For questions involving \(H_2\) liberation:
• Compare the reduction potential of the metal ion with the standard hydrogen electrode (SHE).
• Negative reduction potentials indicate the ability to liberate \(H_2\) gas.
V2+ and Cr2+
V2+ and Mn2+
Cr2+ and Co2+
Mn2+ and Co2+
- Metal cations with negative values of reduction potential (\(\text{M}^{3+}/\text{M}^{2+}\)) or positive values of oxidation potential (\text{M}^{2+}/\text{M}^{3+}\)) can reduce H\(^+\) ions and liberate H\(_2\) gas from dilute acid.
- For the given metals:
V\(^{2+}\) has a reduction potential of \(-0.26~\text{V}\).
Cr\(^{2+}\) has a reduction potential of \(-0.41~\text{V}\).
- Both values are negative, meaning V\(^{2+}\) and Cr\(^{2+}\) can reduce H\(^+\) ions to liberate H\(_2\) gas.
Final Answer: \((3)\) V\(^{2+}\) and Cr\(^{2+}\).
If $ \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p $, then $ 96 \log_e p $ is equal to _______
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: