See image — Aldehydes Ketones and Carboxylic Acids Chemistry Question

💡 Solution & Explanation

Step 1 - Identify the compound: The compound is a cyclopentane-1,1-dicarboxylic acid derivative. At C1, there are two CO2H groups (a gem-dicarboxylic acid). The ring also bears two methyl groups at other positions with defined stereochemistry. Step 2 - Understand decarboxylation of gem-dicarboxylic acids (malonic acid-type decarboxylation): When a carbon bears two carboxylic acid groups (malonic acid type), heating causes loss of one CO2 to give a monocarboxylic acid. This is a well-known thermal decarboxylation. Step 3 - Analyze the stereochemical outcome: C1 originally has two identical CO2H groups and is therefore a quaternary carbon with two identical substituents. After losing one CO2, C1 becomes a carbon bearing one CO2H, one H (gained after decarboxylation), and the two ring carbons. The key question is whether the loss of CO2 generates a new stereocenter at C1 and how many stereoisomeric products result. Step 4 - Assess the new stereocenter at C1 after decarboxylation: Before decarboxylation, C1 has two CO2H groups (identical), so C1 is not a stereocenter. After decarboxylation, C1 gains an H and now bears H, CO2H, and two different ring carbons (C2 with one methyl configuration and C5). This could in principle create a new stereocenter. However, the two CO2H groups are homotopic (C1 is a plane of symmetry position with two identical groups), so loss of either CO2H gives the same product. Step 5 - Consider the overall stereochemistry of the molecule: The molecule has defined stereocenters at C2 and C3 (the two methyl-bearing carbons). The decarboxylation at C1 proceeds via a cyclic transition state and the proton is delivered from the carboxylic acid itself. The reaction goes through a six-membered cyclic transition state (beta-keto acid or malonic acid mechanism), and the configuration at C1 in the product is fixed by the geometry of the ring and the existing stereocenters. Step 6 - Because the two CO2H groups on C1 are identical (homotopic in the context of the symmetric gem-dicarboxylate carbon), removing either one gives the same constitutional product. The ring constraints and existing stereocenters at the adjacent carbons mean that the new H at C1 is delivered in only one specific facial orientation relative to the ring, giving only one stereoisomeric product. Step 7 - Why other options fail: (a) 0 is wrong because decarboxylation does occur readily for malonic acid derivatives. (c) 2 and (d) 3 are wrong because the rigid ring system and the homotopic nature of the two CO2H groups restrict the reaction to give a single stereochemical outcome - only one product is formed. Therefore, the correct answer is B.