Chemistry - Thermochemistry Question with Solution | TestHub

Given the degeneracies: anti = 1, gauche = 2, eclipsed = 2, and fully eclipsed = 1, we can use Boltzmann weighting to determine the conformer energies. The Boltzmann weighting formula is p_i ∝ g_i e^-Ei/RT, where p_i is the probability of state i, g_i is the degeneracy of state i, E_i is the energy of state i, R is the gas constant, and T is the temperature.

We take the anti conformation as the zero-energy reference. At 298 K, RT = 0.592 kcal/mol.

The conformer energies are calculated as follows:

For the gauche conformation:

E_gauche = -RT ln ( 0.2/(2 × 0.7) t) = RT ln(7) = 1.152 kcal/mol

For the eclipsed conformation:

E_eclipsed = -RT ln ( 0.06/(2 × 0.7) t) = RT ln(23.33) = 1.865 kcal/mol

For the fully eclipsed conformation:

E_{fully eclipsed} = -RT ln ( 0.04/0.7 t) = RT ln(17.5) = 1.694 kcal/mol

A conformer with higher energy combusts more exothermically by its extra energy, so the natural enthalpy of combustion is:

Δ H_nat = Δ H_anti - [0.2(1.152) + 0.06(1.865) + 0.04(1.694)] = Δ H_anti - 0.410

This gives Δ H_anti = -689.59 kcal/mol. Then:

Δ H_gauche = Δ H_anti - E_gauche = -689.59 - 1.152 = -690.74 ≈ -691 kcal/mol

This corresponds to option (c).