Question

What are the rotational barriers for Butane, 2- Methylbutane and 2,3 - Dimethylbutane, and how are they related?

Answer 1

Using information on rotational barrier of butane which is about 4.5 kcal / mol we can add more information about rotational barrier which depends mainly on steric hinderences & also electronic effects.The rotation barrier in butane

is summarised as below-

In butane anti conformer there is no steric strain , because methyl groups are far apart.

In butane least stable conformer with methyl groups eclipsed, there is about 1.5 kcal /mol of strain. This 1,5 kcal sterics plus 3.0 kcal of torsion equals the rotational barrier.

In butane's gauch conformer there is no torsion but the amount of sterics appear to be a little less than when methyl is eclipsed.

Further, rotational barrier depends on di-hedral angle & potential energies of different configurations. The energy barriers in butane , methyl butane and 2,3- dimethyl butane are related with their dihedral angles as tabulated below-

Dihedral angle---------------- Conformation -----------------------------------------------Result------------------------------------------------------------

* 0^o or 360^o ------------- syn- conformation in butane------- The two methyl groups are in close proximity with the ------------------------------------------------------------------------------------------------- molecule , therefore potential energy is at its highest.----------------   * 60^o  or 300^o-----------gauch conformation in butane--------methyl groups are farther apart, hence-potential -----------------------------------------------------------------------------------------------------------energy drops by 4,1 kcal / mol----------------------------------------------- * 120^oor 240^o---------Eclipsed conformation in butane ------methyl groups align themselves with hydrogen atoms --------------------------------------------------------------------------------------------------of butane on the same plane . In this case butane has -------------------------------------------------------------------------------------------------a higher potential energy than the gauch conformation , ----------------------------------------------------------------------------------------------but still has a lower potential energy than the syn---------------------------------------------------------------------------------------------------------conformation , by 1.5 kcal /mol----------------------------------------* 180^o---------------------- anti conformation ------------------------------ Potential energy is lowest , hence is most stable. It is ------------------------------------------------------------------------------------------------because of the methyl groups are farthest away from------------------------------------------------------------------------------------- ------------each other in the molecule .---------------------------------------------

It should be noted that methyl group can always rotate ,so multiple hydrogen atoms on one methyl group could potentially interact with multiple hydrogen on another, but not at one time. We need only to take into account the full interaction that could happen simultaneously.

Again. each methyl group increases the rotation barrier by about 1.5 kcal / mol . Because a CH₃ group is substantially larger than a H atom one must expect greater barrier to rotation.However , C-C bond is more than 40% longer than C-H bond reducing the overall steric crowding. Each methyl group adds 1.2 to 1.6 kcal / mol to barrier