The molecular formula `C_3H_9N` cannot represent

Options

A. `1^@` amine
B. `2^@` amine
C. `3^@` amine
D. Quaternary salt

Answer

To determine which type of amine the molecular formula \( C_3H_9N \) cannot represent, we need to analyze the structure of primary, secondary, tertiary amines, and quaternary ammonium salts.

### Step 1: Understanding the General Formula for Amines
The general formula for amines is derived from the formula for alkanes, which is \( C_nH_{2n+2} \). When one hydrogen atom is replaced by an amine group (-NH2), the formula for amines becomes \( C_nH_{2n+3}N \).

### Step 2: Applying the General Formula
For the molecular formula \( C_3H_9N \):
- Here, \( n = 3 \).
- If we substitute \( n \) into the general formula for amines:
\[ C_nH_{2n+3}N \rightarrow C_3H_{2(3)+3}N = C_3H_9N \]
This indicates that \( C_3H_9N \) can represent a primary amine, a secondary amine, or a tertiary amine.

### Step 3: Analyzing Quaternary Ammonium Salts
Quaternary ammonium salts have a nitrogen atom bonded to four carbon atoms. The general formula for quaternary ammonium salts is \( C_nH_{2n+4}N^+ \).

- For \( n = 3 \):
\[ C_nH_{2n+4}N^+ \rightarrow C_3H_{2(3)+4}N^+ = C_3H_{10}N^+ \]
This indicates that a quaternary ammonium salt would require one more hydrogen than \( C_3H_9N \), making it impossible for \( C_3H_9N \) to represent a quaternary ammonium salt.

### Conclusion
Thus, the molecular formula \( C_3H_9N \) cannot represent a quaternary ammonium salt.

### Final Answer
**The molecular formula \( C_3H_9N \) cannot represent a quaternary ammonium salt.**

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