On treatment of acetone with dilute `Ba(OH)_(2)`, the product formed is:

Options

A. Aldol
B. Phorone
C. Propionaldehyde
D. 4-Hydroxy-2-pentanone

Explanation

To solve the question regarding the treatment of acetone with dilute Ba(OH)₂, we will follow these steps:

### Step 1: Understand the Reaction
When acetone (CH₃COCH₃) is treated with dilute barium hydroxide (Ba(OH)₂), it undergoes an aldol condensation reaction. This reaction typically occurs between two molecules of aldehydes or ketones that have alpha-hydrogens.

**Hint:** Remember that aldol reactions involve the formation of a carbon anion from the alpha carbon of the ketone or aldehyde.

### Step 2: Formation of the Enolate Ion
Barium hydroxide, being a strong base, abstracts an alpha-hydrogen from acetone. This leads to the formation of an enolate ion. The structure of the enolate ion formed from acetone is:

\[ \text{CH}_3C(-)C(=O)\text{CH}_3 \]

**Hint:** Identify the alpha hydrogen that is removed to form the enolate ion.

### Step 3: Nucleophilic Attack
The enolate ion then acts as a nucleophile and attacks the carbonyl carbon of another acetone molecule. This results in the formation of a beta-hydroxy ketone.

**Hint:** Visualize the nucleophilic attack on the carbonyl carbon to understand how the new bond is formed.

### Step 4: Formation of the Aldol Product
The product formed from this reaction is 4-hydroxy-4-methylpentan-2-one. The structure can be represented as:

\[ \text{CH}_3C(OH)(C_2H_5)C(=O)\text{CH}_3 \]

This compound has a hydroxyl group (-OH) and a ketone group (C=O) in its structure.

**Hint:** Ensure you count the carbon atoms correctly to name the compound accurately.

### Step 5: Naming the Product
To name the product, we identify the longest carbon chain that includes the functional groups. The longest chain has five carbons, and the hydroxyl group is on the fourth carbon. Therefore, the correct IUPAC name is:

**4-hydroxy-4-methylpentan-2-one**

**Hint:** Use the IUPAC naming rules to derive the name from the structure.

### Conclusion
After analyzing the options given in the question, we find that the correct answer is:

**4-hydroxy-4-methylpentan-2-one**

**Final Answer:** Option D: 4-hydroxy-4-methylpentan-2-one