《有机化学》课程教学资源（教材文献，英文版）CHAPTER 3 CONFORMATIONS OF ALKANES AND CYCLOALKANES.pdf_大学文库

CHAPTER THREE Conformations of Alkanes and Cycloalkanes In this chapter we'll examine the conformations of various alkanes and cycloal kanes. focusing most of our attention on three of them: ethane, butane and cyclohexane. ng A detailed study of even these three will take us a long way toward understand bond in hydrogen peroxide main ideas of conformational analysis. The conformation of a molecule affects many of its properties. Conformational analysis is a tool used not only by chemists but also by researchers in the life sciences as they attempt to develop a clearer picture of how molecules--as simple as hydrogen peroxide or as complicated as DNA--behave in biological processes 3.1 CONFORMATIONAL ANALYSIS OF ETHANE Ethane is the simplest hydrocarbon that can have distinct conformations. Two, the staggered conformation and the eclipsed conformation, deserve special attention and are illustrated in Figure 3. 1. The C-H bonds in the staggered conformation are arranged so that each one bisects the angle made by a pair of C-H bonds on the adjacent car- bon. In the eclipsed conformation each C-H bond is aligned with a C-H bond on the adjacent carbon. The staggered and eclipsed conformations interconvert by rotation around the carbon-carbon bond. Different conformations of the same molecule are some times called conformers or rotamers Among the various ways in which the staggered and eclipsed forms are portrayed wedge-and-dash, sawhorse, and Newman projection drawings are especially usefuL. These are shown for the staggered conformation of ethane in Figure 3.2 and for the eclipsed conformation in Figure 3.3 We used wedge-and-dash drawings in earlier chapters, and so Figures 3. 2a and 3.3a are familiar to us. A sawhorse drawing( Figures 3.2b and 3.3b) shows the conformation of a molecule without having to resort to different styles of bonds. In a devised by Professor Melvin Newman projection(Figures 3.2c and 3.3c), we sight down the C-C bond, and repre- Newman of Ohio State sent the front carbon by a point and the back carbon by a circle. Each carbon has three University in the 1950s. substituents that are placed symmetrically around it. Eclipsed conformation of ethane FIGURE 3.1 The stag ered and eclipsed conf mations of ethane shown as ball-and-spoke models (left) and as space-filling models (right) Back Forward Main MenuToc Study Guide ToC Student o MHHE Website

In this chapter we’ll examine the conformations of various alkanes and cycloalkanes, focusing most of our attention on three of them: ethane, butane, and cyclohexane. A detailed study of even these three will take us a long way toward understanding the main ideas of conformational analysis. The conformation of a molecule affects many of its properties. Conformational analysis is a tool used not only by chemists but also by researchers in the life sciences as they attempt to develop a clearer picture of how molecules—as simple as hydrogen peroxide or as complicated as DNA—behave in biological processes. 3.1 CONFORMATIONAL ANALYSIS OF ETHANE Ethane is the simplest hydrocarbon that can have distinct conformations. Two, the staggered conformation and the eclipsed conformation, deserve special attention and are illustrated in Figure 3.1. The C±H bonds in the staggered conformation are arranged so that each one bisects the angle made by a pair of C±H bonds on the adjacent carbon. In the eclipsed conformation each C±H bond is aligned with a C±H bond on the adjacent carbon. The staggered and eclipsed conformations interconvert by rotation around the carbon–carbon bond. Different conformations of the same molecule are sometimes called conformers or rotamers. Among the various ways in which the staggered and eclipsed forms are portrayed, wedge-and-dash, sawhorse, and Newman projection drawings are especially useful. These are shown for the staggered conformation of ethane in Figure 3.2 and for the eclipsed conformation in Figure 3.3. We used wedge-and-dash drawings in earlier chapters, and so Figures 3.2a and 3.3a are familiar to us. A sawhorse drawing (Figures 3.2b and 3.3b) shows the conformation of a molecule without having to resort to different styles of bonds. In a Newman projection (Figures 3.2c and 3.3c), we sight down the C±C bond, and represent the front carbon by a point and the back carbon by a circle. Each carbon has three substituents that are placed symmetrically around it. 90 CHAPTER THREE Conformations of Alkanes and Cycloalkanes Eclipsed conformation of ethane Staggered conformation of ethane FIGURE 3.1 The staggered and eclipsed conformations of ethane shown as ball-and-spoke models (left) and as space-filling models (right). Newman projections were devised by Professor Melvin S. Newman of Ohio State University in the 1950s. Learning By Modeling contains an animation showing the rotation about the O±O bond in hydrogen peroxide. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website

