO3 is isoelectronic and isostructural with the carbonate anion CO3 that is discussed in Example 9.5 of the text. There are three resonance structures, and the ion is of type AB3; 2 thus, the nitrogen is sp hybridized. − 2− 10.38 (a) Each carbon has four bond pairs and no lone pairs and therefore has a tetrahedral electron pair 3 arrangement. This implies sp hybrid orbitals. H H H (b) C C H H H 3 The left-most carbon is tetrahedral and therefore has sp hybrid orbitals. The two carbon atoms 2 connected by the double bond are trigonal planar with sp hybrid orbitals. H H H H C C C H H (c) 3 Carbons 1 and 4 have sp hybrid orbitals. Carbons 2 and 3 have sp hybrid orbitals. H H H C1 C2 C3 C4 H (d) OH H 3 The left-most carbon is tetrahedral (sp hybrid orbitals). The carbon connected to oxygen is trigonal 2 planar (why?) and has sp hybrid orbitals. H H H C C O H (e) 3 The left-most carbon is tetrahedral (sp hybrid orbitals). The other carbon is trigonal planar with sp hybridized orbitals. H O H C C O H H 10.39 (a) sp (b) 10.40 Strategy: The steps for determining the hybridization of the central atom in a molecule are: draw Lewis Structure of the molecule sp (c) sp use VSEPR to determine the electron pair arrangement surrounding the central atom (Table 10.1 of the text) use Table 10.4 of the text to determine the hybridization state of the central atom 2 Solution: Write the Lewis structure of the molecule. Several resonance forms with formal charges are shown. − 2− − + 2− + − − + − N N N N N N N N N Count the number of electron pairs around the central atom. Since there are two electron pairs around N, the electron arrangement that minimizes electron-pair repulsion is linear (AB2). Remember, for VSEPR purposes a multiple bond counts the same as a single bond. We conclude that N is sp hybridized because it has the electron arrangement of two sp hybrid orbitals. 10.41 2 The Lewis structure is shown below. The two end carbons are trigonal planar and therefore use sp hybrid orbitals. The central carbon is linear and must use sp hybrid orbitals. H H H C C C H A Lewis drawing does not necessarily show actual molecular geometry. Notice that the two CH2 groups at the ends of the molecule must be perpendicular. This is because the two double bonds must use different 2p orbitals on the middle carbon, and these two 2p orbitals are perpendicular. The overlap of the 2p orbitals on each carbon is shown below. C C C Is the allene molecule polar? 10.42 Strategy: The steps for determining the hybridization of the central atom in a molecule are: draw Lewis Structure of the molecule use VSEPR to determine the electron pair arrangement surrounding the central atom (Table 10.1 of the text) use Table 10.4 of the text to determine the hybridization state of the central atom Solution: Write the Lewis structure of the molecule. F F P F F F Count the number of electron pairs around the central atom. Since there are five electron pairs around P, the electron arrangement that minimizes electron-pair repulsion is trigonal bipyramidal (AB5). 3 3 We conclude that P is sp d hybridized because it has the electron arrangement of five sp d hybrid orbitals. 10.43 It is almost always true that a single bond is a sigma bond, that a double bond is a sigma bond and a pi bond, and that a triple bond is always a sigma bond and two pi bonds. (a) (c) sigma bonds: 4; pi bonds: 0 sigma bonds: 10; pi bonds: 3 (b) sigma bonds: 5; pi bonds: 1 10.44 A single bond is usually a sigma bond, a double bond is usually a sigma bond and a pi bond, and a triple bond is always a sigma bond and two pi bonds. Therefore, there are nine pi bonds and nine sigma bonds in the molecule. 10.49 The molecular orbital electron configuration and bond order of each species is shown below. H2 σ 1s H2 + H2 σ 1s ↑↓ σ1s bond order = 1 σ1s 2+ σ 1s ↑ bond order = σ1s 1 2 bond order = 0 The internuclear distance in the +1 ion should be greater than that in the neutral hydrogen molecule. The distance in the +2 ion will be arbitrarly large because there is no bond (bond order zero). 