`(A)(C_(4)H_(8)O)overset(H_(3)O^(o+))rarr(B)overset(CrO_(3))underset("acetic acid")rarr(C )overset(CH_(2)N_(2))underset(Delta)rarr(D)`
The compound 'D' is

Options

A.
B.
C.
D.

Answer

To solve the question step by step, we will analyze the transformations of compound A (C₄H₈O) through the given reactions to determine the final product D.

### Step 1: Identify Compound A
Given that A is C₄H₈O, we can start by calculating its degree of unsaturation (DOU) to understand its structure.

**Degree of Unsaturation Calculation:**
- Formula: DOU = (C + 1 - H + X - N) / 2
- For A (C₄H₈O):
- C = 4
- H = 8
- X = 0 (no halogens)
- N = 0 (no nitrogens)

Plugging in the values:
\[ DOU = (4 + 1 - 8 + 0 - 0) / 2 = (5 - 8) / 2 = -3 / 2 \]
This indicates that there is one degree of unsaturation, suggesting that A is an unsaturated alcohol.

### Step 2: React A with H₃O⁺
When A reacts with H₃O⁺ (which provides H⁺ and water), it undergoes hydration to form an alcohol (B). The reaction mechanism involves protonation of the double bond, leading to the formation of a carbocation, which is then attacked by water.

1. Protonation of the double bond leads to the formation of a carbocation.
2. Water attacks the carbocation, resulting in the formation of an alcohol.

Thus, compound B is an unsaturated alcohol derived from A.

### Step 3: React B with CrO₃ in Acetic Acid
Next, B is reacted with CrO₃ in the presence of acetic acid, which acts as an oxidizing agent. Since B is an alcohol, it will be oxidized to a ketone.

- The oxidation of the alcohol results in the formation of a carbonyl compound (C), specifically a cyclobutanone.

### Step 4: React C with CH₂N₂ (Diazomethane)
Finally, compound C (cyclobutanone) is reacted with CH₂N₂ (diazomethane) under heating conditions. This reaction involves carbene insertion, where the carbene (generated from CH₂N₂) inserts into the carbonyl compound.

1. The carbene (CH₂) inserts into the C=O bond of cyclobutanone.
2. This results in the formation of cyclopentanone (D).

### Conclusion
The final product D after all the reactions is cyclopentanone.

### Final Answer
The compound 'D' is **cyclopentanone**.

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