The correct order of `K_(a)` is :
(i) `CH_(3)-CH_(2)-COOH`
(ii) `OHC-CH_(2)-COOH`
(iii) `Ph-CH_(2)-COOH`

Options

A. `iiigtiigti`
B. `igtiigtiii`
C. `iigtiiigti`
D. `igtiiigtii`

Answer

To determine the correct order of \( K_a \) for the given carboxylic acids, we need to analyze the structure of each acid and how it affects the acidity. The acids given are:

1. \( CH_3CH_2COOH \) (Propanoic acid)
2. \( OHC-CH_2-COOH \) (Glycolic acid)
3. \( Ph-CH_2-COOH \) (Benzoic acid)

### Step 1: Identify the acids and their structures
- **Propanoic acid**: A straight-chain carboxylic acid with no electron-withdrawing or donating groups.
- **Glycolic acid**: Contains an aldehyde group which is an electron-withdrawing group.
- **Benzoic acid**: Contains a phenyl group which can stabilize the carboxylate ion through resonance.

### Step 2: Analyze the effect of substituents on acidity
- **Propanoic acid**: The carboxylate ion formed after deprotonation does not have any significant stabilization from substituents. Therefore, it has a moderate \( K_a \).

- **Glycolic acid**: The presence of the aldehyde group (–CHO) is electron-withdrawing, which stabilizes the negative charge on the conjugate base (carboxylate ion) more than in propanoic acid. This increases the acidity and thus increases \( K_a \).

- **Benzoic acid**: The phenyl group can stabilize the conjugate base through resonance. The negative charge on the carboxylate ion can be delocalized into the aromatic ring, making benzoic acid more acidic than both propanoic and glycolic acids.

### Step 3: Compare the \( K_a \) values
Based on the analysis:
- **Benzoic acid** has the highest \( K_a \) due to resonance stabilization.
- **Glycolic acid** comes next due to the electron-withdrawing effect of the aldehyde group.
- **Propanoic acid** has the lowest \( K_a \) as it lacks any significant stabilization for the conjugate base.

### Conclusion: Order of \( K_a \)
The correct order of \( K_a \) is:
\[ K_a: \text{(iii) } Ph-CH_2-COOH > \text{(ii) } OHC-CH_2-COOH > \text{(i) } CH_3-CH_2-COOH \]