Question

Question: Which conformation in each pair is higher in energy? Calculate the energy difference between the two conformations using the values given in Table 4.3.

a.

b.

Short answer

Answer

a.

The energy differences are 3.8 kJ per mole and 7.6 k J per mole (from left to right).

b.

The energy differences are 7.6 kJ per mole and 18 kJ per mole (from left to right).

Step-by-step solution

Conformation

Conformation is the molecule's structure that is obtained by rotating the single bond in the molecules.

Energy in conformations

The energy of conformations depends upon the substituents on the carbon.

The one gauche $C{H}_3/C{H}_3=3.8kJmo{l}^{-1}$

The one eclipsed $H/C{H}_3=6kJmo{l}^{-1}$

Explanation

a.

The given molecule has one gauche confirmation (staggered conformation with a ${60}^0$angle). Therefore, the energy of the molecule is calculated as:

The energy of one gauche $C{H}_3/C{H}_3=3·8kJ/mol$.

Therefore, the molecule has 3.8 kJ per mole energy.

The second molecule of the given pair has two gauche conformations. Therefore, the energy of the molecule is calculated as:

$$\begin{gathered} 2C{H}_3/C{H}_3=2\times 3.8kJ/mol \\ =7.6kJ/mol \end{gathered}$$

.Therefore, the molecule has 7.6 kJ per mole energy.

Therefore, the second molecule in the given pair is higher in energy.

b.

given molecule has two gauche conformations. Therefore, the energy of the molecule is calculated as:

$$\begin{gathered} 2C{H}_3/C{H}_3=2\times 3·8kJ/mol \\ =7·6kJ/mol \end{gathered}$$

.Therefore, the molecule has 7.6 kJ per mole energy.

The second molecule of the given pair has eclipsed conformation. The hydrogen and methyl molecules overlap each other.

The energy of one eclipsed $H/C{H}_3=6kJ/mol$.

$$\begin{gathered} 3H/C{H}_3=3\times 6kJ/mol \\ =18kJ/mol \end{gathered}$$

Thus, the molecule has 18 kJ per mole energy

Therefore, (the second molecule in the given pair) is higher in energy.