CHAPTER THREE Conformations of Alkanes and Cycloalkanes plane and the C-C-H plane. The torsion angle is easily seen in a Newman projection of ethane as the angle between C-H bonds of adjacent carbons H Torsion angle=60° Eclipsed bonds are characterized by a torsion angle of 0. when the torsion angle is approximately 60, we say that the spatial relationship is gauche; and when it is 180 we say that it is anti. Staggered conformations have only gauche or anti relationships between bonds on adjacent atoms Of the two conformations of ethane, the staggered is more stable than the eclipsed The measured difference in potential energy between them is 12 kJ/mol(2.9 kcal/mol) A simple explanation has echoes of VSEPR(Section 1.10). The staggered conformation allows the electron pairs in the C-H bonds of one carbon to be farther away from the electron pairs in the C-H bonds of the other than the eclipsed conformation allows Electron-pair repulsions on adjacent carbons govern the relative stability of staggered and eclipsed conformations in much the same way that electron-pair repulsions influence the bond angles at a central atom. he destabilization that comes from eclipsed bonds on adjacent atoms is called torsional strain. Torsional strain is one of several structural features resulting from its three-dimensional makeup that destabilize a molecule. The total strain of all of the spa Steric is derived from the tially dependent features is often called steric strain. Because three pairs of eclipsed Greek word stere bonds produce 12 kJ/mol (2.9 kcal/mol) of torsional strain in ethane, it is reasonable to "solid" and refers to the assign an"energy cost"of 4 kJ/mol (1 kcal/mol) to each pair of eclipsed bonds three-dimensional or spatial aspects of chemistry. In principle there are an infinite number of conformations of ethane, differing by only tiny increments in their torsion angles. Not only is the staggered conformation more stable than the eclipsed, it is the most stable of all of the conformations; the eclipsed is the least stable. Figure 3. 4 shows how the potential energy of ethane changes for a 360 rotation about the carbon-carbon bond. Three equivalent eclipsed conformations and The animation on the three equivalent staggered conformations occur during the 360 rotation; the eclipsed earning By Modeling CD shows conformations appear at the highest points on the curve(potential energy maxima), the rotation about the c- taggered ones at the lowest (potential energy minima) TPROBLEM 3.2 Find the conformations in Figure 3.4 in which the red circles arc L(a) gauche and(b)anti Diagrams such as Figure 3. 4 can be quite helpful for understanding how the pot tial energy of a system changes during a process. The process can be a simple one such as the one described here--rotation around a carbon-carbon bond. Or it might be more complicated-a chemical reaction, for example. We will see applications of potentia energy diagrams to a variety of processes throughout the text. Let's focus our attention on a portion of Figure 3. 4. The region that lies between a torsion angle of 60o and 180o tracks the conversion of one staggered conformation of Back Forward Main MenuToc Study Guide ToC Student o MHHE Website

plane and the C±C±H plane. The torsion angle is easily seen in a Newman projection of ethane as the angle between C±H bonds of adjacent carbons. Eclipsed bonds are characterized by a torsion angle of 0°. When the torsion angle is approximately 60°, we say that the spatial relationship is gauche; and when it is 180° we say that it is anti. Staggered conformations have only gauche or anti relationships between bonds on adjacent atoms. Of the two conformations of ethane, the staggered is more stable than the eclipsed. The measured difference in potential energy between them is 12 kJ/mol (2.9 kcal/mol). A simple explanation has echoes of VSEPR (Section 1.10). The staggered conformation allows the electron pairs in the C±H bonds of one carbon to be farther away from the electron pairs in the C±H bonds of the other than the eclipsed conformation allows. Electron-pair repulsions on adjacent carbons govern the relative stability of staggered and