10.50 In order for the two hydrogen atoms to combine to form a H2 molecule, the electrons must have opposite spins. Furthermore, the combined energy of the two atoms must not be too great. Otherwise, the H2 molecule will possess too much energy and will break apart into two hydrogen atoms. 10.51 The energy level diagrams are shown below. He2 HHe He2 + σ 1s ↑↓ σ 1s ↑ σ 1s ↑ σ1s ↑↓ σ1s ↑↓ σ1s ↑↓ bond order = 0 bond order = 1 2 bond order = 1 2 He2 has a bond order of zero; the other two have bond orders of 1/2. Based on bond orders alone, He2 has no stability, while the other two have roughly equal stabilities. 10.52 The electron configurations are listed. Refer to Table 10.5 of the text for the molecular orbital diagram. Li2: 2 2 ( σ1s ) 2 (σ 1s ) (σ 2 s ) bond order = 1 Li +2 : 2 1 ( σ1s ) 2 (σ 1s ) (σ 2 s ) bond order = Li −2 : 2 2  1 ( σ1s ) 2 ( σ 1s ) (σ 2 s ) (σ2 s ) 1 2 1 bond order = 2 Order of increasing stability: Li −2 = Li +2 < Li2 In reality, Li +2 is more stable than Li −2 because there is less electrostatic repulsion in Li +2 . 10.53 The Be2 molecule does not exist because there are equal numbers of electrons in bonding and antibonding molecular orbitals, making the bond order zero. σ 2s ↑↓ σ2 s ↑↓ σ 1s ↑↓ σ1s ↑↓ bond order = 0 + 10.54 See Table 10.5 of the text. Removing an electron from B2 (bond order = 1) gives B2 , which has a bond + order of (1/2). Therefore, B2 has a weaker and longer bond than B2. 10.55 The energy level diagrams are shown below. C2 2− C2 σ 2 px σ 2 px  π 2 py , π2 pz  π 2 py , π2 pz σ 2 px ↑↓ π2 py , π2 pz ↑↓ σ 2s σ2 s σ 2 px ↑↓ π2 py , π2 pz ↑↓ ↑↓ σ 2s ↑↓ ↑↓ σ2 s ↑↓ σ1s ↑↓ σ 1s ↑↓ σ1s ↑↓ σ1s ↑↓ ↑↓ The bond order of the carbide ion is 3 and that of C2 is only 2. With what homonuclear diatomic molecule is the carbide ion isoelectronic? 10.56 In both the Lewis structure and the molecular orbital energy level diagram (Table 10.5 of the text), the oxygen molecule has a double bond (bond order = 2). The principal difference is that the molecular orbital treatment predicts that the molecule will have two unpaired electrons (paramagnetic). Experimentally this is found to be true. 10.57 In forming the N2 from N2, an electron is removed from the sigma bonding molecular orbital. + Consequently, the bond order decreases to 2.5 from 3.0. In forming the O2 ion from O2, an electron is removed from the pi antibonding molecular orbital. Consequently, the bond order increases to 2.5 from 2.0. 10.58 We refer to Table 10.5 of the text. + O2 has a bond order of 2 and is paramagnetic (two unpaired electrons). + O2 has a bond order of 2.5 and is paramagnetic (one unpaired electron). − O2 has a bond order of 1.5 and is paramagnetic (one unpaired electron). O2 2− has a bond order of 1 and is diamagnetic. Based on molecular orbital theory, the stability of these molecules increases as follows: O2 2− − < O2 < O2 < O2 + + + 10.59 From Table 10.5 of the text, we see that the bond order of F2 is 1.5 compared to 1 for F2. Therefore, F2 should be more stable than F2 (stronger bond) and should also have a shorter bond length. 10.60 As discussed in the text (see Table 10.5), the single bond in B2 is a pi bond (the electrons are in a pi bonding molecular orbital) and the double bond in C2 is made up of two pi bonds (the electrons are in the pi bonding molecular orbitals). 10.63 Benzene is stabilized by delocalized molecular orbitals. The C−C bonds are equivalent, rather than alternating single and double bonds. The additional stabilization makes the bonds in benzene much less reactive chemically than isolated double bonds such as those in ethylene. 10.64 The symbol on the left shows the pi bond delocalized over the entire molecule. The symbol on the right shows only one of the two resonance structures of benzene; it is an incomplete representation. 