Q.71. - Organic Chemistry

Question

Question: When two six-membered rings share a C-C bond, this bicyclic system is called decalin. There are two possible arrangements: trans-decalin having two hydrogen atoms at the ring fusion on opposite sides of the rings, and cis-decalin having the two hydrogens at the ring fusion on the same side.

1. Draw trans- and cis-decalin using the chair form for the cyclohexane rings.
2. The trans isomer is more stable. Explain why.

Step-by-Step Solution

Answer

Answer

a. 

b. The trans isomer is more stable as both its bridged hydrogens are present in the equatorial positions and do not show any 1,3-diaxial interactions. In contrast, the cis isomer involves in 1,3-diaxial interaction.

Step 1: Chair form of cyclohexane

The most stable conformation used to represent cyclohexane is the chair conformation.

The chair conformers are preferred to analyze or predict the stability of the substituted cyclohexanes.

Step 2: Chair form of cis-decalin

The chair conformer of trans-decalin is as follows:

Chair conformation of trans-decalin

 

In the case of trans-decalin, both bridged hydrogen atoms project in the opposite direction (i.e., if one points upward, the other points downward).

Step 4: Stability of trans-decalin

In the case of trans-isomer, both hydrogen (bridged) atoms are present on the equatorial positions, while in the case of cis-isomer, one of the hydrogens is in axial and the other in the equatorial position.

The hydrogen atom present on the axial positions can show 1,3-diaxial interactions. These interactions result in a decrease in the stability of the molecule.

Since in the case of cis-isomer, the hydrogen atom present in the axial position gets involved in the 1,3-diaxial interaction, its stability is less than that of the trans isomer.

1,3-diaxial interaction in cis-decalin