Correct acidic strength of given acids is:-
`H_(3)C -underset(I)overset(O)overset(||)C-OH`
(II) `HO-overset(O)overset(||)C-overset(O)overset(||)C-OH`
(III) `HO-overset(O)overset(||)C-CH_(2) -CH_(2)-overset(O)overset(||)C-OH`

Options

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

Answer

To determine the correct acidic strength of the given acids, we will analyze the structures of each acid and their corresponding carboxylate ions. The stability of the carboxylate ion plays a crucial role in determining the acidity of the acid.

### Step-by-Step Solution:

1. **Identify the Acids**:
- (I) `H3C-C(=O)-OH` (Acetic Acid)
- (II) `HO-C(=O)-C(=O)-OH` (Oxalic Acid)
- (III) `HO-C(=O)-CH2-CH2-C(=O)-OH` (Malonic Acid)

2. **Draw the Carboxylate Ions**:
- For (I) Acetic Acid:
- Carboxylate ion: `H3C-C(=O)O-`
- For (II) Oxalic Acid:
- Carboxylate ion: `HO-C(=O)-C(=O)O-`
- For (III) Malonic Acid:
- Carboxylate ion: `HO-C(=O)-CH2-CH2-C(=O)O-`

3. **Analyze the Stability of Carboxylate Ions**:
- **Acetic Acid (I)**:
- The presence of the methyl group (CH3) is an electron-donating group. This reduces the polarity of the O-H bond, making the carboxylate ion less stable.
- **Oxalic Acid (II)**:
- The presence of two carboxyl groups (COOH) allows for resonance stabilization and electron-withdrawing effects. This makes the carboxylate ion more stable than that of acetic acid.
- **Malonic Acid (III)**:
- Although it has two carboxyl groups, the inductive effect is less pronounced due to the presence of two methylene (CH2) groups between the carboxyl groups. Thus, the carboxylate ion is more stable than acetic acid but less stable than oxalic acid.

4. **Rank the Acids Based on Stability**:
- The stability of the carboxylate ions can be ranked as follows:
- Oxalic Acid (II) > Malonic Acid (III) > Acetic Acid (I)

5. **Conclusion**:
- Therefore, the correct order of acidic strength is:
- (II) > (III) > (I)

### Final Answer:
The correct acidic strength of the given acids is:
**(II) > (III) > (I)**