CHAPTER 1 STRUCTURE AND BONDING Problem 14 Convert the following representation of ethane,C2H6,into a conventional drawing that uses solid.wedged,and dashed lines to indicate tetrahedral geometry around each carbon (gray =C,ivory=H). Ethane Problem 15 What are likely formulas for the following substances? (a)CH2Cl2 (b)CHgSH?(c)CHgNH? Problem1.6 Draw line-bond structures for the following substances,showing all nonbond- ing electrons: (a)CH3CH2OH,ethanol (b)H2S,hydrogen sulfide (c)CH3NH2.methylamine (d)N(CH3)3,trimethylamine Problem1.7 Why can't an organic molecule have the formula C2H7? 15 The Nature of Chemical Bonds: Valence Bond Theory How does electron sharing lead to bonding between atoms?Two models have been developed to describec valent bonding:valence bond the ory and molec ular orbital theory.Each model has its strengths and weaknesses,and chem- ists tend to use them interchangeably depending on the circumstances Valence bond theory is the more easily visualized of the two.so most of the descriptions we'll use in this book derive from that approach. According to valence bond theory.a covalent bond forms when two atoms approach each other closely and a singly occupied orbital on one atom over laps a singly occupied orbital on the other atom.The electrons are now paired in the overlapping orbitals and are attracted to the nuclei of both atoms,thus bonding the atoms together.In the H2 molecule,for example,the H-H bond results from the overlap of two singly occupied hydrogen 1s orbitals: 15 H2 molecule
10 chapter 1 structure and bonding Problem 1.4 Convert the following representation of ethane, C2H6, into a conventional drawing that uses solid, wedged, and dashed lines to indicate tetrahedral geometry around each carbon (gray C, ivory H). Ethane Problem 1.5 What are likely formulas for the following substances? (a) CH?Cl2 (b) CH3SH? (c) CH3NH? Problem 1.6 Draw line-bond structures for the following substances, showing all nonbonding electrons: (a) CH3CH2OH, ethanol (b) H2S, hydrogen sulfide (c) CH3NH2, methylamine (d) N(CH3)3, trimethylamine Problem 1.7 Why can’t an organic molecule have the formula C2H7? 1.5 The Nature of Chemical Bonds: Valence Bond Theory How does electron sharing lead to bonding between atoms? Two models have been developed to describe covalent bonding: valence bond theory and molecular orbital theory. Each model has its strengths and weaknesses, and chemists tend to use them interchangeably depending on the circumstances. Valence bond theory is the more easily visualized of the two, so most of the descriptions we’ll use in this book derive from that approach. According to valence bond theory, a covalent bond forms when two atoms approach each other closely and a singly occupied orbital on one atom overlaps a singly occupied orbital on the other atom. The electrons are now paired in the overlapping orbitals and are attracted to the nuclei of both atoms, thus bonding the atoms together. In the H2 molecule, for example, the H–H bond results from the overlap of two singly occupied hydrogen 1s orbitals: g H H H 1s 1s H2 molecule H h hg 39144_01_0001-0032.indd 10 7/27/09 1:28:38 PM
1.5 THE NATURE OF CHEMICAL BONDS:VALENCE BOND THEORY 11 The overlapping orbitals in the Ha molecule have the elongated egg shape the mid If a plane were o pass through ersect apping would I be a the H-H b bond is cylind ric sym metricc orme e h ong a clei. called sig a fo)honds Cal sym ule.The inte a plane cutting through the bond is a circle. Circula During the bond-forming reaction 2 H.H2.436 kJ/mol(104 kcal/mol)of energy I re ed.B the pro uc ecule h ol less the H-H bond ha nd stren of 436 kl/mol.Ir to the H-H bond to brea hH molecule port int atome gu ve'll erally s in both kilocalorie 1823901kca4184 2H·→H2 Relative ule The H molerule ha Two hydrogen atoms 436 k]/mol (104 kcal/mol)less energy than the two H atc 436 kJ/mol Released when bond for m 436 nd b Conversely.36 k)/mol must be added to the molecule to H2molecule break the H-H bond How close are the two nuclei in the H2 molecule?If they are too close,they will repel each other because both are positively charged.yet if they are too far apart,they won't be able to s are the bonding electrons. hus,there is an opt between nucl s o maximum sta lty (Figure1.10） very cova