eclipsed conformations in much the same way that electron-pair repulsions influence the bond angles at a central atom. The destabilization that comes from eclipsed bonds on adjacent atoms is called torsional strain. Torsional strain is one of several structural features resulting from its three-dimensional makeup that destabilize a molecule. The total strain of all of the spatially dependent features is often called steric strain. Because three pairs of eclipsed bonds produce 12 kJ/mol (2.9 kcal/mol) of torsional strain in ethane, it is reasonable to assign an “energy cost” of 4 kJ/mol (1 kcal/mol) to each pair of eclipsed bonds. In principle there are an infinite number of conformations of ethane, differing by only tiny increments in their torsion angles. Not only is the staggered conformation more stable than the eclipsed, it is the most stable of all of the conformations; the eclipsed is the least stable. Figure 3.4 shows how the potential energy of ethane changes for a 360° rotation about the carbon–carbon bond. Three equivalent eclipsed conformations and three equivalent staggered conformations occur during the 360° rotation; the eclipsed conformations appear at the highest points on the curve (potential energy maxima), the staggered ones at the lowest (potential energy minima). PROBLEM 3.2 Find the conformations in Figure 3.4 in which the red circles are (a) gauche and (b) anti. Diagrams such as Figure 3.4 can be quite helpful for understanding how the potential energy of a system changes during a process. The process can be a simple one such as the one described here—rotation around a carbon–carbon bond. Or it might be more complicated—a chemical reaction, for example. We will see applications of potential energy diagrams to a variety of processes throughout the text. Let’s focus our attention on a portion of Figure 3.4. The region that lies between a torsion angle of 60° and 180° tracks the conversion of one staggered conformation of Torsion angle 180° Anti H H 180° Torsion angle 60° Gauche H H 60° Torsion angle 0° Eclipsed HH 0° 92 CHAPTER THREE Conformations of Alkanes and Cycloalkanes Steric is derived from the Greek word stereos for “solid” and refers to the three-dimensional or spatial aspects of chemistry. The animation on the Learning By Modeling CD shows rotation about the C±C bond in ethane. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website

3. 1 Conformational Analysis of Ethane 55:5 FIGURE 3. 4 Potential energy diagram for rotation about the carbon -carbon bond in ethane. two of the hydrogens are shown in re and four in green so as 2.9 kcal/m 12 k/mol ei dicate more clearly the bond Torsion angl ethane to the next one. Both staggered conformations are equivalent and equal in energy, out for one staggered conformation to get to the next, it must first pass through an eclipsed conformation and needs to gain 12 kJ/mol (2.9 kcal/mol) of energy to reach it. This amount of energy is the activation energy(Eact) for the process. Molecules must become energized in order to undergo a chemical reaction or, as in this case, to undergo rotation around a carbon-carbon bond. Kinetic(thermal)energy is absorbed by a mole cule from collisions with other molecules and is transformed into potential energy. When instant can relr rgy exceeds Eact, the unstable arrangement of atoms that exists at that the potential er lisions with other molecules or with the walls of a container. The point of maximum potential energy encountered by the reactants as they proceed to products is called the transition state. The eclipsed conformation is the transition state for the conversion of The structure that exists at one staggered conformation of ethane to another the transition state is some. Rotation around carbon-carbon bonds is one of the fastest processes in chemistry. times referred to as the tran- Among the ways that we can describe the rate of a process is by its half-life, which is activated compler the length of time it takes for one half of the molecules to react It takes less than 10-6 econds for half of the molecules in a sample of ethane to go from one staggered con- formation to another at 25C. At any instant, almost all of the molecules are in staggered onformations; hardly any are in eclipsed conformations As with all chemical processes, the rate of rotation about the carbon-carbon bond increases with temperature. The reason for this can be seen by inspecting Figure 3.5, where it can be seen that most of the molecules in a sample have energies that are clus- tered around some average value; some have less energy, a few have more. Only mole- cules with a potential energy greater than Eact, however, are able to go over the transi- tion state and proceed on to products. The number of these molecules is given by the shaded areas under the curve in Figure 3. 5. The energy distribution curve flattens out at higher temperatures, and a greater proportion of molecules have energies in excess of Eact at T2(higher) than at TI(lower). The effect of temperature is quite pronounced; an increase of only 10oC produces a two-to threefold increase in the rate of a typical chem Back Forward Main MenuToc Study Guide ToC Student o MHHE Website

