The strength of an acid is determined by the stability of its conjugate base.
Electron-withdrawing groups (-I and -M effects) stabilize the conjugate base by delocalizing the negative charge after the loss of \( \text{H}^+ \). Electron-donating groups (+I and +M effects) destabilize the conjugate base.
In the given options, all are substituted phenols. The substituents are:
Since the nitro group (\( \text{-NO}_2 \)) has the strongest electron-withdrawing effect (-I and -M), it stabilizes the conjugate base of the phenol most effectively. Therefore, the compound with the \( \text{-NO}_2 \) substituent (option 4) is the strongest acid among the given options.
The acid strength of a phenolic compound depends on the electron-withdrawing or electron-donating groups attached to the benzene ring. The electron-withdrawing group increases the acidity of the compound. Among the options, the nitro group (-NO\(_2\)) is a strong electron-withdrawing group through the inductive effect (-I), making the compound with -NO\(_2\) attached to the ring the most acidic.
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:
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: