The relative configurations of the stereoisomers of tartaric acid were established by the following syntheses:
(1) D-(+)-glyceraldehyde $\stackrel{HCN}{\to }$ diastereomers A and B (separated)
(2) Hydrolysis of A and B using aqueous Ba(OH)₂ gave C and D, respectively.
(3) HNO₃ oxidation of C and D gave (-)-tartaric acid and meso-tartaric acid, respectively.
(a) You know the absolute configuration of D-(+)-glyceraldehyde. Use Fischer projections to show the absolute configurations of products A, B, C, and D.
(b) Show the absolute configurations of the three stereoisomers of tartaric acid: (+)-tartaric acid, (-)-tartaric acid, and meso-tartaric acid.

Verified step by step guidance

1. Step 1: Begin by analyzing the reaction of D-(+)-glyceraldehyde with HCN. This reaction forms two diastereomers, A and B, due to the addition of the cyanide ion to the carbonyl group. Use the known absolute configuration of D-(+)-glyceraldehyde to draw Fischer projections for A and B, ensuring that the new stereocenter is correctly assigned based on the addition of HCN.
2. Step 2: Hydrolyze A and B using aqueous Ba(OH)2 to form C and D. This step converts the nitrile group (-CN) into a carboxylic acid (-COOH). Use the Fischer projections of A and B to determine the absolute configurations of C and D, ensuring that the stereochemistry at the original stereocenters remains unchanged.
3. Step 3: Oxidize C and D using HNO3. This reaction oxidizes the primary alcohol group (-CH2OH) to a carboxylic acid (-COOH), resulting in tartaric acid stereoisomers. Use the Fischer projections of C and D to determine the absolute configurations of the resulting tartaric acid stereoisomers. Note that C gives (-)-tartaric acid, while D gives meso-tartaric acid.
4. Step 4: Draw the Fischer projections for the three stereoisomers of tartaric acid: (+)-tartaric acid, (-)-tartaric acid, and meso-tartaric acid. Recall that meso-tartaric acid is achiral due to an internal plane of symmetry, while (+)- and (-)-tartaric acid are enantiomers.
5. Step 5: Verify the absolute configurations of all intermediates (A, B, C, D) and final products (the three stereoisomers of tartaric acid) by comparing their Fischer projections and ensuring consistency with the known stereochemical outcomes of the reactions described in the problem.

Key Concepts

Stereochemistry

Stereochemistry is the study of the spatial arrangement of atoms in molecules and how this affects their chemical behavior. It includes concepts such as chirality, where molecules can exist as non-superimposable mirror images (enantiomers), and diastereomers, which are stereoisomers that are not mirror images. Understanding stereochemistry is crucial for analyzing the configurations of compounds like tartaric acid and its derivatives.

Fischer Projections

Fischer projections are a two-dimensional representation of three-dimensional organic molecules, particularly useful for depicting the stereochemistry of carbohydrates and amino acids. In a Fischer projection, vertical lines represent bonds that go back into the plane, while horizontal lines represent bonds that come out of the plane. This format allows for easy visualization of the absolute configurations of chiral centers, which is essential for solving the given problem.

Oxidation and Hydrolysis Reactions

Oxidation and hydrolysis are fundamental chemical reactions that involve the transformation of organic compounds. Oxidation typically involves the addition of oxygen or the removal of hydrogen, while hydrolysis involves the reaction of a compound with water, leading to the breakdown of that compound. In the context of the question, understanding these reactions is key to tracing the synthesis of tartaric acid from its precursors and determining the configurations of the resulting products.