The order of stability of the following tautomeric compound is
`underset("(I)")(CH_(2)=C(OH)-CH_(2)-CO-CH_(3))`
`underset("(II)")(rarrCH_(3)-CO-CH_(2)-CO-CH_(3))`
`underset("(III)")(rarrCH_(3)-C(OH)=CH-CO-CH_(3))`

Options

A. `III gt II gt I`
B. `II gt I gt III`
C. `II gt I gt III`
D. `I gt II gt III`

Answer

To determine the order of stability of the given tautomeric compounds, we will analyze each compound based on the presence of functional groups, resonance structures, and the stability of double bonds.

### Step 1: Identify the Compounds
We have three tautomeric compounds:
1. Compound (I): \( CH_2=C(OH)-CH_2-CO-CH_3 \)
2. Compound (II): \( CH_3-CO-CH_2-CO-CH_3 \)
3. Compound (III): \( CH_3-C(OH)=CH-CO-CH_3 \)

### Step 2: Analyze Compound (I)
- Compound (I) has a double bond between carbon atoms and an alcohol group (–OH).
- The presence of the double bond (C=C) and the –OH group indicates that it can participate in resonance, but the stability is limited due to the presence of a double bond that does not allow for extended conjugation.
- Thus, the stability of Compound (I) is relatively low.

### Step 3: Analyze Compound (II)
- Compound (II) has two carbonyl groups (C=O).
- The presence of two C=O bonds indicates a higher stability due to the resonance stabilization provided by the carbonyl groups.
- Carbonyl groups are generally more stable than alkenes due to their stronger bond character and ability to stabilize negative charges through resonance.
- Therefore, Compound (II) is more stable than Compound (I).

### Step 4: Analyze Compound (III)
- Compound (III) has a hydroxyl group and a double bond (C=CH).
- The presence of the hydroxyl group allows for resonance stabilization, as the lone pair on oxygen can participate in resonance with the double bond.
- Additionally, the extended conjugation due to the presence of the C=O bond increases the stability of Compound (III) significantly.
- Therefore, Compound (III) is the most stable among the three due to the resonance and extended conjugation.

### Step 5: Order of Stability
Based on the analysis:
1. Compound (III) is the most stable due to resonance and extended conjugation.
2. Compound (II) is next stable due to the presence of two carbonyl groups.
3. Compound (I) is the least stable due to limited resonance and the presence of a double bond without extended conjugation.

### Final Order of Stability
The order of stability is:
\[ \text{(III) > (II) > (I)} \]