Vanillin is an organic compound with the molecular formula \( C_8H_8O_3 \). It is a phenolic aldehyde with functional groups including an aldehyde, hydroxyl, and ether, and is the primary component of vanilla bean extract.
Structure of Vanillin:
\[\text{HO-C}_6H_3(\text{OCH}_3)\text{CHO}\]
Counting oxygen atoms and \(\pi\) electrons:
Total number of oxygen atoms = 3.
Total number of \(\pi\)-bonds = 4 (one in the carbonyl group and three in the benzene ring).
Since each \(\pi\)-bond has two \(\pi\)-electrons:
\[\text{Total number of \(\pi\)-electrons} = 4 \times 2 = 8\]
Therefore, the sum of oxygen atoms and \(\pi\)-electrons is:
\[3 + 8 = 11\]
Which of the following are chiral molecules?
Choose the correct answer from the options given below:
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: