Question

Write the balanced chemical equation describing the dissolving of the following solids in water. Write the expression for \(K_{\mathrm{sp}}\) for each process. a. \(\mathrm{Co}_{2} \mathrm{S}_{3}(\mathrm{s})\) b. \(\operatorname{Ag} \mathrm{I}(s)\) c. \(\mathrm{MgCO}_{3}(s)\) d. \(\operatorname{Fe}(\mathrm{OH})_{3}(s)\)

Short answer

a. \(\mathrm{Co}_{2} \mathrm{S}_{3}(\mathrm{s}) \rightleftharpoons 2\,\mathrm{Co}^{3+}(aq) + 3\,\mathrm{S}^{2-}(aq)\), \(K_\mathrm{sp} = [\mathrm{Co}^{3+}]^2[\mathrm{S}^{2-}]^3\) b. \(\mathrm{AgI}(s) \rightleftharpoons \mathrm{Ag}^{+}(aq) + \mathrm{I}^{-}(aq)\), \(K_\mathrm{sp} = [\mathrm{Ag}^{+}][\mathrm{I}^{-}]\) c. \(\mathrm{MgCO}_{3}(s) \rightleftharpoons \mathrm{Mg}^{2+}(aq) + \mathrm{CO}_{3}^{2-}(aq)\), \(K_\mathrm{sp} = [\mathrm{Mg}^{2+}][\mathrm{CO}_{3}^{2-}]\) d. \(\mathrm{Fe(OH)}_{3}(s) \rightleftharpoons \mathrm{Fe}^{3+}(aq) + 3\,\mathrm{OH}^{-}(aq)\), \(K_\mathrm{sp} = [\mathrm{Fe}^{3+}][\mathrm{OH}^{-}]^3\)

Step-by-step solution

Write the dissolution equation

First, we need to write the balanced chemical equation for the dissolution of cobalt(III) sulfide in water: \[\mathrm{Co}_{2} \mathrm{S}_{3}(\mathrm{s}) \rightleftharpoons 2\,\mathrm{Co}^{3+}(aq) + 3\,\mathrm{S}^{2-}(aq)\]

Write the expression for Ksp

Now, we can write the expression for the solubility product (Ksp) for this process: \[K_\mathrm{sp} = [\mathrm{Co}^{3+}]^2[\mathrm{S}^{2-}]^3\] b. Dissolving \(\operatorname{Ag} \mathrm{I}(s)\)

Write the dissolution equation

First, we need to write the balanced chemical equation for the dissolution of silver iodide in water: \[\mathrm{AgI}(s) \rightleftharpoons \mathrm{Ag}^{+}(aq) + \mathrm{I}^{-}(aq)\]

Write the expression for Ksp

Now, we can write the expression for the solubility product (Ksp) for this process: \[K_\mathrm{sp} = [\mathrm{Ag}^{+}][\mathrm{I}^{-}]\] c. Dissolving \(\mathrm{MgCO}_{3}(s)\)

Write the dissolution equation

First, we need to write the balanced chemical equation for the dissolution of magnesium carbonate in water: \[\mathrm{MgCO}_{3}(s) \rightleftharpoons \mathrm{Mg}^{2+}(aq) + \mathrm{CO}_{3}^{2-}(aq)\]

Write the expression for Ksp

Now, we can write the expression for the solubility product (Ksp) for this process: \[K_\mathrm{sp} = [\mathrm{Mg}^{2+}][\mathrm{CO}_{3}^{2-}]\] d. Dissolving \(\operatorname{Fe}(\mathrm{OH})_{3}(s)\)

Write the dissolution equation

First, we need to write the balanced chemical equation for the dissolution of iron(III) hydroxide in water: \[\mathrm{Fe(OH)}_{3}(s) \rightleftharpoons \mathrm{Fe}^{3+}(aq) + 3\,\mathrm{OH}^{-}(aq)\]

Write the expression for Ksp

Now, we can write the expression for the solubility product (Ksp) for this process: \[K_\mathrm{sp} = [\mathrm{Fe}^{3+}][\mathrm{OH}^{-}]^3\]

Key concepts

Dissolution Equations

Understanding dissolution equations is fundamental to grasp the behavior of ionic compounds in water. When a compound dissolves, it breaks apart into its constituent ions. This process is represented by a balanced chemical equation. Let's take cobalt(III) sulfide as an example. In water, it dissolves according to the equation:

• \( \mathrm{Co}_{2} \mathrm{S}_{3}(\mathrm{s}) \rightleftharpoons 2\,\mathrm{Co}^{3+}(aq) + 3\,\mathrm{S}^{2-}(aq) \)
• The solid on the left turns into aqueous ions on the right as it dissolves.
• The double arrow \( \rightleftharpoons \) indicates equilibrium between the solid compound and its dissolved ions.

Each dissolution equation includes the phases of the reactants and products. Solids are denoted with \((\mathrm{s})\), and aqueous ions with \((aq)\). This notation helps us understand the state of each component in the reaction.

Ionic Solubility

Ionic solubility refers to how well an ionic compound can dissolve in water, which is dependent on various factors including temperature and the ionic strength of the solution. Highly soluble compounds dissociate completely, while less soluble ones dissociate partially.

• For example, silver iodide (\( \mathrm{AgI} \)) is known to have low solubility.
• Its dissolution leads to fewer ions in solution: \( \mathrm{AgI}(s) \rightleftharpoons \mathrm{Ag}^{+}(aq) + \mathrm{I}^{-}(aq) \).
• Low solubility often implies the ion products don't surpass a stable concentration easily.

The degree of solubility also affects the saturation of a solution. A solution becomes saturated when no more dissolution can occur at a given temperature, meaning the maximum amount of solute is dissolved.

Equilibrium Expressions

Equilibrium expressions describe the concentrations of reactants and products at equilibrium. For dissolved ionic compounds, we use the solubility product constant \(K_{sp}\) to express this balance. Each \(K_{sp}\) value is unique to a compound and indicates how much of it will dissolve before reaching saturation.

• The equation for \(K_{sp}\) is derived from the dissolution equation.
• For magnesium carbonate (\( \mathrm{MgCO}_{3} \)), the equation is: \( K_{sp} = [\mathrm{Mg}^{2+}][\mathrm{CO}_{3}^{2-}] \).
• This takes into account the stochiometry of the ions in the dissolution.

Having the correct \(K_{sp}\) helps chemists predict the behavior of solutions under different conditions, such as changes in concentration or temperature.

Chemical Reactions in Aqueous Solutions

In aqueous solutions, chemical reactions occur in a medium where water acts as the solvent. The role of water is critical because it dissolves ionic compounds, leading to reactions between ions.

• Iron(III) hydroxide (\( \mathrm{Fe(OH)}_{3} \)) when dissolved, changes as follows: \( \mathrm{Fe(OH)}_{3}(s) \rightleftharpoons \mathrm{Fe}^{3+}(aq) + 3\,\mathrm{OH}^{-}(aq) \).
• These reactions are influenced by factors like pH, as hydroxide ions contribute to the basicity of a solution.
• The ions in solution can further react with other ionic species or compounds.

Reactions in aqueous solutions can be reversible, like many dissolution reactions, and they establish an equilibrium. This dynamic balance dictates the concentrations of reactants and products at any given time.