ethane to the next one. Both staggered conformations are equivalent and equal in energy, but for one staggered conformation to get to the next, it must first pass through an eclipsed conformation and needs to gain 12 kJ/mol (2.9 kcal/mol) of energy to reach it. This amount of energy is the activation energy (Eact) for the process. Molecules must become energized in order to undergo a chemical reaction or, as in this case, to undergo rotation around a carbon–carbon bond. Kinetic (thermal) energy is absorbed by a molecule from collisions with other molecules and is transformed into potential energy. When the potential energy exceeds Eact, the unstable arrangement of atoms that exists at that instant can relax to a more stable structure, giving off its excess potential energy in collisions with other molecules or with the walls of a container. The point of maximum potential energy encountered by the reactants as they proceed to products is called the transition state. The eclipsed conformation is the transition state for the conversion of one staggered conformation of ethane to another. Rotation around carbon–carbon bonds is one of the fastest processes in chemistry. Among the ways that we can describe the rate of a process is by its half-life, which is the length of time it takes for one half of the molecules to react. It takes less than 106 seconds for half of the molecules in a sample of ethane to go from one staggered conformation to another at 25°C. At any instant, almost all of the molecules are in staggered conformations; hardly any are in eclipsed conformations. As with all chemical processes, the rate of rotation about the carbon–carbon bond increases with temperature. The reason for this can be seen by inspecting Figure 3.5, where it can be seen that most of the molecules in a sample have energies that are clustered around some average value; some have less energy, a few have more. Only molecules with a potential energy greater than Eact, however, are able to go over the transition state and proceed on to products. The number of these molecules is given by the shaded areas under the curve in Figure 3.5. The energy distribution curve flattens out at higher temperatures, and a greater proportion of molecules have energies in excess of Eact at T2 (higher) than at T1 (lower). The effect of temperature is quite pronounced; an increase of only 10°C produces a two- to threefold increase in the rate of a typical chemical process. 3.1 Conformational Analysis of Ethane 93 Potential energy, kcal/mol Potential energy, kJ/mol 0 60 120 180 240 300 360 Torsion angle, 3 2 1 0 12 8 4 0 2.9 kcal/mol 12 kJ/mol The structure that exists at the transition state is sometimes referred to as the transition structure or the activated complex. FIGURE 3.4 Potential energy diagram for rotation about the carbon–carbon bond in ethane. Two of the hydrogens are shown in red and four in green so as to indicate more clearly the bond rotation. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website

CHAPTER THREE Conformations of Alkanes and Cycloalkanes MOLECULAR MECHANICS APPLIED TO ALKANES AND CYCLOALKANES f the numerous applications of computer Nonbonded interactions are the forces be technology to chemistry, one that has been tween atoms that aren't bonded to one another; enthusiastically embraced by organic chemists they may be either attractive or repulsive. It often examines molecular structure from a perspective sim- happens that the shape of a molecule may cause two ilar to that gained by manipulating molecular models atoms to be close in space even though they are sep- but with an additional quantitative dimension. Mo- arated from each other by many bonds. Induced- ecular mechanics is a computational method that dipole/induced-dipole interactions make van der allows us to assess the stability of a molecule by com- Waals forces in alkanes weakly attractive at most dis- paring selected features of its structure with those of tances, but when