The product of the given reaction ,
`CH_3 - underset( OH )underset( |) overset(| ) overset( CH_3 ) overset(|) C-underset(NH_2 ) underset(|) overset(CH_(3) ) overset( |) C -CH_(3) overset( HNO_2 ) to ` Product is :

Options

A. `CH_(3) - underset(OH) underset( |) overset( CH_3)overset(|)C-underset(OH)underset(|) overset(CH_3)overset(|)C-CH_3`
B. `CH_(3) - overset(O) overset(||) C- underset(CH_3) underset(|) overset( CH_3) overset( |) C- CH_3`
C. `CH_(3) - underset( OH) underset( |) overset(CH_3) overset(|)C- underset(CH_3 )underset(|) CH-CH_3`
D. `CH_3 - underset(CH_3) underset(|)C=underset(CH_3 ) underset(|)C-CH_3`

Answer

To solve the question regarding the product of the reaction between the given compound and HNO2, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Reactant**:
The reactant is a tertiary amine with the structure:
\[ CH_3 - OH \\ | \\ CH_3 - C - NH_2 \\ | \\ C - CH_3 \]
This structure indicates that we have a hydroxyl group (OH) and an amino group (NH2) attached to a carbon skeleton.

2. **Understand the Role of HNO2**:
HNO2 (Nitrous acid) acts as an acid and can protonate the amine group (NH2) to form an ammonium ion (NH3+). This process involves the donation of a proton (H+) to the nitrogen atom.

3. **Formation of Carbocation**:
When HNO2 donates a proton to the NH2 group, it forms a carbocation. The lone pair on the nitrogen atom will be used to bond with the proton, leading to the formation of a positively charged intermediate:
\[ CH_3 - OH \\ | \\ CH_3 - C - NH_3^+ \\ | \\ C - CH_3 \]

4. **Stability of Carbocation**:
The carbocation formed is electron-deficient. Alkyl groups (like CH3) are electron-donating and can stabilize this carbocation through hyperconjugation.

5. **Rearrangement of the Carbocation**:
The carbocation can undergo rearrangement. In this case, a 1,2-methyl shift occurs where a methyl group from an adjacent carbon moves to the positively charged carbon, stabilizing the carbocation further.

6. **Final Product Formation**:
After the rearrangement, the final product will be a ketone. The oxygen from the hydroxyl group can form a double bond with the carbon, leading to the formation of a carbonyl group:
\[ CH_3 - C(=O) - CH_3 \]
This structure corresponds to a ketone.

7. **Conclusion**:
The product of the reaction is therefore a ketone, specifically 2-pentanone.

### Final Answer:
The product of the reaction is 2-pentanone.

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