Naming tartaric acid systematically starts with drawing out its four-carbon skeleton and numbering it so the principal characteristic group, the two -COOH carbons, get the lowest possible locants.
- 1,3-dihydroxybutane-1,4-dioic acid: Since the suffix "-1,4-dioic acid" already fixes carbons 1 and 4 as the carboxylic acid carbons, carbon 1 cannot simultaneously be listed as carrying a hydroxyl group, so this name contradicts itself.
- 2,3-dihydroxybutane-1,4-dioic acid: Numbering the chain HOOC(C1)-CHOH(C2)-CHOH(C3)-COOH(C4) places the carboxyl groups correctly at C1 and C4, and the two hydroxyl groups correctly at C2 and C3, which is a full, correct systematic name for tartaric acid's actual structure.
- 2,3-dihydroxy-4-butanoic acid: "Butanoic acid" names a four-carbon chain with a single carboxylic acid, but tartaric acid needs a dicarboxylic acid name to account for both -COOH groups, so this suffix under-describes the molecule.
- 2,2-dihydroxy-4-butanoic acid: Both hydroxyls on one carbon (C2) would describe a gem-diol, an unstable arrangement that does not match tartaric acid's vicinal diol structure, and again the monoacid suffix leaves out the second carboxylic acid group.
Since only the 2,3-dihydroxybutane-1,4-dioic acid name correctly places both carboxylic acids at the chain ends and both hydroxyls on the two middle carbons, the correct answer is 2,3-dihydroxybutane-1,4-dioic acid.