`CH_(3)`COOH + `CH_(3) CH_(2)"COOH" underset(300^(@)C)overset(MnO //Th O_(2))(rarr) X + CO_(2) + H_(2) O ` . Find out X.

Options

A. `CH_(3)"COCH"_(3)`
B. `C_(2)H_(5)"COCH"_(3)`
C. `CH_(3) "COCH"_(2) CH_(3)`
D. All of these

Answer

To solve the given reaction of acetic acid (CH₃COOH) and propanoic acid (CH₃CH₂COOH) under the influence of MnO₂ and heat, we need to analyze the possible reactions and products formed.

### Step-by-Step Solution:

1. **Identify the Reactants**:
The reactants are acetic acid (CH₃COOH) and propanoic acid (CH₃CH₂COOH).

2. **Understand the Reaction Conditions**:
The reaction is conducted at 300°C in the presence of MnO₂ (manganese dioxide), which is a dehydrating agent. This suggests that dehydration (loss of water) and decarboxylation (loss of carbon dioxide) may occur.

3. **Consider Possible Reactions**:
- **Dehydration**: When two carboxylic acids react, they can undergo dehydration to form ketones or aldehydes.
- **Decarboxylation**: The carboxyl group (-COOH) can be removed as carbon dioxide (CO₂).

4. **Reactions Between Acetic Acid and Propanoic Acid**:
- When acetic acid reacts with itself, it can form acetone (CH₃COCH₃) through dehydration.
- When propanoic acid reacts with itself, it can form 3-pentanone (CH₃CH₂COCH₂CH₃) through dehydration.
- Additionally, the reaction between acetic acid and propanoic acid can lead to the formation of 2-butanone (CH₃COCH₂CH₃).

5. **Final Products**:
After considering the possible reactions, the products formed from the reaction of acetic acid and propanoic acid under the given conditions will include:
- Acetone (CH₃COCH₃)
- 2-Butanone (CH₃COCH₂CH₃)
- 3-Pentanone (CH₃CH₂COCH₂CH₃)

6. **Conclusion**:
Since all three products can be formed, the final answer for the compound X is that it could be any of the products formed from the reaction. Therefore, the correct answer is option 4: all of the above.