2.4 Relative abundance of conformers
2.4 Relative abundance of conformers
Ethane has two conformers; eclipsed and staggered. Does then ethane consist in two equal amount of two conformers? By any means not. The two conformers have different steric energy, and hence the relative population of two conformers may be different.
This situation can be visualized if we assume that the tortion angle-energy plot is a kind of reaction coordinate, which exhibit the energy change associated with the progress of the reaction. The vertical coordinate, the reaction coordinate corresponds to tortion angle. The eclipsed form is equivalent to the activate complex of a chemical reaction. Such a high energy species will have a very short lifetime, and is impossible to isolate. In addition to the case of ethane, for propane and butane, the eclipsed form is an intermediate of a reaction which has a very short lifetime.
One can assume that ethane exists most of the time as the most stable staggered form. In the case of butane there are two staggered form, and hence it exists as a mixture of these two conformers. In such a case the relative amount of two conformers will depend on the difference of Gibbs free energy ΔG. Generally speaking, for an equilibrium A ・ B, ΔG is expressed by the following equation
ΔG = -2.303 RT log K
where K is the equilibrium constant(K = [B]/[A]), R is the gas constant(=1.98 cal deg-1 mol-1) and T is the absolute temperature.
If x is the molar fraction of the gauche form, (1 - x )/x = 4.95; ∴x = 0.168. i.e., anti form 83% and gauche form 17%. This does not, however, mean that one can separate butane into the anti and gauche forms. In order to separate two rapidly exchanging species. e. g., 6 and 8 at room temperature, the energy of barrier of the exchange--in the case of butane, the energy difference between 6 and 8 or 5 and 7, should be at least as large as 100 kJ mol-1. As is indicated in the Fig. 2.4, the energy difference is ca. 15-20 kJ mol-1, indicating that at room temperature the exchange is very rapid.