Correct order of `K_a` for following compounds:-
`H_3 overset(+)(N)-CH_3-COOH`
`NC-COOH`
`CH_3 - CH_2-COOH`
`overset(ϴ)(O)OC-CH_2-COOH`

Options

A. a gt b gt c gt d
B. b gt a gt c gt d
C. a gt c gt b gt d
D. d gt c gt b gt a

Answer

To determine the correct order of \( K_a \) for the given compounds, we need to analyze their acidity based on the substituents attached to the carboxylic acid group. The acidity of a compound is influenced by the nature of its substituents; electron-withdrawing groups increase acidity while electron-donating groups decrease acidity.

### Step-by-Step Solution:

1. **Identify the Compounds:**
- Compound A: \( H_3^{+}(N)-CH_3-COOH \) (Amino acid with a methyl group)
- Compound B: \( NC-COOH \) (Cyanocarboxylic acid)
- Compound C: \( CH_3-CH_2-COOH \) (Propanoic acid)
- Compound D: \( O^{\theta}C-CH_2-COOH \) (Carboxylic acid with an ether group)

2. **Analyze the Substituents:**
- **Compound A:** The \( NH_3^{+} \) group is an electron-withdrawing group. This increases the acidity of the carboxylic acid.
- **Compound B:** The \( CN \) (cyano) group is a strong electron-withdrawing group, making this compound more acidic than Compound A.
- **Compound C:** The \( CH_2-CH_3 \) (ethyl) group is an electron-donating group, which decreases the acidity of the carboxylic acid.
- **Compound D:** The \( O^{\theta}C \) (ether) group is also electron-donating, making this compound the least acidic.

3. **Rank the Acidity:**
- **Most Acidic:** Compound B (due to the strong electron-withdrawing \( CN \) group)
- **Next Acidic:** Compound A (due to the \( NH_3^{+} \) group)
- **Less Acidic:** Compound C (due to the \( CH_2-CH_3 \) group)
- **Least Acidic:** Compound D (due to the ether group)

4. **Order of \( K_a \):**
- Based on the analysis, the correct order of \( K_a \) values from highest to lowest is:
\[ K_a: B > A > C > D \]

### Final Answer:
The correct order of \( K_a \) for the compounds is:
\[ K_a: NC-COOH > H_3^{+}(N)-CH_3-COOH > CH_3-CH_2-COOH > O^{\theta}C-CH_2-COOH \]