10.65 If the two rings happen to be perpendicular in biphenyl, the pi molecular orbitals are less delocalized. In naphthalene the pi molecular orbital is always delocalized over the entire molecule. What do you think is the most stable structure for biphenyl: both rings in the same plane or both rings perpendicular? 10.66 (a) Two Lewis resonance forms are shown below. Formal charges different than zero are indicated. F O N + F O − − O N + O (b) There are no lone pairs on the nitrogen atom; it should have a trigonal planar electron pair arrangement 2 and therefore use sp hybrid orbitals. (c) The bonding consists of sigma bonds joining the nitrogen atom to the fluorine and oxygen atoms. In addition there is a pi molecular orbital delocalized over the N and O atoms. Is nitryl fluoride isoelectronic with the carbonate ion? 10.67 The ion contains 24 valence electrons. Of these, six are involved in three sigma bonds between the nitrogen 2 and oxygen atoms. The hybridization of the nitrogen atom is sp . There are 16 non-bonding electrons on the oxygen atoms. The remaining two electrons are in a delocalized pi molecular orbital which results from the overlap of the pz orbital of nitrogen and the pz orbitals of the three oxygen atoms. The molecular orbitals are similar to those of the carbonate ion (See Section 10.8 of the text). 10.68 The Lewis structures of ozone are: O 2 O O O O O The central oxygen atom is sp hybridized (AB2E). The unhybridized 2pz orbital on the central oxygen overlaps with the 2pz orbitals on the two end atoms. 10.69 Only (c) will not be tetrahedral. All the others have AB4−type Lewis structures and will therefore be tetrahedral. For SF4 the Lewis structure is of the AB4E type which gives rise to a distorted tetrahedral geometry (Table 10.2 of the text). 10.70 Strategy: The sequence of steps in determining molecular geometry is as follows: → find arrangement of ⎯⎯ → find arrangement ⎯⎯ → determine geometry draw Lewis ⎯⎯ structure electrons pairs of bonding pairs based on bonding pairs Solution: Write the Lewis structure of the molecule. Br Hg Br Count the number of electron pairs around the central atom. There are two electron pairs around Hg. Since there are two electron pairs around Hg, the electron-pair arrangement that minimizes electron-pair repulsion is linear. In addition, since there are no lone pairs around the central atom, the geometry is also linear (AB2). You could establish the geometry of HgBr2 by measuring its dipole moment. If mercury(II) bromide were bent, it would have a measurable dipole moment. Experimentally, it has no dipole moment and therefore must be linear. 10.71 Dot structure Label Shape Bond dipole Resultant dipole moment AB2E2 bent μ>0 AB3E trigonal pyramidal μ>0 AB4E2 square planar μ=0 AB5 trigonal bipyramid μ=0 O H H P Cl Cl Cl F F Xe F F Cl Cl Cl P Cl Cl F F F S F F F AB6 μ=0 octahedral Why do the bond dipoles add to zero in PCl5? 10.72 According to valence bond theory, a pi bond is formed through the side-to-side overlap of a pair of p orbitals. As atomic size increases, the distance between atoms is too large for p orbitals to overlap effectively in a side-to-side fashion. If two orbitals overlap poorly, that is, they share very little space in common, then the resulting bond will be very weak. This situation applies in the case of pi bonds between silicon atoms as well as between any other elements not found in the second period. It is usually far more energetically favorable for silicon, or any other heavy element, to form two single (sigma) bonds to two other atoms than to form a double bond (sigma + pi) to only one other atom. 10.73 Geometry: bent; hybridization: sp . 10.74 The Lewis structures and VSEPR geometries of these species are shown below. The three nonbonding pairs of electrons on each fluorine atom have been omitted for simplicity. 