Boltzmann Equation for Entropy:
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You would usually use delta S to find the change in entropy of a reaction (so some change to the system has to happen in order for there to be a delta S). We've only been using S to find the entropy of a molecule as a result of its structure (so there doesn't have to be any change in its state).
S as described by the Boltzmann equation describes positional entropy. That is, the total entropy or disorder as a result of the orientations of the molecules, rather than their thermal entropy, which is determined by their motion. Delta S usually combines both these quantities to describe how entropy changes over the course of a reaction.
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