two atoms are closer to each other ideal "unstrained" standards. molecular mechanics than the sum of their van der waals radii makes no attempt to explain why the van der Waals nuclear-nuclear and electron-electron repulsive radius of hydrogen is 120 pm, why the bond angles in forces between them dominate the evan der waals term methane are 109.5, why the C-C bond distance in The resulting destabilization is called van der Waals ethane is 153 pm, or why the staggered conforma- strain tion of ethane is 12 k/mol more stable than the At its most basic level, separating the tota eclipsed, but instead uses these and other experi- strain of a structure into its components is a qualita nental observations as benchmarks to which the cor- tive exercise. For example, a computer-drawn model responding features of other substances are com- of the eclipsed conformation of butane using ideal bond angles and bond distances( Figure 3.8) reveals If we assume that there are certain"ideal"val- that two pairs of hydrogens are separated by ues for bond angles, bond distances, and so on, it fol- a distance of only 175 pm, a value considerably lows that deviations from these ideal values will smaller than the sum of their van der Waals radii destabilize a particular structure and increase its po-(2 120 pm 240 pm). Thus, this conformation is tential energy. this increase in potential energy is re- destabilized not only by the torsional strain associ- ferred to as the strain energy of the structure. other ated with its eclipsed bonds but also by van der terms include steric energy and steric strain Arith- Waals strain metically, the total strain energy(Es)of an alkane or At a higher level, molecular mechanics is ap. cycloalkane can be considered as plied quantitatively to strain energy calculations. Each component of strain is separately described by a Es= Bond stretching Eangle bending Torsional mathematical expression developed and refined so that it gives solutions that match experimental obser vations for reference molecules. These empirically d rived and tested expressions are then used to calcu- Bond stretching is the strain that results when C-c late the most stable structure of a substance. The and C-H bond distances are distorted from various structural features are interdependent; van their ideal values of 153 pm and 111 pm, re- der Waals strain, for example, might be decreased at the expense of introducing some angle strain, tor Anole bending is the strain that results from the ex- sional strain, or both. The computer program normal values of 109.5 for sp hybridized ces,torsion angles, and nonbonded interac carbon tions that gives the molecule the lowest total strain Torsional is the strain that results from deviation of This procedure is called strain energy minimization torsion angles from their stable staggered rela- and is based on the commonsense notion that the tionship most stable structure is the one that has the least straIn Evan der waals is the strain that results from"non- bonded interactions -Cont Back Forward Main MenuToc Study Guide ToC Student o MHHE Website

96 CHAPTER THREE Conformations of Alkanes and Cycloalkanes MOLECULAR MECHANICS APPLIED TO ALKANES AND CYCLOALKANES Of the numerous applications of computer technology to chemistry, one that has been enthusiastically embraced by organic chemists examines molecular structure from a perspective similar to that gained by manipulating molecular models but with an additional quantitative dimension. Molecular mechanics is a computational method that allows us to assess the stability of a molecule by comparing selected features of its structure with those of ideal “unstrained” standards. Molecular mechanics makes no attempt to explain why the van der Waals radius of hydrogen is 120 pm, why the bond angles in methane are 109.5°, why the C±C bond distance in ethane is 153 pm, or why the staggered conformation of ethane is 12 kJ/mol more stable than the eclipsed, but instead uses these and other experimental observations as benchmarks to which the corresponding features of other substances are compared. If we assume that there are certain “ideal” values for bond angles, bond distances, and so on, it follows that deviations from these ideal values will destabilize a particular structure and increase its potential energy. This increase in potential energy is referred to as the strain energy of the structure. Other terms include steric energy and steric strain. Arithmetically, the total strain energy (Es) of an alkane or cycloalkane can be considered as Es Ebond stretching Eangle