3 F + Xe F F Xe + F F F AB3E2 T-shaped 10.75 (a) F F F − F Sb F F AB5E Square Pyramidal F F AB6 Octahedral The Lewis structure is: F B F F The shape will be trigonal planar (AB3) (b) The Lewis structure is: O Cl O - O The molecule will be a trigonal pyramid (nonplanar). (c) The Lewis structure and the dipole moment for H2O is presented in Problem 10.71. The dipole moment is directed from the positive hydrogen end to the more negative oxygen. (d) The Lewis structure is: O F The molecule is bent and therefore polar. F (e) The Lewis structure is: N O O The nitrogen atom is of the AB2E type, but there is only one unshared electron rather than the usual pair. As a result, the repulsion will not be as great and the O−N−O angle will be greater than 120° expected for AB2E geometry. Experiment shows the angle to be around 135°. Which of the species in this problem has resonance structures? 10.76 To predict the bond angles for the molecules, you would have to draw the Lewis structure and determine the geometry using the VSEPR model. From the geometry, you can predict the bond angles. (a) BeCl2: AB2 type, 180° (linear). (b) BCl3: AB3 type, 120° (trigonal planar). (c) CCl4: AB4 type, 109.5° (tetrahedral). (d) CH3Cl: AB4 type, 109.5° (tetrahedral with a possible slight distortion resulting from the different sizes of the chlorine and hydrogen atoms). (e) Hg2Cl2: Each mercury atom is of the AB2 type. The entire molecule is linear, 180° bond angles. (f) SnCl2: AB2E type, roughly 120° (bent). (g) H 2O 2 : The atom arrangement is HOOH. Each oxygen atom is of the AB2E2 type and the H−O−O angles will be roughly 109.5°. (h) SnH4: AB4 type, 109.5° (tetrahedral). 10.77 The two approaches are discussed in Sections 10.1, 10.3, and 10.4 of the textbook. 10.78 Since arsenic and phosphorus are both in the same group of the periodic table, this problem is exactly like Problem 10.42. AsF5 is an AB5 type molecule, so the geometry is trigonal bipyramidal. We conclude that 3 3 As is sp d hybridized because it has the electron arrangement of five sp d hybrid orbitals. 10.79 (a) The Lewis structure is: O O S O The geometry is trigonal planar; the molecule is nonpolar. (b) The Lewis structure is: F F P F The molecule has trigonal pyramidal geometry. It is polar. (c) The Lewis structure is: H F Si F F The molecule will be tetrahedral (AB4). Both fluorine and hydrogen are more electronegative than silicon, but fluorine is the most electronegative element, so the molecule will be polar (fluorine side negative). (d) The Lewis structure is: − H H Si H The ion has a trigonal pyramidal geometry (AB3E). (e) The Lewis structure is: H Br C Br H The molecule will be tetrahedral (AB4) but still polar. The negative end of the dipole moment will be on the side with the two bromine atoms; the positive end will be on the hydrogen side. − 10.80 Only ICl2 and CdBr2 will be linear. The rest are bent. 10.81 The Lewis structure is shown below. 2− Cl Cl Be Cl Cl The molecule is of the AB4 type and should therefore be tetrahedral. The hybridization of the Be atom 3 should be sp . 10.82 (a) Strategy: The steps for determining the hybridization of the central atom in a molecule are: draw Lewis Structure of the molecule use VSEPR to determine the electron pair arrangement surrounding the central atom (Table 10.1 of the text) use Table 10.4 of the text to determine the hybridization state of the central atom Solution: The geometry around each nitrogen is identical. To complete an octet of electrons around N, you must add a lone pair of electrons. Count the number of electron pairs around N. There are three electron pairs around each N. Since there are three electron pairs around N, the electron-pair arrangement that minimizes electron-pair repulsion is trigonal planar. 