The overlapping orbitals in the H2 molecule have the elongated egg shape we might get by pressing two spheres together. If a plane were to pass through the middle of the bond, the intersection of the plane and the overlapping orbitals would be a circle. In other words, the H–H bond is cylindrically symmetrical, as shown in Figure 1.8. Such bonds, which are formed by the headon overlap of two atomic orbitals along a line drawn between the nuclei, are called sigma () bonds. Circular cross-section H H During the bond-forming reaction 2 H· n H2, 436 kJ/mol (104 kcal/mol) of energy is released. Because the product H2 molecule has 436 kJ/mol less energy than the starting 2 H· atoms, the product is more stable than the reactant and we say that the H–H bond has a bond strength of 436 kJ/mol. In other words, we would have to put 436 kJ/mol of energy into the H–H bond to break the H2 molecule apart into H atoms (Figure 1.9.) [For convenience, we’ll generally give energies in both kilocalories (kcal) and the SI unit kilojoules (kJ): 1 kJ 0.2390 kcal; 1 kcal 4.184 kJ.] Two hydrogen atoms 2 H H2 H2 molecule 436 kJ/mol Released when bond forms Energy Absorbed when bond breaks How close are the two nuclei in the H2 molecule? If they are too close, they will repel each other because both are positively charged, yet if they are too far apart, they won’t be able to share the bonding electrons. Thus, there is an optimum distance between nuclei that leads to maximum stability (Figure 1.10). Called the bond length, this distance is 74 pm in the H2 molecule. Every covalent bond has both a characteristic bond strength and bond length. FIGURE 1.8 The cylindrical symmetry of the H–H bond in an H2 molecule. The intersection of a plane cutting through the bond is a circle. FIGURE 1.8 The cylindrical symmetry of the H–H bond in an H2 molecule. The intersection of a plane cutting through the bond is a circle. FIGURE 1.9 Relative energy levels of H atoms and the H2 molecule. The H2 molecule has 436 kJ/mol (104 kcal/mol) less energy than the two H atoms, so 436 kJ/mol of energy is released when the H–H bond forms. Conversely, 436 kJ/mol must be added to the H2 molecule to break the H–H bond. FIGURE 1.9 Relative energy levels of H atoms and the H2 molecule. The H2 molecule has 436 kJ/mol (104 kcal/mol) less energy than the two H atoms, so 436 kJ/mol of energy is released when the H–H bond forms. Conversely, 436 kJ/mol must be added to the H2 molecule to break the H–H bond. 1.5 the nature of chemical bonds: valence bond theory 11 39144_01_0001-0032.indd 11 7/27/09 1:28:38 PM
2 CHAPTER 1 STRUCTURE AND BONDING eunc。 (too close two hydrogen atoms.The dis. ength. H---H(too fa Bond length Interuclear distance- 16sp3 Hybrid Orbitals and the Structure of Methane The bonding in the hydrogen molecule is fairly straightforward,but the situa- o'uo so trons (2s2 2p2)and for nhas valence elec. kin als for bonding.2s and 2p.w miaht oy ct methane to hay wo kinds ofCI bonds.In fact.though.all bonds in methane are identical and ar spatially oriented toward the corners of a regular tetrahedron (Figure 1.7). ACTIVE FIGURE 1.11 Four How can we explain this? An answer was provided in 1931 by Linus Pauling.who showed mathe- matically how an s orbital and three p orbitals on an atom can combine,or regular tetrahedron,are formed hybridize,to form four equivalent atomic orbitals with tetrahedral orienta- by combination of an s orbital tion.Shown in Figure 1.11,these tetrahedrally oriented orbitals are called sp3 hybrids.Note that the superscript 3 in the name sp3 tells how many of each type of atomic orbital combine to form the hybrid,not how many electrons about the nucleus occupy it. ng them a directionality and allowing at mcmurry to explore an interactive ersion of this figure. An sp3orbital
12 chapter 1 structure and bonding HH (too close) Bond length 74 pm H H (too far) 0 + – H H Internuclear distance Energy 1.6 sp3 Hybrid Orbitals and the Structure of Methane The bonding in the hydrogen molecule is fairly straightforward, but the situation is more complicated in organic molecules with tetravalent carbon atoms. Take methane, CH4, for instance. As we’ve seen, carbon has four valence electrons (2s2 2p2) and forms four bonds. Because carbon uses two kinds of orbitals for bonding, 2s and 2p, we might expect methane to have two kinds of C–H bonds. In fact, though, all four C–H bonds in methane are identical and are spatially oriented toward the corners of a regular tetrahedron (Figure 1.7). How can we explain this? An answer was provided in 1931 by Linus Pauling, who showed mathematically how an s orbital and three p orbitals on an atom can combine, or hybridize, to form four equivalent atomic orbitals with tetrahedral orientation. Shown in Figure 1.11, these tetrahedrally oriented orbitals are called sp3 hybrids. Note that the superscript 3 in the name sp3 tells how many of each type of atomic orbital combine to form the hybrid, not how many electrons occupy it. 2s 2py 2px Four tetrahedral sp3 orbitals An sp3 orbital Hybridization 2pz FIGURE 1.10 A plot of energy versus internuclear distance for two hydrogen atoms. The distance between nuclei at the minimum energy point is the bond length. FIGURE 1.10 A plot of energy versus internuclear distance for two hydrogen atoms. The distance between nuclei at the minimum energy point is the bond length. ACTIVE FIGURE 1.11 Four sp3 hybrid orbitals (green), oriented to the corners of a regular tetrahedron, are formed by combination of an s orbital (red) and three p orbitals (red/ blue). The sp3 hybrids have two lobes and are unsymmetrical about the nucleus, giving them a directionality and allowing them to form strong bonds to other atoms. Go to this book’s student companion site at www.cengage.com/chemistry/ mcmurry to explore an interactive version of this figure. ACTIVE FIGURE 1.11 Four sp3 hybrid orbitals (green), oriented to the corners of a regular tetrahedron, are formed by combination of an s orbital (red) and three p orbitals (red/ blue). The sp3 hybrids have two lobes and are unsymmetrical about the nucleus, giving them a directionality and allowing them to form strong bonds to other atoms. Go to this book’s student companion site at www.cengage.com/chemistry/ mcmurry to explore an interactive version of this figure. 39144_01_0001-0032.indd 12 7/27/09 1:28:39 PM
1.7 Sp3 HYBRID ORBITALS AND THE STRUCTURE OF ETHANE carbon forms fo so. sh our equivalen sts the tcal aboutthe uc eus.One of th e tw 1、1 rger ther orbitals d As ger bonds than do unhybridized s orr bitals The asymmetry of sp orbitals arises because.as noted and-TThus who orbital s with an s orbital.the positive p lobe adds to the s orbital but ther tive p lobe subtra rmmetrical about the nucleus and is strongly oriented in one direction When each of the four identical sp3 hybrid orbitals of a carbon atom overlaps with the 1s orbital of a hydrogen atom,four identical C-H bonds are formed and methane results.Each C-H bond in methane has a strength of 439 kJ/mol (105 kcal/mol)and a length of 109 pm.Because the four bonds have a specific geometry,we also can define a property called the bond angle.The angle formed by each H-C-H is 109.5,the so-called tetrahedral angle.Methane thus has the structure shown in Figure 1.12. FIGURE 1.12 The structure of owing its 109.5 7sp3 Hybrid Orbitals and the Structure of Ethane The same kind of orbital hybridization that accounts for the methane structure also accounts for the bonding together of carbon atoms into chains and rings to make possible many millions of organic compounds.Ethane,C2H6.is the simplest molecule containing a carbon-carbon bond: CH3CHa HH Some representations of ethane the othe by o overlap from eac 1.1 ogens to I rm the se in me ol2gha we 421 th the k f377 are near, value of 10 ugn not exa at.the tetr
