An organic compound 'X' is oxidized by using acidified `K_(2)Cr_(2)O_(7)`. The product obtained reacts with phenyl hydrazine but does not answer silver mirror test. The possible structure of 'X' is `:`

Options

A. `CH_(3)COCH_(3)`
B. `(CH_3)_(2)CHOH`
C. `CH_(3)CHO`
D. `CH_(3)CH_(2)OH`

Answer

To solve the question, we need to analyze the information provided about the organic compound 'X' and the reactions it undergoes.

### Step-by-Step Solution:

1. **Identify the Oxidation Reaction**:
- The compound 'X' is oxidized using acidified \( K_2Cr_2O_7 \). This reagent is a strong oxidizing agent that can oxidize alcohols to ketones or carboxylic acids, depending on the type of alcohol.
- We need to determine what type of compound 'X' could be to produce a ketone after oxidation.

2. **Determine the Product 'Y'**:
- The product obtained from the oxidation of 'X' is denoted as 'Y'. Since 'Y' reacts with phenyl hydrazine but does not give a silver mirror test (which is indicative of aldehydes), we conclude that 'Y' must be a ketone.
- Therefore, 'X' must be a secondary alcohol (since secondary alcohols are oxidized to ketones).

3. **Evaluate the Options**:
- We have four options to consider for 'X':
- A: \( CH_3COCH_3 \) (acetone) - This is already a ketone and would not be oxidized.
- B: \( CH_3CHOHCH_3 \) (2-propanol) - This is a secondary alcohol that can be oxidized to acetone (a ketone).
- C: \( CH_3CHO \) (acetaldehyde) - This is an aldehyde, which would be oxidized to acetic acid, not a ketone.
- D: \( CH_3CH_2OH \) (ethanol) - This is a primary alcohol that would be oxidized to acetic acid, not a ketone.

4. **Confirm the Reaction with Phenyl Hydrazine**:
- The ketone produced from the oxidation of 'X' (which we identified as 2-propanol) will react with phenyl hydrazine to form a phenylhydrazone.
- The reaction proceeds as follows:
\[ \text{Ketone} + \text{Phenylhydrazine} \rightarrow \text{Phenylhydrazone} + \text{Water} \]
- Since 'Y' is a ketone, it will react with phenyl hydrazine, confirming that option B is correct.

5. **Final Conclusion**:
- Since option B is the only one that fits all the criteria (oxidizes to a ketone, reacts with phenyl hydrazine, and does not give a silver mirror test), we conclude that the structure of 'X' is:
\[ \text{B: } CH_3CHOHCH_3 \]