2 2 We conclude that each N is sp hybridized because it has the electron arrangement of three sp hybrid orbitals. (b) Strategy: Keep in mind that the dipole moment of a molecule depends on both the difference in electronegativities of the elements present and its geometry. A molecule can have polar bonds (if the bonded atoms have different electronegativities), but it may not possess a dipole moment if it has a highly symmetrical geometry. Solution: An N−F bond is polar because F is more electronegative than N. The structure on the right has a dipole moment because the two N−F bond moments do not cancel each other out and so the molecule has a net dipole moment. On the other hand, the two N−F bond moments in the left-hand structure cancel. The sum or resultant dipole moment will be zero. 10.83 (a) The structures for cyclopropane and cubane are H H C H C H C C H C H H Cyclopropane 10.84 H H H C C H H C C C C H H Cubane (b) The C−C−C bond in cyclopropane is 60° and in cubane is 90°. Both are smaller than the 109.5° 3 expected for sp hybridized carbon. Consequently, there is considerable strain on the molecules. (c) They would be more difficult to make than an sp hybridized carbon in an unconstrained (that is, not in a small ring) system in which the carbons can adopt bond angles closer to 109.5°. 3 In 1,2-dichloroethane, the two C atoms are joined by a sigma bond. Rotation about a sigma bond does not destroy the bond, and the bond is therefore free (or relatively free) to rotate. Thus, all angles are permitted and the molecule is nonpolar because the C−Cl bond moments cancel each other because of the averaging effect brought about by rotation. In cis-dichloroethylene the two C−Cl bonds are locked in position. The π bond between the C atoms prevents rotation (in order to rotate, the π bond must be broken, using an energy source such as light or heat). Therefore, there is no rotation about the C=C in cis-dichloroethylene, and the molecule is polar. 10.85 Consider the overlap of the 2p orbitals on each carbon atom. C C C The geometric planes containing the CHCl groups at each end of the molecule are mutually perpendicular. This is because the two carbon-carbon double bonds must use different 2p orbitals on the middle carbon, and these two 2p orbitals are perpendicular. This means that the two chlorine atoms can be considered to be on one side of the molecule and the two hydrogen atoms on the other. The molecule has a dipole moment. Draw the end-on view if you aren't convinced. 10.86 O3, CO, CO2, NO2, N2O, CH4, and CFCl3 are greenhouse gases. 10.87 Both sulfur−to−oxygen bonds are double bonds which occupy more space than single bonds and the repulsion between the double bonds spread out the angle close to 120°. 10.88 The Lewis structure is: O H C* N *C HO O CH2 N * CH3 C C* H O CH HC HC CH *N H N# N * 2 The carbon atoms and nitrogen atoms marked with an asterisk (C∗ and N∗) are sp hybridized; unmarked 3 carbon atoms and nitrogen atoms are sp hybridized; and the nitrogen atom marked with (#) is sp hybridized. 10.89 For an octahedral AX4Y2 molecule only two different structures are possible: one with the two Y’s next to each other like (b) and (d), and one with the two Y’s on opposite sides of the molecule like (a) and (c). The different looking drawings simply depict the same molecule seen from a different angle or side. It would help to develop your power of spatial visualization to make some simple models and convince yourself of the validity of these answers. How many different structures are possible for octahedral AX5Y or AX3Y3 molecules? Would an octahedral AX2Y4 molecule have a different number of structures from AX4Y2? Ask your instructor if you aren’t sure. 10.90 C has no d orbitals but Si does (3d). Thus, H2O molecules can add to Si in hydrolysis (valence-shell expansion). 10.91 2 2  2 1 1 B2 is (σ1s )2 (σ 1s ) (σ 2 s ) (σ2 s ) ( π2 py ) ( π2 pz ) . It is paramagnetic. 10.92 The carbons are in sp hybridization states. The nitrogens are in the sp hybridization state, except for the 2 2 ring nitrogen double-bonded to a carbon that is sp hybridized. The oxygen atom is sp hybridized. 