What is the configuration of the following compounds? (Use the given structures to answer the question.)
c. ($+$)-lactic acid

Verified step by step guidance

1. Step 1: Analyze the given structure of lactic acid. The central carbon atom is a chiral center because it is bonded to four different groups: a hydroxyl group (-OH), a carboxylic acid group (-COOH), a methyl group (-CH3), and a hydrogen atom (H).
2. Step 2: Assign priorities to the substituents around the chiral center based on the Cahn-Ingold-Prelog priority rules. The highest priority is given to the group with the atom of highest atomic number directly attached to the chiral center. In this case: (1) -COOH, (2) -OH, (3) -CH3, and (4) H.
3. Step 3: Orient the molecule so that the lowest priority group (H) is pointing away from you (on the dashed wedge). This allows you to determine the configuration by tracing the path of the remaining groups in order of priority.
4. Step 4: Trace the path from the highest priority group (1) to the second (2) and then to the third (3). If the path is clockwise, the configuration is R. If the path is counterclockwise, the configuration is S.
5. Step 5: Based on the given structure, determine the configuration for both (+)-lactic acid and (-)-lactic acid using the above steps. Note that (+)-lactic acid and (-)-lactic acid are enantiomers, meaning they have opposite configurations.

Key Concepts

Stereochemistry

Stereochemistry is the study of the spatial arrangement of atoms in molecules and how this affects their chemical behavior. It is crucial for understanding isomers, particularly enantiomers, which are non-superimposable mirror images of each other. In the case of lactic acid, the configuration (R or S) determines its optical activity and biological properties.

Chirality

Chirality refers to the property of a molecule that makes it non-superimposable on its mirror image, akin to how left and right hands are mirror images but not identical. A chiral center, typically a carbon atom bonded to four different groups, is essential for the formation of enantiomers. Lactic acid has one chiral center, leading to the existence of two enantiomers: (+)-lactic acid and (−)-lactic acid.

Optical Activity

Optical activity is the ability of a chiral compound to rotate the plane of polarized light. The direction and degree of rotation depend on the specific enantiomer and its concentration. In the case of lactic acid, the (+) and (−) designations indicate the direction of rotation, with (+) rotating light to the right (dextrorotatory) and (−) to the left (levorotatory), which is essential for identifying the configuration of the compound.