(i) $\mathrm{AgNO_3 + NaCl \longrightarrow NaNO_3 + AgCl}$ (ii) $\mathrm{K_2SO_4 + BaCl_2 \longrightarrow BaSO_4 + 2KCl}$ Which of the following options clearly describes both the reactions?

As per the NCERT text (Section 1.2.4, Double Displacement Reaction), "reactions in which there is an exchange of ions between the reactants are called double displacement reactions," and "any reaction that produces a precipitate can be called a precipitation reaction."

Reaction (i): $\mathrm{AgNO_3 + NaCl \longrightarrow NaNO_3 + AgCl}$

Here $\mathrm{Ag^+}$ and $\mathrm{Na^+}$ ions exchange partners: $\mathrm{Ag^+}$ combines with $\mathrm{Cl^-}$ (from NaCl) and $\mathrm{Na^+}$ combines with $\mathrm{NO_3^-}$ (from $\mathrm{AgNO_3}$). This is exactly the ion-exchange pattern the book uses to define a double displacement reaction (analogous to Eq. 1.27, $\mathrm{Na_2SO_4 + BaCl_2 \rightarrow BaSO_4(s) + 2NaCl}$, which the text explicitly calls a double displacement reaction). Silver chloride, $\mathrm{AgCl}$, is insoluble in water and separates out as a white precipitate, so this is simultaneously a precipitation reaction.

Reaction (ii): $\mathrm{K_2SO_4 + BaCl_2 \longrightarrow BaSO_4 + 2KCl}$

This is structurally identical to the book's own worked example, Eq. (1.27): $\mathrm{Na_2SO_4(aq) + BaCl_2(aq) \rightarrow BaSO_4(s) + 2NaCl(aq)}$, with $\mathrm{K_2SO_4}$ simply replacing $\mathrm{Na_2SO_4}$. Here too, $\mathrm{Ba^{2+}}$ and $\mathrm{K^+}$ (or equivalently $\mathrm{SO_4^{2-}}$ and $\mathrm{Cl^-}$) exchange partners, and insoluble $\mathrm{BaSO_4}$ precipitates out. The NCERT text states this is exactly "the white precipitate of $\mathrm{BaSO_4}$ ... formed by the reaction of $\mathrm{SO_4^{2-}}$ and $\mathrm{Ba^{2+}}$" — a double displacement (precipitation) reaction.

Thus both (i) and (ii) are double displacement reactions as well as precipitation reactions, since in both cases ions are exchanged between the two reactant compounds and an insoluble solid ($\mathrm{AgCl}$ or $\mathrm{BaSO_4}$) is formed. Option (C) is correct.

Why the other options are wrong:

• (A) and (D) incorrectly label one of the two reactions as a simple "displacement" reaction. A displacement reaction (Section 1.2.3) involves a single, more reactive element displacing a less reactive element from its compound, e.g. $\mathrm{Fe(s) + CuSO_4(aq) \rightarrow FeSO_4(aq) + Cu(s)}$ — only one element changes places. Here, in both (i) and (ii), no free element is displacing another; instead, two ionic compounds swap their ions to form two new compounds, which is the defining feature of double displacement, not simple displacement.
• (B) is wrong because it calls both reactions "displacement reactions," using the wrong category name even though it correctly notes both are precipitation reactions. Neither (i) nor (ii) involves a single element displacing another from a compound; both involve mutual ion exchange between two compounds, making "double displacement," not "displacement," the correct classification.