Butane exists in anti and gauche conformations in nature. At any given instant, the probability that a given butane molecule is in the anti and gauche conformation is 0.8 and 0.2, respectively. If the

Question

Butane exists in anti and gauche conformations in nature. At any given instant, the probability that a given butane molecule is in the anti and gauche conformation is 0.8 and 0.2, respectively. If the molar enthalpy of combustion of natural butane is -688 kcal/mol at 25°C, then calculate the enthalpy of combustion of butane if all the butane molecules are in the anti conformation.

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With degeneracies anti = 1, gauche = 2: E g = -RTln(0.2/(2 × 0.8)) = RTln8 = 0.592 × 2.079 = 1.231 kcal/mol (RT = 0.592 kcal/mol at 298 K). Natural butane: ΔH nat = 0.8 ΔH anti + 0.2(ΔH anti - 1.231) = ΔH anti - 0.246. So ΔH anti = -688 + 0.246 = -687.75 ≈ -687.8 kcal/mol. This is option (a).

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