ChAPTER 3 CONFORMATIONS OF ALKANES AND CYCLOALKANES H础c drogen peroxide is formed in the cells of plants and animals but is toxic to them onsequently, living systems have developed mechanisms to rid themselves of hydrogen peroxide, usually by enzyme-catalyzed reduction to water. An under- standing of how reactions take place, be they reactions in living systems or reactions in test tubes, begins with a thorough knowledge of the structure of the reactants, products, and catalysts. Even a simple molecule such as hydrogen peroxide may be structurally more complicated than you think. Suppose we wanted to write the structural formula for H2O2 in enough detail to show the positions of the atoms relative to one another. We could write two different planar geometries A and B that differ by a 180 rotation about the o-o bond. We could also write an infinite number of nonplanar structures, of which C is but one example, that differ from one another by tiny increments of rotation about the o-o bond Structures A, B, and C represent different conformations of hydrogen peroxide. informations are different spatial arrangements of a molecule that are generated by rotation about single bonds. Although we cant tell from simply looking at these struc- tures, we now know from experimental studies that C is the most stable conformation Back Forward Main MenuToc Study Guide ToC Student o MHHE Website
89 CHAPTER 3 CONFORMATIONS OF ALKANES AND CYCLOALKANES Hydrogen peroxide is formed in the cells of plants and animals but is toxic to them. Consequently, living systems have developed mechanisms to rid themselves of hydrogen peroxide, usually by enzyme-catalyzed reduction to water. An understanding of how reactions take place, be they reactions in living systems or reactions in test tubes, begins with a thorough knowledge of the structure of the reactants, products, and catalysts. Even a simple molecule such as hydrogen peroxide may be structurally more complicated than you think. Suppose we wanted to write the structural formula for H2O2 in enough detail to show the positions of the atoms relative to one another. We could write two different planar geometries A and B that differ by a 180° rotation about the O±O bond. We could also write an infinite number of nonplanar structures, of which C is but one example, that differ from one another by tiny increments of rotation about the O±O bond. Structures A, B, and C represent different conformations of hydrogen peroxide. Conformations are different spatial arrangements of a molecule that are generated by rotation about single bonds. Although we can’t tell from simply looking at these structures, we now know from experimental studies that C is the most stable conformation. A B C Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website
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
3. 1 Conformational Analysis of Ethane HH H (a) wedge-and-dash H H b) Sawhorse (b) Sawhorse H (c) Newman projection (c)Newman projection FIGURE 3.3 Some commonly used rep- resentations of the eclipsed conformation FIGURE 3.2 Some commonly used rep- resentations of the staggered conforma- PROBLEM 3. 1 Identify the alkanes corresponding to each of the drawings shown H CH3 CH2o H-H CH2CH3 SAMPLE SOLUTION (a)The Newman projection of this alkane resembles that of ethane except one of the hydrogens has been replaced by a methyl group. the drawing is a Newman projection of propane, CH3CH2 CH3 The structural feature that Figures 3. 2 and 3.3 illustrate is the spatial relationship between atoms on adjacent carbon atoms. Each H-C-C-H unit in ethane is charac- terized by a torsion angle or dihedral angle, which is the angle between the H-C Back Forward Main MenuToc Study Guide ToC Student o MHHE Website
PROBLEM 3.1 Identify the alkanes corresponding to each of the drawings shown. (a) (c) (b) (d) SAMPLE SOLUTION (a) The Newman projection of this alkane resembles that of ethane except one of the hydrogens has been replaced by a methyl group. The drawing is a Newman projection of propane, CH3CH2CH3. The structural feature that Figures 3.2 and 3.3 illustrate is the spatial relationship between atoms on adjacent carbon atoms. Each H±C±C±H unit in ethane is characterized by a torsion angle or dihedral angle, which is the angle between the H±C±C CH2CH3 CH2CH3 CH3 H H H CH3 H CH3 H H H H H H CH3 CH3 CH3 H H H H H CH3 3.1 Conformational Analysis of Ethane 91 H H H H H H (a) Wedge-and-dash H H H H H H (b) Sawhorse H H H H H H (c) Newman projection H H H H H (a) Wedge-and-dash H H H (b) Sawhorse H H H H H (c) Newman projection H H H H H FIGURE 3.2 Some commonly used representations of the staggered conformation of ethane. FIGURE 3.3 Some commonly used representations of the eclipsed conformation of ethane. 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