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In other words, are these two structures equivalent?

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Yes, they are both (S)-2-chlorobutane.

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The difference between these structures is a rotation of the molecule by 60 degrees. You could build a model to convince yourself that they are the same. The arrangement of the atoms around the chiral center does matter.

The utility of the R/S convention is that you can unambiguously decide whether the two compounds are the same or different, which can be difficult depending on the orientation of the compound.

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