Question

Silver chloride dissolves readily in \(2 \mathrm{M} \mathrm{NH}_{3}\), but is quite insoluble in \(2 \mathrm{M} \mathrm{NH}_{4} \mathrm{NO}_{3}\). Explain.

Short answer

Silver chloride (AgCl) is more soluble in 2 M NH₃ due to the formation of a soluble complex ion, [Ag(NH₃)₂]⁺, which removes Ag⁺ ions from the equilibrium and shifts the dissolution equilibrium to the right according to Le Chatelier's principle. In contrast, AgCl is quite insoluble in 2 M NH₄NO₃ because there is not enough free NH₃ to react with the Ag⁺ ions and form the soluble complex ion, and the presence of a common ion, Cl⁻, further suppresses the dissolution of AgCl.

Step-by-step solution

Write the silver chloride dissolution equilibrium equation

First, we will write the balanced equilibrium equation for silver chloride dissolving in water: \[ \text{AgCl (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^- (aq) \]

Explain the solubility of AgCl in 2 M NH₃

Next, we'll look at the interaction between silver chloride and ammonia (NH₃). Ammonia reacts with the silver ion (Ag⁺) to form a soluble complex ion, [Ag(NH₃)₂]⁺. The balanced equation for this reaction is: \[ \text{Ag}^+ (aq) + 2 \, \text{NH}_3 (aq) \rightleftharpoons [\text{Ag}(\text{NH}_3)_2]^+ (aq) \] Due to the formation of this soluble complex ion, the presence of ammonia (NH₃) helps to remove the Ag⁺ ions from the solution. According to Le Chatelier's principle, this will shift the equilibrium of the dissolution of AgCl to the right, causing more AgCl to dissolve, thus increasing the solubility of AgCl in NH₃.

Explain the insolubility of AgCl in 2 M NH₄NO₃

Now, let's explore the effect of ammonium nitrate (NH₄NO₃) on the solubility of AgCl. When NH₄NO₃ dissolves in water, it dissociates into NH₄⁺ and NO₃⁻ ions: \[ \text{NH}_4 \text{NO}_3 (aq) \rightarrow \text{NH}_4^+ (aq) + \text{NO}_3^- (aq) \] The presence of excess NH₄⁺ ions in the solution suppresses the dissociation of NH₃ from the equilibrium: \[ \text{NH}_4^+ (aq) \rightleftharpoons \text{NH}_3 (aq) + \text{H}^+ (aq) \] Therefore, there is not enough free NH₃ to react with the Ag⁺ ions and form the soluble complex ion [Ag(NH₃)₂]⁺. As a result, very little AgCl dissolves in NH₄NO₃. Moreover, the presence of high concentrations of the common ion (Cl⁻) in the solution from NH₄Cl formed by NH₄⁺ and Cl⁻ would further suppress the dissolution of AgCl according to Le Chatelier's principle. This will make AgCl less soluble in 2 M NH₄NO₃. To summarize, silver chloride is more soluble in 2 M NH₃ due to the formation of a soluble complex ion, [Ag(NH₃)₂]⁺, which removes Ag⁺ ions from the equilibrium and shifts the dissolution equilibrium to the right, while it is less soluble in 2 M NH₄NO₃ due to the lack of free NH₃ and the presence of a common ion, Cl⁻.

Key concepts

Silver Chloride Solubility

Silver chloride, denoted as AgCl, is known to be poorly soluble in water. However, its solubility can be influenced by various factors, leading to increased dissolution in certain conditions. A key factor is the nature of the solvent used. Different solvents, or chemical interactions within the solution, can either enhance or diminish the solubility of AgCl.

In pure water, the dissolution process of AgCl can be depicted by the equilibrium:
\[ \text{AgCl (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^- (aq) \]
This equilibrium equation shows that AgCl slightly dissolves to yield silver ions (Ag⁺) and chloride ions (Cl⁻). However, due to its low solubility product \'K_{sp}\', the concentration of dissolved ions is minimal under normal conditions.

The addition of specific agents, such as ammonia (NH₃), can greatly alter this equilibrium. This happens because ammonia reacts with the dissolved silver ions to form a complex ion, which influences the overall solubility of silver chloride in the solution.

Ammonia Complex Ion Formation

When silver chloride is introduced to an ammonia solution, a fascinating chemical interaction occurs. Ammonia molecules ligate with silver ions, forming a stable complex ion, [Ag(NH₃)₂]⁺. This is an example of a metal-ammonia complex that often significantly increases solubility.

The reaction can be described by the equation:
\[ \text{Ag}^+ (aq) + 2 \, \text{NH}_3 (aq) \rightleftharpoons [\text{Ag}(\text{NH}_3)_2]^+ (aq) \]
This reaction is important because it reduces the concentration of free Ag⁺ ions in the solution. Through Le Chatelier's Principle, this depletion causes the dissolution equilibrium to shift to the right, driving more AgCl to dissolve. As more silver ions are converted into the complex ion, more solid AgCl will dissolve to replace the silver ions removed from the solution.

This behavior underpins why AgCl is more soluble in ammonia-rich solutions than in water or other solvents lacking conforming ligands.

Common Ion Effect

The common ion effect is a key principle in understanding solubility, particularly in electrolyte solutions containing a shared ion. When an additional source of ions, chemically identical to those produced by a dissolving salt, is added to a solution, the solubility of the original compound decreases.

This effect illustrates itself when AgCl is placed in a solution containing ammonium ions, such as ammonium nitrate (NH₄NO₃). These solutions provide extra chloride ions, which are also produced when AgCl dissolves.
The presence of these common ions (Cl⁻) in excess shifts the equilibrium backward:
\[ \text{AgCl (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^- (aq) \]
According to Le Chatelier's Principle, adding excess Cl⁻ ions suppresses the dissolution of AgCl, reducing its apparent solubility.

Moreover, in NH₄NO₃ solutions, the equilibrium:
\[ \text{NH}_4^+ (aq) \rightleftharpoons \text{NH}_3 (aq) + \text{H}^+ (aq) \]
Does not support free NH₃ availability, which further hinders complex ion formation with Ag⁺. Therefore, the AgCl remains mostly undissolved, demonstrating the pronounced effect of the common ion phenomenon.