Final answer:
The exact ΔG for vitamin D synthesis in the skin under physiological conditions is not given in the resources provided, and based on the information available, a definite answer from the options cannot be identified. None of the options are correct.
Step-by-step explanation:
The change in free energy (ΔG) for the synthesis of vitamin D can be calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy and TΔS is the product of the absolute temperature and the change in entropy.
For the synthesis of vitamin D, the relevant ΔG must be calculated under the conditions in which the synthesis occurs, which includes body temperature and the fact that the synthesis is initiated by UV radiation in the skin.
Considering that the actual synthesis in the skin is not easily replicated in a lab setting and the complexities involving multiple steps and regulation by various factors, an exact ΔG value for in vivo vitamin D synthesis isn't typically found in standard textbooks.
However, a related calculation in the provided reference denoted as 'B Substituting the appropriate quantities into Equation 13.7.14' gives a ΔG° of -120.31 kJ/mol for a related reaction at standard conditions (298K), which is not the exact condition for Vitamin D synthesis in the skin.
The options provided in the question do not match this value, and therefore, based on the given data, we cannot definitively answer with one of the four options provided for the ΔG of vitamin D synthesis.None of the options are correct.