ISC Class 12 — free MCQ practice

NaCl dissociates in water: $\mathrm{NaCl} \rightarrow \mathrm{Na^+} + \mathrm{Cl^-}$. One formula unit produces two particles in solution. Van't Hoff factor $i = \dfrac{\text{actual moles of particles}}{\text{moles of solute formula units}}$. For complete dissociation of NaCl, $i = 2$. In reality, ion pairing slightly reduces $i$ below the theoretical value, especially at higher concentrations. At dilute $0.01$ M the assumption of complete dissociation is reasonable, and the experimental $i$ is close to $1.9$. The question asks for the theoretical value assuming complete dissociation, so 2 is the cleanest answer. Compare with $\mathrm{CaCl_2}$: dissociates into 3 ions, so $i = 3$ (option D) — common trap.

$E^{\circ}_{\text{cell}} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}}$, where both potentials are listed as standard *reduction* potentials. For a spontaneous galvanic cell, $E^{\circ}_{\text{cell}} > 0$, which means the cathode has the higher reduction potential. This is just an algebraic restatement of "reduction happens at the cathode".

The principal-value range of $\sin^{-1}$ is $\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right]$. This is the unique interval on which $\sin$ is monotonic and covers its full range $[-1, 1]$. Quick reference: - $\sin^{-1}, \tan^{-1}, \csc^{-1}$: range $\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right]$ (with closed/open variations). - $\cos^{-1}, \sec^{-1}, \cot^{-1}$: range $[0, \pi]$ (option A is for these).