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What is the relationship between R/S configurations and the direction of rotation of plane-polarized light for a given chiral compound? Provide an example with a clear explanation.

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The R/S configuration and the direction of rotation of plane-polarized light for a given chiral compound are two different concepts that describe the stereochemistry of chiral molecules. The R/S configuration refers to the absolute configuration of a chiral center, while the direction of rotation of plane-polarized light  optical activity  refers to the way a chiral compound interacts with plane-polarized light.The R/S configuration is determined by the Cahn-Ingold-Prelog  CIP  priority rules, which assign priorities to the substituents around a chiral center based on their atomic numbers. The configuration is labeled as R  rectus  if the priority order is clockwise and S  sinister  if the priority order is counterclockwise when viewed from the side where the lowest priority group is pointing away from the observer.The optical activity of a chiral compound is described as either dextrorotatory  + or D  if it rotates plane-polarized light to the right  clockwise  or levorotatory  - or L  if it rotates plane-polarized light to the left  counterclockwise .It is important to note that there is no direct correlation between the R/S configuration and the direction of rotation of plane-polarized light. In other words, an R-configured molecule can be either dextrorotatory or levorotatory, and the same applies to an S-configured molecule. The relationship between the absolute configuration and optical activity can only be determined experimentally or through advanced computational methods.Example: Lactic acidLactic acid has one chiral center, and it exists in two enantiomeric forms: D-lactic acid and L-lactic acid. The R/S configuration of D-lactic acid is R, and it is dextrorotatory  + . The R/S configuration of L-lactic acid is S, and it is levorotatory  - . In this case, the R-configuration corresponds to the dextrorotatory form, and the S-configuration corresponds to the levorotatory form. However, this relationship is specific to lactic acid and cannot be generalized for all chiral compounds.
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