bending Etorsional Evan der Waals where Ebond stretching is the strain that results when C±C and C±H bond distances are distorted from their ideal values of 153 pm and 111 pm, respectively. Eangle bending is the strain that results from the expansion or contraction of bond angles from the normal values of 109.5° for sp3 hybridized carbon. Etorsional is the strain that results from deviation of torsion angles from their stable staggered relationship. Evan der Waals is the strain that results from “nonbonded interactions.” Nonbonded interactions are the forces between atoms that aren’t bonded to one another; they may be either attractive or repulsive. It often happens that the shape of a molecule may cause two atoms to be close in space even though they are separated from each other by many bonds. Induceddipole/induced-dipole interactions make van der Waals forces in alkanes weakly attractive at most distances, but when two atoms are closer to each other than the sum of their van der Waals radii, nuclear–nuclear and electron–electron repulsive forces between them dominate the Evan der Waals term. The resulting destabilization is called van der Waals strain. At its most basic level, separating the total strain of a structure into its components is a qualitative exercise. For example, a computer-drawn model of the eclipsed conformation of butane using ideal bond angles and bond distances (Figure 3.8) reveals that two pairs of hydrogens are separated by a distance of only 175 pm, a value considerably smaller than the sum of their van der Waals radii (2 120 pm 240 pm). Thus, this conformation is destabilized not only by the torsional strain associated with its eclipsed bonds, but also by van der Waals strain. At a higher level, molecular mechanics is applied quantitatively to strain energy calculations. Each component of strain is separately described by a mathematical expression developed and refined so that it gives solutions that match experimental observations for reference molecules. These empirically derived and tested expressions are then used to calculate the most stable structure of a substance. The various structural features are interdependent; van der Waals strain, for example, might be decreased at the expense of introducing some angle strain, torsional strain, or both. The computer program searches for the combination of bond angles, distances, torsion angles, and nonbonded interactions that gives the molecule the lowest total strain. This procedure is called strain energy minimization and is based on the commonsense notion that the most stable structure is the one that has the least strain. —Cont. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website

3.3 Conformations of Higher Alkanes The first widely used molecular mechanics pro- that molecular mechanics is no longer considered a gram was developed by Professor N L Allinger of the novelty but rather as one more tool to be used by the University of Georgia and was known in its various practicing organic chemist. They have been joined by versions as MM2, MM3, and so on. they have been re- programs that calculate the energies of conforma- fined to the extent that many structural features can tions by molecular orbital methods. The Learning by be calculated more easily and more accurately than Modeling CD that accompanies this text contains hey can be measured experimentally molecular mechanics software that lets you seek out Once requiring minicomputers and worksta. the most stable conformation of the structures you tions, many molecular mechanics programs are avail- assemble. It also contains the most stable conforma- strain energy calculations can provide is so helpful orbital calculations les as determined by molecular FIGURE 3.8 Ball-and-spoke and space-filling models of methyl-methyl eclipsed conformation of butane. 3.3 CONFORMATIONS OF HIGHER ALKANES Higher alkanes having unbranched carbon chains are like butane most stable in their all-anti conformations. The energy difference between gauche and anti conformations is similar to that of butane, and appreciable quantities of the gauche conformation are present in liquid alkanes at 25C. In depicting the conformations of higher alkanes it is often more helpful to look at them from the side rather than end-on as in a Newman projection. Viewed from this perspective, the most stable conformations of pentane and hexane have their carbon ""backbones"arranged in a zigzag fashion, as shown in Figure 3.9. All the bonds are staggered, and the chains are characterized by anti arrangements 68 Hexane FIGURE 3.9 Ball-and-spoke models of pentane and hexane in their all-anti (zigzag)con- Back Forward Main MenuToc Study Guide ToC Student o MHHE Website

