Question

Is the solubility of \(\mathrm{Fe}(\mathrm{OH})_{3}\) increased, decreased, or unchanged on addition of each of the following substances? Write a balanced net ionic equation for each dissolution reaction. (See Appendix C. 6 for formulas of complex ions.) (a) \(\mathrm{HBr}(a q)\) (b) \(\mathrm{NaOH}(a q)\) (c) \(\mathrm{KCN}(a q)\)

Short answer

(a) Increased solubility. (b) Decreased solubility.

Step-by-step solution

Analyze the effect of HBr

Adding \(\mathrm{HBr}(aq)\) will increase the solubility of \(\mathrm{Fe(OH)}_{3} \), as the \(\mathrm{H^+}\) ions from \(\mathrm{HBr}\) react with \(\mathrm{OH^-}\) ions, forming water: \[\mathrm{Fe(OH)}_{3}(s) + 3\mathrm{H^+}(aq) \rightarrow \mathrm{Fe^{3+}}(aq) + 3\mathrm{H_2O}(l)\] This shifts the equilibrium to the right as per Le Chatelier's principle, increasing solubility.

Analyze the effect of NaOH

Adding \(\mathrm{NaOH}(aq)\) will decrease the solubility of \(\mathrm{Fe(OH)}_{3} \) because the increase in \(\mathrm{OH^-}\) ions due to \(\mathrm{NaOH}\) shifts the equilibrium to the left, forming more solid \(\mathrm{Fe(OH)}_{3}(s)\). The net ionic equation is: \[\mathrm{Fe^{3+}}(aq) + 3\mathrm{OH^-}(aq) \rightarrow \mathrm{Fe(OH)}_{3}(s)\]

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that predicts how a change in conditions can affect chemical equilibria. Consider a system at equilibrium: any stress applied to this system will result in a shift that balances out this stress. For example, if a reactant or product is added to the system, the equilibrium will shift to either use up the added substance or produce more of it. This is often referred to as "shifting to the left or right". In the case of the solubility of substances, adding an acid like HBr increases the concentration of H\(^+\) ions, which react with OH\(^-\) ions from a solid like Fe(OH)\(_3\), forming water. This consumption of OH\(^-\) reduces its concentration, causing the equilibrium to shift right, dissolving more Fe(OH)\(_3\). Conversely, adding more OH\(^-\) shifts the equilibrium left, decreasing solubility. Understanding these shifts can help predict how various substances will impact solubility.

Net Ionic Equation

Net ionic equations simplify chemical reactions by showing only the species that change during the reaction. They omit the spectator ions, which do not participate in the reaction. Writing a net ionic equation involves simplification: start with the full equation and eliminate ions that appear unchanged on both sides. For instance, the dissolution of Fe(OH)\(_3\) in the presence of HBr involves hydronium ions (H\(^+\)) reacting with hydroxide ions (OH\(^-\)), leading to the formation of water and Fe\(^{3+}\). The net ionic equation focuses on these changes and looks like: \[ \mathrm{Fe(OH)_{3}(s)} + 3\mathrm{H^{+}(aq)} \rightarrow \mathrm{Fe^{3+}(aq)} + 3\mathrm{H_2O(l)} \]This equation succinctly captures the chemistry of the reaction, highlighting the chemical species directly involved in the change.

Complex Ions

Complex ions are ions formed from a central metal ion bonded to one or more molecules or ions, such as water or ammonia, known as ligands. These bonds involve coordination, where electrons are shared between the metal and ligands. Complex ions significantly alter the solubility of certain compounds. For example, when a complex ion forms, it can stabilize certain metal ions in solution, increasing their solubility. In our reaction, if a ligand like CN\(^-\) from KCN is added, it might form a complex ion with Fe\(^{3+}\), such as \([\mathrm{Fe(CN)_{6}}]^{3-}\). This interaction can further dissolve Fe(OH)\(_3\) as the complex ion is very stable and reduces the concentration of free Fe\(^{3+}\), shifting the equilibrium right and increasing solubility. Understanding the formation of complex ions is crucial, as they play a significant role in reactions involving transition metals.

Equilibrium

Equilibrium is a state in a chemical reaction where the forward and reverse reactions occur at equal rates. This results in the concentrations of reactants and products remaining constant over time. Equilibrium doesn't mean the quantities of reactants and products are equal but rather that their ratios are constant. When discussing solubility, equilibrium is relevant because the dissolution of solids into ions is often a reversible reaction. For Fe(OH)\(_3\), the equilibrium can be expressed as:\[ \mathrm{Fe(OH)_{3}(s)} \rightleftharpoons \mathrm{Fe^{3+}(aq)} + 3\mathrm{OH^{-}(aq)} \]Changes in conditions, such as concentration of ions or pH, can shift this balance. Adding a reactant shifts equilibrium according to Le Chatelier's Principle, altering solubility. Thus, understanding equilibrium enables prediction of how changes will affect solubility and, more broadly, the behavior of chemical systems.