(i) The first ionization enthalpy order for the given elements is correctly stated as \( \text{Na} < \text{Li} < \text{Cl} < \text{F} \). This is supported by the ionization energies (in kJ/mol):
\[\text{Na} \, (496) < \text{Li} \, (520) < \text{Cl} \, (1256) < \text{F} \, (1681)\]
(ii)The order of negative electron gain enthalpy for these elements is also correctly stated as \( \text{Na} < \text{Li} < \text{F} < \text{Cl} \).
The values (in kJ/mol) are:
\[\Delta_{\text{eg}}H : \text{Na} \, (-53), \, \text{Li} \, (-60), \, \text{F} \, (-328), \, \text{Cl} \, (-349)\]
Thus, both statements are true.
Match List I with List II.
In which of the following reactions of H$_2$O$_2$ acts as an oxidizing agent (either in acidic, alkaline, or neutral medium)?
% Given Reactions
(i) \( 2Fe^{2+} + H_2O_2 \rightarrow \)
(ii) \( 2MnO_4^- + 6H^+ + 5H_2O_2 \rightarrow \)
(iii) \( I_2 + H_2O_2 + 2OH^- \rightarrow \)
(iv) \( Mn^{2+} + H_2O_2 \rightarrow \)
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32