3.3 Conformations of Higher Alkanes 97 The first widely used molecular mechanics program was developed by Professor N. L. Allinger of the University of Georgia and was known in its various versions as MM2, MM3, and so on. They have been re- fined to the extent that many structural features can be calculated more easily and more accurately than they can be measured experimentally. Once requiring minicomputers and workstations, many molecular mechanics programs are available for personal computers. The information that strain energy calculations can provide is so helpful that molecular mechanics is no longer considered a novelty but rather as one more tool to be used by the practicing organic chemist. They have been joined by programs that calculate the energies of conformations by molecular orbital methods. The Learning By Modeling CD that accompanies this text contains molecular mechanics software that lets you seek out the most stable conformation of the structures you assemble. It also contains the most stable conformations of some molecules as determined by molecular orbital calculations. 3.3 CONFORMATIONS OF HIGHER ALKANES Higher alkanes having unbranched carbon chains are, like butane, most stable in their all-anti conformations. The energy difference between gauche and anti conformations is similar to that of butane, and appreciable quantities of the gauche conformation are present in liquid alkanes at 25°C. In depicting the conformations of higher alkanes it is often more helpful to look at them from the side rather than end-on as in a Newman projection. Viewed from this perspective, the most stable conformations of pentane and hexane have their carbon “backbones” arranged in a zigzag fashion, as shown in Figure 3.9. All the bonds are staggered, and the chains are characterized by anti arrangements of C±C±C±C units. Pentane Hexane FIGURE 3.8 Ball-and-spoke and space-filling models of methyl-methyl eclipsed conformation of butane. FIGURE 3.9 Ball-and-spoke models of pentane and hexane in their all-anti (zigzag) conformations. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website

CHAPTER THREE Conformations of Alkanes and Cycloalkanes 3. 4 THE SHAPES OF CYCLOALKANES: PLANAR OR NONPLANAR? During the nineteenth century it was widely believed--incorrectly, as we'lI soon see- that cycloalkane rings are planar. A leading advocate of this view was the German chemist Adolf von Baeyer. He noted that compounds containing rings other than those based on cyclopentane and cyclohexane were rarely encountered naturally and were dif- ficult to synthesize. Baeyer connected both observations with cycloalkane stability, which he suggested was related to how closely the angles of planar rings match the tetrahedral value of 109.5. For example, the 60 bond angle of cyclopropane and the 90 bond angles of a planar cyclobutane ring are much smaller than the tetrahedral angle of 109.5 Baeyer suggested that three- and four-membered rings suffer from what we now call angle strain. Angle strain is the strain a molecule has because one or more of its bond angles deviate from the ideal value; in the case of alkanes the ideal value is 109.5 Although better known now According to Baeyer, cyclopentane should be the most stable of all the cycloal rrect theory that kanes because the ring angles of a planar pentagon, 1080, are closer to the tetrahedra e plan Baeyer was responsible for angle than those of any other cycloalkane. A prediction of the Baeyer strain theory notable advances in the that the cycloalkanes beyond cyclopentane should become increasingly strained and cor respondingly less stable. The angles of a regular hexagon are 1200, and the angles of larger polygons deviate more and more from the ideal tetrahedral angle warded the 1905 Nobel Prize in chemistry for his Some of the inconsistencies in the Baeyer strain theory will become evident as ork in that area use heats of combustion (Table 3. 