This question involves identifying the number of carboxylic acid groups formed after the hydrolysis of a cyclic anhydride. Let's break it down step by step.

Step 1: Understand the Structure

The given compound is a cyclic anhydride. It contains a five-membered ring with two carbonyl groups (C=O) and an oxygen atom, which is characteristic of a succinic anhydride derivative. The structure shows a fused ring system, but the key reactive part is the anhydride functional group.

Step 2: Hydrolysis Reaction

Anhydrides undergo hydrolysis when treated with water. The general reaction for hydrolysis of an anhydride is:

For a cyclic anhydride, hydrolysis opens the ring and produces a dicarboxylic acid. Specifically, succinic anhydride hydrolyzes to succinic acid, which has two carboxylic acid groups.

Step 3: Apply to the Given Compound

The compound in the image is a bicyclic system with a cyclic anhydride. Hydrolysis will open the anhydride ring, converting it into a dicarboxylic acid. The rest of the structure (the fused ring) remains unchanged and does not contain additional hydrolyzable groups that would produce more carboxylic acids under these conditions.

Step 4: Final Product

The product P after hydrolysis is a dicarboxylic acid. Therefore, it contains two carboxylic acid groups.

Related Topics and Formulae

Hydrolysis of Anhydrides: Anhydrides react with water to form carboxylic acids. For cyclic anhydrides, this results in a diacid.

Carboxylic Acid Functional Group: Recognized by -COOH. Each anhydride group produces two -COOH groups upon hydrolysis.

Reactivity: Anhydrides are highly reactive towards nucleophiles like water due to the electrophilic carbonyl carbon.

Final Answer: The total number of carboxylic acid groups in product P is 2.