Q.3-42 - Organic Chemistry (Mcmurry)

Question

Consider 2-methylbutane (isopentane) sighting along C-2, C-3 bond:

1. Draw a Newman Projection of the most stable conformer.
2. Draw a Newman Projection of the most stable conformer.
3. If a ${\mathbf{CH}}_{\mathbf{3}}\mathbf{-}{\mathbf{CH}}_{\mathbf{3}}$ eclipsing interaction costs 11kJ/mol (2.5 kcal/mol) and a  ${\mathbf{CH}}_{\mathbf{3}}\mathbf{-}{\mathbf{CH}}_{\mathbf{3}}$ gauche interaction costs 3.8kJ/mol (0.9 kcal/mol), make a quantitative plot of energy versus rotation about the C-2 C-3 bond.

Step-by-Step Solution

Answer

Conformation

An infinite number of spatial arrangement of group or atoms possible, in a molecule due to the free rotation of constituent group or atoms around carbon-carbon single bond is called conformation.

Conformations can be classifies into two types- Eclipsed and staggered,

For example- in ethane eclipsed is when the hydrogen atoms present on singly bonded carbon atoms are as near as possible to each other. The dihedral angle in eclipsed conformation is least i.e., 0^o.

                                                            

                            Eclipsed                                                            Staggared

Newman’s projection for ethane molecule

Staggered conformation is when hydrogen atoms attached to the singly bonded carbon atoms in consideration are as far apart as possible. The dihedral angle is 60^o. Staggard conformations are more stable because, due to large separation between the electron clouds of C-H bonds, the repulsion is minimum and hence energy is minimum.

The conformation can be represented both by Sawhorse and Newman’s Projection formula.

It is to be noted that, when two bulky groups are placed at a dihedral angle 180^o of  in a staggered conformation, the conformation is called as an anti conformation, as both the bulky groups are anti periplaner to each other.

 

While when two bulky groups are positioned at a dihedral angle of more than 0^o but less than 120^o , the staggered conformation then is called as Gauche conformation.

Drawing the conformations obtained on rotation about the C-2 C-3 bond of 2-Methylbutane

Of all these conformers, the stable are the staggered ones (a,c and e). Out of these three, those where one Gauche interaction is present, are the most stable (conformation c and e), both accounting for a energy of 3.8 kJ/mol each. 

While the unstable ones are those where eclipsing interactions are present (i.e., (conformations b,d and f). Out of these three most unstable are b and f conformations accounting for a total energy of 21.0 kJ/mol each.

Energies of conformers

• In   eclipsing conformation (b and f)  the energy due to

One ${\text{CH}}_{\text{3}}{\text{ - CH}}_{\text{3}}$eclipsing interaction $1\times 11.0 kJ/mol$ 

One ${\text{CH}}_{\text{3}}\text{ - H}$  eclipsing interaction $1\times 6.0 kJ/mol$

One H-H eclipsing interaction $1\times 4.0 kJ/mol$

Total energy$21.0 kJ/mol$

• In an eclipsed conformation d, the energy due to 

Three ${\text{CH}}_{\text{3}}\text{ - H}$ eclipsing interaction $=3\times 6.0 kJ/mol=18.0 kJ/mol$ .

• In the staggered conformation (c and e), the energy due to 

One ${\text{CH}}_{\text{3}}{\text{ - CH}}_{\text{3}}$ Gauche interaction

• The other staggered conformation (a) is having two gauche interactions, therefore, the energy due to

Two gauche interaction $=2\times 3.8 kJ/mol=7.6 kJ/mol$.

Constructing potential energy versus angle of rotation curve