Optically active amine having molecular formula `C_5 H_13 N` on reaction with `NaNO_2 + HCI` produces, 3° optically inactive alcohol. Find out structures of amines:

Options

A.
B.
C.
D.

Explanation

To solve the problem of identifying the structure of the optically active amine with the molecular formula \( C_5H_{13}N \) that reacts with \( NaNO_2 + HCl \) to produce a tertiary optically inactive alcohol, we can follow these steps:

### Step 1: Understand the Molecular Formula
The molecular formula given is \( C_5H_{13}N \). This indicates that the compound contains 5 carbon atoms, 13 hydrogen atoms, and 1 nitrogen atom.

### Step 2: Identify the Type of Amine
Since the amine is optically active, it must be a primary amine (1° amine) because a primary amine has a nitrogen atom bonded to one carbon atom and two hydrogen atoms, allowing for chirality (four different substituents).

### Step 3: Determine the Structure of the Amine
To satisfy the molecular formula \( C_5H_{13}N \) and the requirement for chirality, we can propose a structure. The primary amine can be structured as follows:

- One carbon is attached to the nitrogen (the amine group).
- The remaining four carbons can be arranged to ensure that the carbon attached to the nitrogen is chiral.

A possible structure could be:
```
CH3
|
CH3-CH-CH2-CH2-NH2
|
CH2
```
This structure has a chiral center at the carbon that is attached to the nitrogen, thus making it optically active.

### Step 4: Reaction with Sodium Nitrite and Hydrochloric Acid
When this primary amine reacts with \( NaNO_2 \) and \( HCl \), it forms a diazonium salt, which upon hydrolysis leads to the formation of an alcohol. The reaction can be summarized as:
1. Formation of diazonium salt:
\[ R-NH_2 + NaNO_2 + HCl \rightarrow R-N_2^+Cl^- + 2H_2O \]
2. Hydrolysis of the diazonium salt to form an alcohol:
\[ R-N_2^+Cl^- + H_2O \rightarrow R-OH + N_2 + HCl \]
The resulting alcohol is a tertiary alcohol, which is optically inactive.

### Step 5: Verify the Structure
Now, we need to check the options provided to see which one corresponds to our proposed structure.

- **Option A**: Not chiral.
- **Option B**: Tertiary amine, not suitable.
- **Option C**: Has the correct number of carbons and is chiral.
- **Option D**: Secondary amine, not suitable.

Thus, **Option C** is the correct structure of the optically active amine.

### Final Answer
The structure of the optically active amine with the molecular formula \( C_5H_{13}N \) is a primary amine that upon reaction with \( NaNO_2 + HCl \) produces a tertiary optically inactive alcohol.

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