1)to probe the relative energies of cycloalkanes most important column in the table is the heat of combustion per methylene(CH2) group Since all of the cycloalkanes have molecular formulas of the type CnH2n. dividing the heat of combustion by n allows direct comparison of ring size and potential energy Cyclopropane has the highest heat of combustion per methylene group, which is con- sistent with the idea that its potential energy is raised by angle strain. Cyclobutane has less angle strain at each of its carbon atoms and a lower heat of combustion per meth- ylene group. Cyclopentane, as expected, has a lower value still Notice, however, that ontrary to the prediction of the Baeyer strain theory, cyclohexane has a smaller heat of combustion per methylene group than cyclopentane. If bond angle distortion were greater in cyclohexane than in cyclopentane, the opposite would have been observed TABLE 3.1 Heats of Combustion(-AHo)of Cycloalkanes Heat of combustion Heat of combustion per CH2 group Number of Cycloalkane CH2 groups kJ/mol (kcal/mol) kJ/mol (kcal/mol) Cyclo (499.8) 697 (166.6) Cyclobutane (650.3) 681 1627) Cyclopentane 3.291 (786.6 658 (157.3) Cyclohexane 3.920 (936.8) 653 (156.0 Cycloheptane 3456789 599(1099.2) 657 (157.0) Cyclooctane 5,26712588) 658 (157.3) Cyclononane 5933(14180) 659 (157.5) Cyclodecane 659 (157.5) Cycloundecane 7,237(17298 658 (157.3) Cyclododecane 7,845(1875.1) 654 (156.3) Cyclotetradecane 9139(2184.2) 653 (156.0) Cyclohexadecane 10.46 (2501.4) 654 (156.3) Back Forward Main MenuToc Study Guide ToC Student o MHHE Website

3.4 THE SHAPES OF CYCLOALKANES: PLANAR OR NONPLANAR? During the nineteenth century it was widely believed—incorrectly, as we’ll soon see— that cycloalkane rings are planar. A leading advocate of this view was the German chemist Adolf von Baeyer. He noted that compounds containing rings other than those based on cyclopentane and cyclohexane were rarely encountered naturally and were dif- ficult to synthesize. Baeyer connected both observations with cycloalkane stability, which he suggested was related to how closely the angles of planar rings match the tetrahedral value of 109.5°. For example, the 60° bond angle of cyclopropane and the 90° bond angles of a planar cyclobutane ring are much smaller than the tetrahedral angle of 109.5°. Baeyer suggested that three- and four-membered rings suffer from what we now call angle strain. Angle strain is the strain a molecule has because one or more of its bond angles deviate from the ideal value; in the case of alkanes the ideal value is 109.5°. According to Baeyer, cyclopentane should be the most stable of all the cycloalkanes because the ring angles of a planar pentagon, 108°, are closer to the tetrahedral angle than those of any other cycloalkane. A prediction of the Baeyer strain theory is that the cycloalkanes beyond cyclopentane should become increasingly strained and correspondingly less stable. The angles of a regular hexagon are 120°, and the angles of larger polygons deviate more and more from the ideal tetrahedral angle. Some of the inconsistencies in the Baeyer strain theory will become evident as we use heats of combustion (Table 3.1) to probe the relative energies of cycloalkanes. The most important column in the table is the heat of combustion per methylene (CH2) group. Since all of the cycloalkanes have molecular formulas of the type CnH2n, dividing the heat of combustion by n allows direct comparison of ring size and potential energy. Cyclopropane has the highest heat of combustion per methylene group, which is consistent with the idea that its potential energy is raised by angle strain. Cyclobutane has less angle strain at each of its carbon atoms and a lower heat of combustion per methylene group. Cyclopentane, as expected, has a lower value still. Notice, however, that contrary to the prediction of the Baeyer strain theory, cyclohexane has a smaller heat of combustion per methylene group than cyclopentane. If bond angle distortion were greater in cyclohexane than in cyclopentane, the opposite would have been observed. 98 CHAPTER THREE Conformations of Alkanes and Cycloalkanes TABLE 3.1 Heats of Combustion (H°) of Cycloalkanes Heat of combustion per CH2 group Cycloalkane Cyclopropane Cyclobutane Cyclopentane Cyclohexane Cycloheptane Cyclooctane Cyclononane Cyclodecane Cycloundecane Cyclododecane Cyclotetradecane Cyclohexadecane Number of CH2 groups 3 4 5 6 7 8 9 10 11 12 14 16 Heat of combustion kJ/mol 2,091 2,721 3,291 3,920 4,599 5,267 5,933 6,587 7,237 7,845 9,139 10,466 (kcal/mol) (499.8) (650.3) (786.6) (936.8) (1099.2) (1258.8) (1418.0) (1574.3) (1729.8) (1875.1) (2184.2) (2501.4) kJ/mol 697 681 658 653 657 658 659 659 658 654 653 654 (kcal/mol) (166.6) (162.7) (157.3) (156.0) (157.0) (157.3) (157.5) (157.5) (157.3) (156.3) (156.0) (156.3) Although better known now for his incorrect theory that cycloalkanes were planar, Baeyer was responsible for notable advances in the chemistry of organic dyes such as indigo and was awarded the 1905 Nobel Prize in chemistry for his work in that area. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website