The energy difference in these two conformations has been measured to be about 23 kj per mole. how much of this energy difference is due to the torsional energy of gauche relationships?

The answer is 7.8 kJ / mol.

Explanation:

Energy = (number of methyl group) (Gauche interactions) (3.8kJ/mol per interaction)

= (2) (2) (3.8 kJ / mol)

= 15.2 kJ / mol.

The energy = (number of methyl group) - (energy of gauche interactions)

= (23 kJ/mol) - 15.2 kJ/mol

= 7.8 kJ / mol.