10.93 Referring to Table 10.5, we see that F2 has an extra electron in σ 2 px . Therefore, it only has a bond order of 2 3 − 1 (compared with a bond order of one for F2). 2 10.94 (a) Use a conventional oven. A microwave oven would not cook the meat from the outside toward the center (it penetrates). (b) Polar molecules absorb microwaves and would interfere with the operation of radar. (c) Too much water vapor (polar molecules) absorbed the microwaves, interfering with the operation of radar. 10.95 P P P P 3 The four P atoms occupy the corners of a tetrahedron. Each phosphorus atom is sp hybridized. The P2 molecule has a triple bond, which is composed of one sigma bond and two pi bonds. The pi bonds are formed by sideways overlap of 3p orbitals. Because the atomic radius of P is larger than that of N, the overlap is not as extensive as that in the N2 molecule. Consequently, the P2 molecule is much less stable than N2 and also less stable than P4, which contains only sigma bonds. 10.96 The smaller size of F compared to Cl results in a shorter F−F bond than a Cl−Cl bond. The closer proximity of the lone pairs of electrons on the F atoms results in greater electron-electron repulsions that weaken the bond. 10.97 Since nitrogen is a second row element, it cannot exceed an octet of electrons. Since there are no lone pairs on the central nitrogen, the molecule must be linear and sp hybrid orbitals must be used. N + N N 2− − N + N N − 2− N + N N The 2py orbital on the central nitrogen atom overlaps with the 2py on the terminal nitrogen atoms, and the 2pz orbital on the central nitrogen overlaps with the 2pz orbitals on the terminal nitrogen atoms to form delocalized molecular orbitals. 10.98 1 D = 3.336 × 10 −30 C⋅m electronic charge (e) = 1.6022 × 10 1.92 D × −19 C 3.336 × 10−30 C ⋅ m 1D μ × 100% = × 100% = 43.6% ionic character ed (1.6022 × 10−19 C) × (91.7 × 10−12 m) 10.99 F C F H F H H C polar C F F H H C polar H C C nonpolar F 10.100 The second and third vibrational motions are responsible for CO2 to behave as a greenhouse gas. CO2 is a nonpolar molecule. The second and third vibrational motions, create a changing dipole moment. The first vibration, a symmetric stretch, does not create a dipole moment. Since CO, NO2, and N2O are all polar molecules, they will also act as greenhouse gases. Cl 10.101 (a) Cl Al Cl Cl Al Cl Cl 2 (b) The hybridization of Al in AlCl3 is sp . The molecule is trigonal planar. The hybridization of Al in 3 Al2Cl6 is sp . (c) The geometry about each Al atom is tetrahedral. Cl Cl Al Cl (d) 10.102 (a) Cl Al Cl Cl The molecules are nonpolar; they do not possess a dipole moment. A σ bond is formed by orbitals overlapping end-to-end. Rotation will not break this end-to-end overlap. A π bond is formed by the sideways overlapping of orbitals. The two 90° rotations (180° total) will break and then reform the pi bond, thereby converting cis-dichloroethylene to transdichloroethylene. (b) The pi bond is weaker because of the lesser extent of sideways orbital overlap, compared to the end-toend overlap in a sigma bond. (c) The bond enthalpy is given in the unit, kJ/mol. To find the longest wavelength of light needed to bring about the conversion from cis to trans, we need the energy to break a pi bond in a single molecule. We convert from kJ/mol to J/molecule. 270 kJ 1 mol × = 4.48 × 10−22 kJ/molecule = 4.48 × 10 −19 J/molecule 23 1 mol 6.022 × 10 molecules Now that we have the energy needed to cause the conversion from cis to trans in one molecule, we can calculate the wavelength from this energy. E = hc λ λ = hc (6.63 × 10−34 J ⋅ s)(3.00 × 108 m/s) = E 4.48 × 10−19 J λ = 4.44 × 10 −7 m = 444 nm 10.103 The complete structure of progesterone is shown below. CH3 H2 C CH3 H2C H2 C H2C C* O CH3 H O CH CH2 CH C *C C *C CH CH *C C H2 CH2 C H2 2 3 The four carbons marked with an asterisk are sp hybridized. The remaining carbons are sp hybridized. 