Consider the following equilibrium:
$$AgCl \downarrow + 2NH_3 \rightleftharpoons [Ag(NH_3)_2]^+ + Cl^-$$
White precipitate of AgCl appears on adding which of the following?

The given equilibrium is:

$$AgCl \downarrow + 2NH_3 \rightleftharpoons [Ag(NH_3)_2]^+ + Cl^-$$

Here, solid silver chloride (AgCl) reacts with ammonia (NH₃) to form the complex ion [Ag(NH₃)₂]⁺ and chloride ion (Cl⁻). The white precipitate is AgCl on the left side. To make the white precipitate appear, we need to shift the equilibrium towards the left (towards the formation of AgCl solid). According to Le Chatelier's principle, we can do this by increasing the concentration of reactants or decreasing the concentration of products.

Now, let's analyze each option:

Option A: Adding NH₃

NH₃ is a reactant in the equilibrium. Adding more NH₃ increases the concentration of the reactant, which shifts the equilibrium to the right to consume the added NH₃. This produces more [Ag(NH₃)₂]⁺ and Cl⁻, dissolving more AgCl and reducing the precipitate. Therefore, adding NH₃ will not cause the white precipitate to appear.

Option B: Adding aqueous NaCl

NaCl dissociates into Na⁺ and Cl⁻ ions. Cl⁻ is a product in the equilibrium. Adding Cl⁻ increases the concentration of the product, which should shift the equilibrium to the left to reduce the added Cl⁻, favoring the formation of AgCl precipitate. However, the complex [Ag(NH₃)₂]⁺ is very stable, and the free Ag⁺ concentration is low. For AgCl to precipitate, the ion product [Ag⁺][Cl⁻] must exceed the solubility product (Ksp) of AgCl. Due to the stability of the complex, a significant amount of Cl⁻ may be needed to achieve this, depending on the concentrations of NH₃ and the complex. Thus, adding NaCl may not always be effective in forming the precipitate.

Option C: Adding aqueous HNO₃

HNO₃ is a strong acid that dissociates completely into H⁺ and NO₃⁻ ions. The H⁺ ions react with NH₃ (a weak base) to form NH₄⁺ ions: $$NH_3 + H^+ \rightarrow NH_4^+$$ This reaction reduces the concentration of free NH₃, which is a reactant in the equilibrium. Decreasing the reactant concentration shifts the equilibrium to the left to replace the consumed NH₃, favoring the formation of AgCl precipitate. Additionally, reducing [NH₃] increases the free Ag⁺ concentration, making it easier for Ag⁺ and Cl⁻ to combine and exceed Ksp, ensuring precipitation. Acidification is a reliable method to decompose the complex and form the precipitate.

Option D: Adding aqueous NH₄Cl

NH₄Cl dissociates into NH₄⁺ and Cl⁻ ions. Cl⁻ is a product, so adding it should shift the equilibrium to the left. However, NH₄⁺ acts as a weak acid and establishes a buffer system with NH₃: $$NH_4^+ + H_2O \rightleftharpoons NH_3 + H_3O^+$$ In the presence of existing NH₃, adding NH₄⁺ reduces the free [NH₃] due to the common ion effect, but this reduction is limited because the buffer resists large changes in [NH₃]. The decrease in [NH₃] is not as significant as when adding a strong acid like HNO₃. While both Cl⁻ addition and [NH₃] reduction shift the equilibrium left, the effect is less pronounced compared to acidification, and precipitation may not occur reliably.

Comparing all options, adding aqueous HNO₃ (Option C) is the most effective way to shift the equilibrium left and ensure the appearance of the white AgCl precipitate, as it drastically reduces [NH₃] by converting it to NH₄⁺.

Hence, the correct answer is Option C.