Question

How to decide the stability of gauche and anti conformation?

Answer 1

Large groups on adjacent carbon atoms increase the interaction energy.

Explanation:

Let's use butane as an example.

In staggered conformations, the energy of gauche interactions is zero for `"H, H"` and `"CH"_3, "H"` interactions.

However, each `"CH"_3, "CH"_3` interaction increases the conformational energy by about `"4 kJ·mol"^"-1""`.

The anti conformation has only `"H, H"` and `"CH"_3, "H"` interactions.

However, the gauche conformer has a `"CH"_3, "CH"_3` repulsion.

Thus, the gauche conformer is about `"4 kJ·mol"^"-1"` higher in energy than the anti isomer.

You can see the energy differences graphically in the diagram below.

You can interact with 3D models of the anti conformer here and of the gauche form here.