Understanding the Question:
The question asks for the correct IUPAC name of tartaric acid.
Key Concept:
Tartaric acid is \(\text{HOOC-CH(OH)-CH(OH)-COOH}\), so naming it correctly means treating it as a four-carbon dioic acid with the two carboxyl carbons numbered 1 and 4, and locating the hydroxyl groups on whichever carbons they actually sit on.
Checking Each Option:
Placing a hydroxyl at position 1 is impossible since that carbon is already the carboxylic acid carbon in the 1,4-dioic acid backbone.
Naming it as a "4-butanoic acid" is not valid IUPAC form for a compound with acid groups at both ends of the chain, ruling out both options written that way.
Putting both hydroxyls on carbon 2 would describe a geminal diol on one carbon, which does not match tartaric acid's actual structure of one hydroxyl per middle carbon.
Numbering the four carbons so the acids sit at 1 and 4 leaves the two hydroxyls correctly placed at 2 and 3, giving 2,3-dihydroxybutane-1,4-dioic acid.
Final Answer:
The IUPAC name of tartaric acid is 2,3-dihydroxybutane-1,4-dioic acid.