Question

Each $\mathbf{H}\mathbf{\leftrightarrow }\mathbf{H}$eclipsing interaction in ethane costs about 4.0 kJ/mol. Howmany such interactions are present in cyclopropane? What fraction of theoverall 115 kJ/mol (27.5 kcal/mol) strain energy of cyclopropane is due totorsional strain?

Short answer

Here in total 6$\mathrm{H}\leftrightarrow \mathrm{H}$ eclipsing interactions are present, and 21% is the fraction of strain energy of cyclopropane due to torsional strain.

Step-by-step solution

Torsional strain

Torsional strain or eclipsing strain is an increase in the potential energy of a molecule because of repulsion in electrons of bonds that do not share any atom.

Strain energy

Strain energy is the energy released when the constituent atoms of the molecule are allowed to rearrange themselves in a reaction.

Structures of cyclopropane

• Here the ring has 3 carbon.
• Each carbon form 2 bonds with neighboring carbon atoms and 2 bonds with hydrogen
• So, the total number of hydrogen in cyclopropane is 6.

Calculation of total torsional strain in cyclopropane

• As each $\mathrm{H}\leftrightarrow \mathrm{H}$eclipsing interaction in ethane costs about 4.0 kJ/mol and as 6 hydrogens are present, here are total 6 $\mathrm{H}\leftrightarrow \mathrm{H}$eclipsing interactions.
• Torsional strain due to a total of 6 $\mathrm{H}\leftrightarrow \mathrm{H}$eclipsing interactions is $6\times 4=24\mathrm{kJ}/\mathrm{mol}$
• The fraction of the overall strain energy of cyclopropane due to torsional strain is $\frac{24}{115}\times 100=21\%$