The concept of hybridization explains how carbon forms four equivalent tetrahedral bonds but not why it does so. The shape of the hybrid orbital suggests the answer. When an s orbital hybridizes with three p orbitals, the resultant sp3 hybrid orbitals are unsymmetrical about the nucleus. One of the two lobes is much larger than the other and can therefore overlap more effectively with an orbital from another atom when it forms a bond. As a result, sp3 hybrid orbitals form stronger bonds than do unhybridized s or p orbitals. The asymmetry of sp3 orbitals arises because, as noted previously, the two lobes of a p orbital have different algebraic signs, and . Thus, when a p orbital hybridizes with an s orbital, the positive p lobe adds to the s orbital but the negative p lobe subtracts from the s orbital. The resultant hybrid orbital is therefore unsymmetrical about the nucleus and is strongly oriented in one direction. When each of the four identical sp3 hybrid orbitals of a carbon atom overlaps with the 1s orbital of a hydrogen atom, four identical C–H bonds are formed and methane results. Each C–H bond in methane has a strength of 439 kJ/mol (105 kcal/mol) and a length of 109 pm. Because the four bonds have a specific geometry, we also can define a property called the bond angle. The angle formed by each H–C–H is 109.5°, the so-called tetrahedral angle. Methane thus has the structure shown in Figure 1.12. H H H H Bond angle 109.5° Bond length C 109 pm 1.7 sp3 Hybrid Orbitals and the Structure of Ethane The same kind of orbital hybridization that accounts for the methane structure also accounts for the bonding together of carbon atoms into chains and rings to make possible many millions of organic compounds. Ethane, C2H6, is the simplest molecule containing a carbon–carbon bond: Some representations of ethane CH H H C H H H CH H H C CH H 3CH3 H H We can picture the ethane molecule by imagining that the two carbon atoms bond to each other by overlap of an sp3 hybrid orbital from each (Figure 1.13). The remaining three sp3 hybrid orbitals of each carbon overlap with the 1s orbitals of three hydrogens to form the six C–H bonds. The C–H bonds in ethane are similar to those in methane, although a bit weaker— 421 kJ/mol (101 kcal/mol) for ethane versus 439 kJ/mol for methane. The C–C bond is 154 pm long and has a strength of 377 kJ/mol (90 kcal/mol). All the bond angles of ethane are near, although not exactly at, the tetrahedral value of 109.5°. FIGURE 1.12 The structure of methane, showing its 109.5° bond angles. 1.7 sp3 hybrid orbitals and the structure of ethane 13 39144_01_0001-0032.indd 13 7/27/09 1:28:39 PM
14 CHAPTER 1 STRUCTURE AND BONDING FIGURE1.13 The structure of ethane.The carbon-carbon bond is formed by over sp3 hybrid orbitals are not show carbo Problem1.8 Draw a n bond structure CHaCH2CH3.Predict the value of each bond angle,and indicate the overa the following mo) model of hexane,a component of gasoline. into a line-bon structure (gray Hexane 1sp2 Hybrid Orbitals and the Structure of Ethylene Aoughsp'hbidzaionisthemoscononeehmesheotcabonts ylene ao avaler H2C=CH2 Top view Side view Some representations of ethylene When we discussed sp3 hybrid orbitals in Section 1.6.we said that the four valence-shell atomic orbitals of carbon combine to form four equivalent
14 chapter 1 structure and bonding Ethane C C C C 111.2 C C H H H H H H 154 pm sp3 carbon sp3 carbon sp3–sp3 bond Problem 1.8 Draw a line-bond structure for propane, CH3CH2CH3. Predict the value of each bond angle, and indicate the overall shape of the molecule. Problem 1.9 Convert the following molecular model of hexane, a component of gasoline, into a line-bond structure (gray C, ivory H). Hexane 1.8 sp2 Hybrid Orbitals and the Structure of Ethylene Although sp3 hybridization is the most common electronic state of carbon, it’s not the only possibility. Look at ethylene, C2H4, for example. It was recognized more than 100 years ago that ethylene carbons can be tetravalent only if they share four electrons and are linked by a double bond. Furthermore, ethylene is planar (flat) and has bond angles of approximately 120° rather than 109.5°. Some representations of ethylene C H H C H H C H H H H C C C H2C H H Top view H H Side view CH2 When we discussed sp3 hybrid orbitals in Section 1.6, we said that the four valence-shell atomic orbitals of carbon combine to form four equivalent FIGURE 1.13 The structure of ethane. The carbon–carbon bond is formed by overlap of two carbon sp3 hybrid orbitals. For clarity, the smaller lobes of the sp3 hybrid orbitals are not shown. FIGURE 1.13 The structure of ethane. The carbon–carbon bond is formed by overlap of two carbon sp3 hybrid orbitals. For clarity, the smaller lobes of the sp3 hybrid orbitals are not shown. 39144_01_0001-0032.indd 14 7/27/09 1:28:40 PM