10.104 In each case, we examine the molecular orbital that is occupied by the valence electrons of the molecule to see if it is a bonding or antibonding molecular orbital. If the electron is in a bonding molecular orbital, it is more stable than an electron in an atomic orbital (1s or 2p atomic orbital) and thus will have a higher ionization energy compared to the lone atom. On the other hand, if the electron is in an antibonding molecular orbital, it is less stable than an electron in an atomic orbital (1s or 2p atomic orbital) and thus will have a lower ionization energy compared to the lone atom. Refer to Table 10.5 of the text. (a) H2 (b) N2 (c) O (d) F H 10.105 H H H The normal bond angle for a hexagon is 60°. However, the triple bond requires an angle of 180° (linear) and therefore there is a great deal of strain in the molecule. Consequently, the molecule is very reactive (breaking the bond to relieve the strain). 10.106 (a) Looking at the electronic configuration for N2 shown in Table 10.5 of the text, we write the electronic configuration for P2. 2 2 2 2 [Ne2 ]( σ3s )2 ( σ 3s ) ( π3 py ) ( π3 pz ) (σ3 px ) (b) Past the Ne2 core configuration, there are 8 bonding electrons and 2 antibonding electrons. The bond order is: bond order = ½(8 − 2) = 3 (c) All the electrons in the electronic configuration are paired. P2 is diamagnetic. 10.107 (a) (b) From Table 10.5 of the text:  __________ π 2 py or π2 pz First excited state: N∗2 __________ σ2 px Ground state: N2 The bond order for N2 is 3. The bond order for N∗2 is ½(5 − 1) = 2. N∗2 should have a longer bond length than N2. (c) N∗2 is diamagnetic. Electrons do not change their spins during transitions. (d) E = hc (6.63 × 10−34 J ⋅ s)(3.00 × 108 m/s) = = 4.23 × 10−19 J −9 λ 470 × 10 m 10.108 The Lewis structure shows 4 pairs of electrons on the two oxygen atoms. From Table 10.5 of the text, we see  that these 8 valence electrons are placed in the σ2 px , π2 py , π2 pz , π 2 py , and π2 pz orbitals. For all the electrons to be paired, energy is needed to flip the spin in one of the antibonding molecular orbitals  ( π 2 py or π2 pz ). According to Hund’s rule, this arrangement is less stable than the ground-state configuration shown in Table 10.5, and hence the Lewis structure shown actually corresponds to an excited state of the oxygen molecule. 10.109 H C H sp2 C O sp H σ bonds C C O H π bonds C C O 10.110 (a) (b) 3 Although the O atoms are sp hybridized, they are locked in a planar structure by the benzene rings. The molecule is symmetrical and therefore does not possess a dipole moment. 20 σ bonds and 6 π bonds. 10.111 Referring to Table 10.5 of the text, we see that C2 and N2 have a similar energy order for their molecular − orbitals. Therefore, we expect CN to have the same order. 2 2 2 2 (σ1s ) 2 (σ1s )2 (σ2 s )2 (σ 2 s ) ( π2 py ) ( π2 pz ) (σ 2 p x ) − CO is isoelectronic with CN (both contain 14 electrons). 10.112 (a) − C + O This is the only reasonable Lewis structure for CO. The electronegativity difference suggests that electron density should concentrate on the O atom, but assigning formal charges places a negative charge on the C atom. Therefore, we expect CO to have a small dipole moment. (b) The Lewis structure shows a triple bond. The molecular orbital description gives a bond order of 3, just like N2 (see Table 10.5 of the text). (c) Normally, we would expect the more electronegative atom to bond with the metal ion. In this case, 2+ however, the small dipole moment suggests that the C atom may form a stronger bond with Fe than O. More elaborate analysis of the orbitals involved shows that this is indeed the case. 10.113 CCl4 can be represented by: Cl Cl C Cl θ Cl Let ρ be a C−Cl bond moment. Thus, ρ = 3ρ cos θ cos θ = Tetrahedral angle = 180° − 70.5° = 109.5° 1 3 θ = 70.5°