Four isomeric optically active compounds `overset (NaHCO_3) rarr CO_2 (g) (A, B , C, D) (C_4 H_8 O_3)`
Compound `(A) overset (LAH) rarr ( E)` (Archiral compound)
Compound `(B) overset (KMnO_4) underset (or CrO_3) rarr` Inert to oxidation.
Compound `( C) underset (NaOI//H_3 O^(oplus)) rarr CHI_3 (Yellow ppt.) + Compound (F)`.
Compound `( C)` is :

Options

A. `(I)`
B. `(II)`
C. `(III)`
D. `(IV)`

Explanation

To determine the structure of compound C based on the provided information, we will follow a systematic approach.

### Step 1: Determine the molecular formula and degree of unsaturation
The molecular formula given is C₄H₈O₃.

To calculate the degree of unsaturation (DU), we use the formula:
\[ \text{DU} = \frac{2 \times \text{number of Carbons} + 2 - \text{number of Hydrogens}}{2} \]

Substituting the values:
\[ \text{DU} = \frac{2 \times 4 + 2 - 8}{2} = \frac{8 + 2 - 8}{2} = \frac{2}{2} = 1 \]

### Step 2: Identify possible functional groups
A degree of unsaturation of 1 suggests the presence of either a double bond or a ring structure. Given the context of carboxylic acids and their derivatives, we can assume that compound C may contain a carboxylic acid group (–COOH) or an alcohol (–OH) group.

### Step 3: Analyze the reactions of compounds A, B, and C
- **Compound A** reacts with LAH (Lithium Aluminium Hydride) to form an achiral compound E. This suggests that A likely contains a functional group that can be reduced, such as a carbonyl group (C=O).

- **Compound B** is inert to oxidation with KMnO₄, indicating that it likely does not have a hydrogen atom attached to a carbon adjacent to a carbonyl group (which would be oxidizable).

- **Compound C** reacts with NaOI/H₃O⁺ to yield CHI₃ (iodoform), which indicates that C must contain a methyl ketone or a secondary alcohol adjacent to a carbonyl group.

### Step 4: Propose a structure for compound C
Given the above information, we can propose a structure for compound C. It should have:
- A carboxylic acid group (due to the molecular formula).
- A structure that allows for the formation of CHI₃ upon treatment with NaOI/H₃O⁺.

A possible structure for compound C could be:
- 3-hydroxybutanoic acid (or 2-hydroxybutanoic acid), which has the following structure:

```
CH3
|
CH
|
COOH
|
CH2OH
```

### Conclusion
Based on the analysis, compound C is likely to be 3-hydroxybutanoic acid (or 2-hydroxybutanoic acid), which fits the criteria of being optically active and capable of yielding CHI₃ upon treatment with NaOI/H₃O⁺.