Question

Explain the following observations in terms of complex-ion formation. (a) \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) is soluble in \(\mathrm{NaOH}(\mathrm{aq})\) but insoluble in \(\mathrm{NH}_{3}(\mathrm{aq})\) (b) \(\mathrm{ZnCO}_{3}(\mathrm{s})\) is soluble in \(\mathrm{NH}_{3}(\mathrm{aq}),\) but \(\mathrm{ZnS}(\mathrm{s})\) is not. (c) The molar solubility of AgCl in pure water is about \(1 \times 10^{-5} \mathrm{M} ;\) in \(0.04 \mathrm{M} \mathrm{NaCl}(\mathrm{aq}),\) it is about \(2 \times 10^{-6}; \mathrm{M}\) but in \(1 \mathrm{M} \mathrm{NaCl}(\mathrm{aq}),\) it is about \(8 \times 10^{-5} \mathrm{M}\).

Short answer

The solubility of \(\mathrm{Al}(\mathrm{OH})_{3}\) in \(\mathrm{NaOH}\) is due to the formation of \(\mathrm{Al(OH)}_{4}^{-}\) complex which doesn't happen in \(\mathrm{NH}_{3}\). \(\mathrm{ZnCO}_{3}\) forms soluble \(\mathrm{[Zn(NH}_{3})_{4}]^{2+}\) in \(\mathrm{NH}_{3}\) but \(\mathrm{ZnS}\) doesn't. The solubility behavior of AgCl in \(\mathrm{NaCl}\) is due to Le Chatelier's principle, with AgCl solubility decreasing initially with added chloride ions, but increasing at higher \(\mathrm{NaCl}\) concentrations.

Step-by-step solution

\(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) in \(\mathrm{NaOH}(\mathrm{aq})\) and \(\mathrm{NH}3_{(aq)}\)

Aluminium hydroxide, \(\mathrm{Al}(\mathrm{OH})_{3}\), reacts with sodium hydroxide, \(\mathrm{NaOH}\), to form a soluble complex ion \(\mathrm{Al(OH)}_{4}^{-}\) as per the reaction: \[\mathrm{Al(OH)}_{3} + \mathrm{OH}^{-} => \mathrm{Al(OH)}_{4}^{-}\] However, such a complex does not form with ammonia, \(\mathrm{NH}_{3}\), hence, \(\mathrm{Al(OH)}_{3}\) is insoluble in \(\mathrm{NH}_{3(\mathrm{aq})}\)

\(\mathrm{ZnCO}_{3}(\mathrm{s})\) and \(\mathrm{ZnS}(\mathrm{s})\) in \(\mathrm{NH}_{3}(\mathrm{aq})\)

Zinc carbonate, \(\mathrm{ZnCO}_{3}\), reacts with water to form the soluble ammonium zincate ion, \(\mathrm{[Zn(NH}_{3})_{4}]^{2+}\) as per the following reaction: \[\mathrm{ZnCO}_{3} + 4\mathrm{NH}_{3} + \mathrm{H}_{2}\mathrm{O} => \mathrm{[Zn(NH}_{3})_{4}]^{2+} + \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O}\] However, no such complex forms with Zinc sulfide, \(\mathrm{ZnS}\), hence it is insoluble in \(\mathrm{NH}_{3(\mathrm{aq})}\)

Solubility of AgCl in different solutions

The solubility of AgCl is dependent on the concentration of chloride ions in the solution. In pure water, the solubility product expression of AgCl is: \[AgCl <=> Ag+ + Cl-\] When dissolved in a solution of \(\mathrm{NaCl}\), the increased concentration of chloride ions causes a shift in the equilibrium to the left (Le Chatelier's principle), decreasing the solubility of AgCl. As \(\mathrm{NaCl}\) concentration increases, there is a limit to how much it can suppress solubility, leading to the enhanced solubility at very high \(\mathrm{NaCl}\) concentrations.

Key concepts

Solubility of Inorganic Compounds

Solubility is a measure of how well a substance (solute) can dissolve in a solvent to form a homogeneous solution. Inorganic compounds vary widely in their solubility in water and other solvents due to differences in their ionic and molecular structures.

Understanding solubility is fundamental to predicting the behavior of substances in various environments. For instance, when \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) is placed in \(\mathrm{NaOH}(\mathrm{aq})\), it dissolves to form a soluble complex ion \(\mathrm{Al(OH)}_{4}^{-}\). Such behavior can be explained by the compound's ability to react with the hydroxide ions in the solution to form a more stable complex, altering its solubility characteristics.

In contrast, the same compound shows a drastically different solubility behavior in \(\mathrm{NH}_{3}(\mathrm{aq})\) due to the absence of a similar complex formation. As such, fundamental principles concerning the interaction between solute particles and solvent molecules, the formation of complex ions, and the overall solvation process govern the solubilities of inorganic compounds.

Le Chatelier's Principle

In chemistry, Le Chatelier's principle can be described as a rule of thumb for predicting the effect of changes in conditions on chemical equilibria. Essentially, it states that when a chemical system at equilibrium experiences a change in concentration, temperature, or pressure, the system will adjust to counteract that change and restore a new equilibrium state.

Applying this principle to the solubility of AgCl, we can better understand the observed changes in solubility when NaCl is added to the solution. An increase in NaCl concentration introduces more Cl⁻ ions, which shifts the dissolution equilibrium of AgCl towards the undissolved solid (left side), thus reducing its solubility. However, at very high concentrations of NaCl, other factors come into play, leading to an increase in the solubility of AgCl. This is a nuanced example of Le Chatelier's principle at work, adjusting to changes that might not be immediately intuitive.

Equilibrium Shift in Chemical Reactions

Chemical equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction, leading to a constant concentration of reactants and products. However, this dynamic balance can be disturbed by changing the conditions of the reaction. Factors such as changes in concentration, temperature, pressure, or the addition of a catalyst can lead to a shift in equilibrium, favoring either the reactants or products.

In the context of complex ion formation and solubility, the dissolution of AgCl in the presence of varying concentrations of NaCl demonstrates how equilibrium can shift. As the concentration of chloride ions increases due to the addition of NaCl, the system shifts to reduce the stress (increase in Cl⁻ ions) by forming more solid AgCl, thus decreasing its solubility. Understanding the equilibrium shift in chemical reactions is crucial for manipulating reactions to obtain desired products or to enhance or reduce the solubility of substances.

Ligand Exchange Reactions

Ligand exchange reactions are a type of chemical reaction that involves the substitution of one ligand (an ion or molecule that binds to a central atom to form a coordination complex) for another in a complex ion. These reactions are central to the understanding of complex ion formation and solubility.

For example, in the reaction where \(\mathrm{ZnCO}_{3}(\mathrm{s})\) dissolves in \(\mathrm{NH}_{3}(\mathrm{aq})\), a ligand exchange occurs, forming the soluble complex ion \(\mathrm{[Zn(NH}_{3})_{4}]^{2+}\). Here, ammonia (NH₃) acts as the new ligand, replacing water molecules or other groups surrounding the central zinc ion. It's important to note that ligand exchange reactions influence the chemical properties, including solubility, and are affected by various factors such as the nature of the ligand, the central metal ion, and the reaction conditions.