The reaction of cyclohexane with potassium permanganate (\(\text{KMnO}_4\)) in an acidic medium (\(\text{H}_2\text{SO}_4\)) and heat results in the oxidation of cyclohexane to adipic acid.
Step 1: Oxidation of cyclohexane
Cyclohexane (\(\text{C}_6\text{H}_{12}\)) undergoes oxidation in the presence of \(\text{KMnO}_4\) and \(\text{H}_2\text{SO}_4\).
- The \(\text{KMnO}_4\) oxidizes the \(-\text{CH}_2-\) groups in cyclohexane to carboxylic acid (\(-\text{COOH}\)) groups.
- This results in the formation of adipic acid (\(\text{HOOC} - (\text{CH}_2)_4 - \text{COOH}\)).
\[\text{C}_6\text{H}_{12} \rightarrow [\text{KMnO}_4, \text{H}_2\text{SO}_4, \text{Heat}] \text{HOOC} - (\text{CH}_2)_4 - \text{COOH} \, (\text{Adipic Acid})\]
Step 2: Conclusion
The product \(A\) is adipic acid.
Final Answer: (4).
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to: