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Conformations of Alkanes: Rotation About Carbon–Carbon Bonds

We have seen that a carbon–carbon single bond (a ϭ bond) is formed when an sp3 orbital of one carbon overlaps an sp3 orbital of a second carbon (Section 1.7). Because ϭ bonds are cylindrically symmetrical (i.e., symmetrical about an imaginary line connecting the centers of the two atoms joined by the ϭ bond), rotation about a carbon–carbon single bond can occur without any change in the amount of orbital overlap (Figure 2.3). The different spatial arrangements of the atoms that result from rotation about a single bond are called conformations. A specific conformation is called a conformer.
carbon–carbon single bond

Figure 2.3 A carbon–carbon bond is formed by the overlap of cylindrically symmetrical sp3 orbitals. Therefore, rotation about the bond can occur without changing the amount of orbital overlap.

When rotation occurs about the carbon–carbon bond of ethane, two extreme conformations can result-a staggered conformation and an eclipsed conformation. An infinite number of conformations between these two extremes are also possible. Compounds are three dimensional, but we are limited to a two-dimensional sheet of paper when we show their structures. Perspective formulas, sawhorse projections, and Newman projections are methods chemists commonly use to represent on paper the three-dimensional spatial arrangements of the atoms that result from rotation about a ϭ bond. In a perspective formula, solid lines are used for bonds that lie in the plane of the paper, solid wedges for bonds protruding out from the plane of the paper, and hatched wedges for bonds extending behind the paper. In a sawhorse projection, you are looking at the carbon–carbon bond from an oblique angle. In a Newman projection, you are looking down the length of a particular carbon–carbon bond. The carbon in front is represented by the point at which three bonds intersect, and the carbon in back is represented by a circle. The three lines emanating from each of the carbons represent its other three bonds. In discussing the conformations of alkanes, we will use Newman projections because they are easy to draw and they do a good job of representing the spatial relationships of the substituents on the two carbon atoms.
“Melvin S. Newman (1908–1993) was born in New York. He received a Ph.D. from Yale University in 1932 and was a professor of chemistry at Ohio State University from 1936 to 1973.”
ethane staggered conformation and eclipsed conformation
The electrons in a C-H bond will repel the electrons in another C-H bond if the bonds get too close to each other. The staggered conformation, therefore, is the most stable conformation of ethane because the C-H bonds are as far away from each other as possible. The eclipsed conformation is the least stable conformation because in no other conformation are the C-H bonds as close to one another. The extra energy of the eclipsed conformation is called torsional strain. Torsional strain is the name given to the repulsion felt by the bonding electrons of one substituent as they pass close to the bonding electrons of another substituent. The investigation of the various conformations of a compound and their relative stabilities is called conformational analysis. Rotation about a carbon–carbon single bond is not completely free because of the energy difference between the staggered and eclipsed conformers. The eclipsed conformer is higher in energy, so an energy barrier must be overcome when rotation about the carbon–carbon bond occurs (Figure 2.4). However, the barrier in ethane is small enough (2.9 kcal mol or 12 kJ mol) to allow the conformers to interconvert millions of times per second at room temperature. Because the conformers interconvert, they cannot be separated.
potential energy of ethane

Figure 2.4 Potential energy of ethane as a function of the angle of rotation about the carbon–carbon bond.

Figure 2.4 shows the potential energies of all the conformers of ethane obtained during one complete 360° rotation. Notice that the staggered conformers are at energy minima, whereas the eclipsed conformers are at energy maxima. Butane has three carbon–carbon single bonds, and the molecule can rotate about each of them. In the following figure, staggered and eclipsed conformers are drawn for rotation about the C-1¬C-2 bond:
butane staggered and eclipsed conformation
Note that the carbon in the foreground in a Newman projection has the lower number. Although the staggered conformers resulting from rotation about the C-1¬C-2 bond in butane all have the same energy, the staggered conformers resulting from rotation about the C-2¬C-3 bond do not have the same energy. The staggered conformers for rotation about the C-2¬C-3 bond in butane are shown below.
staggered conformers for rotation about the C-2¬C-3 bond in butane
Conformer D, in which the two methyl groups are as far apart as possible, is more stable than the other two staggered conformers (B and F). The most stable of the staggered conformers (D) is called the anti conformer, and the other two staggered conformers (B and F) are called gauche (“goesh”) conformers. (Anti is Greek for “opposite of ”; gauche is French for “left.”) In the anti conformer, the largest substituents are opposite each other; in a gauche conformer, they are adjacent. The two gauche conformers have the same energy, but each is less stable than the anti conformer. Anti and gauche conformers do not have the same energy because of steric strain. Steric strain is the train (i.e., the extra energy) put on a molecule when atoms or groups are too close to one another, which results in repulsion between the electron clouds of these atoms or groups. For example, there is more steric strain in a gauche conformer than in the anti conformer because the two methyl groups are closer together in a gauche conformer. This type of steric strain is called a gauche interaction.
potential energy of butane

Figure 2.5 Potential energy of butane as a function of the degree of rotation about the C-2¬C-3 bond. Green letters refer to the conformers (A–F) shown on page 90.

The eclipsed conformers resulting from rotation about the C-2¬C-3 bond in butane also have different energies. The eclipsed conformer in which the two methyl groups are closest to each other (A) is less stable than the eclipsed conformers in which they are farther apart (C and E). The energies of the conformers obtained from rotation about the C-2¬C-3 bond of butane are shown in Figure 2.5. (The dihedral angle is the angle between the CH3¬C¬C and C¬C¬CH3 planes. Therefore, the conformer in which one methyl group stands directly in front of the other—the least stable conformer—has a dihedral angle of 0°.) All the eclipsed conformers have both torsional and steric strain—torsional strain due to bond–bond repulsion and steric strain due to the closeness of the groups. In general, steric strain in molecules increases as the size of the group increases. Because there is continuous rotation about all the carbon–carbon single bonds in a molecule, organic molecules with carbon–carbon single bonds are not static balls and sticks—they have many interconvertible conformers. The conformers cannot be separated, however, because their small energy difference allows them to interconvert rapidly. The relative number of molecules in a particular conformation at any one time depends on the stability of the conformation: The more stable the conformation, the greater is the fraction of molecules that will be in that conformation. Most molecules, therefore, are in staggered conformations, and more molecules are in an anti conformation than in a gauche conformation. The tendency to assume a staggered conformation causes carbon chains to orient themselves in a zigzag fashion, as shown by the ball-and-stick model of decane.
ball and stick model of decane

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