In ring expansion reactions, smaller rings typically convert to larger rings to achieve greater stability and reduce ring strain. When both rings 'A' and 'B' undergo ring expansion, they both increase in size. The most common and stable outcome of such expansions is the formation of six-membered rings, which are energetically favorable due to their optimal bond angles and minimal ring strain. Therefore, both rings 'A' and 'B' will become six-membered rings after the expansion process.
Calculate the potential for half-cell containing 0.01 M K\(_2\)Cr\(_2\)O\(_7\)(aq), 0.01 M Cr\(^{3+}\)(aq), and 1.0 x 10\(^{-4}\) M H\(^+\)(aq).
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: