Question

As you learned in Chapter 7 , most metal hydroxides are sparingly soluble in water. Write balanced chemical equations describing the dissolving of the following metal hydroxides in water. Write the expression for \(K_{\mathrm{sp}}\) for each process. a. \(\mathrm{Cu}(\mathrm{OH})_{2}(s)\) b. \(\mathrm{Cr}(\mathrm{OH})_{3}(s)\) c. \(\mathrm{Ba}(\mathrm{OH})_{2}(s)\) d. \(\operatorname{Sn}(\mathrm{OH})_{2}(s)\)

Short answer

a. Cu(OH)\(_2\)(s) \(\rightleftharpoons\) Cu\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq); \(K_{sp}\) = [Cu\(^{2+}\)] [OH\(^{-}\)]\(^{2}\) b. Cr(OH)\(_3\)(s) \(\rightleftharpoons\) Cr\(^{3+}\)(aq) + 3 OH\(^{-}\)(aq); \(K_{sp}\) = [Cr\(^{3+}\)] [OH\(^{-}\)]\(^{3}\) c. Ba(OH)\(_2\)(s) \(\rightleftharpoons\) Ba\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq); \(K_{sp}\) = [Ba\(^{2+}\)] [OH\(^{-}\)]\(^{2}\) d. Sn(OH)\(_2\)(s) \(\rightleftharpoons\) Sn\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq); \(K_{sp}\) = [Sn\(^{2+}\)] [OH\(^{-}\)]\(^{2}\)

Step-by-step solution

Write the balanced chemical equations

We will write down the balanced chemical equations representing the dissolving of each metal hydroxide in water. a. Cu(OH)\(_2\)(s) \(\rightleftharpoons\) Cu\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq) b. Cr(OH)\(_3\)(s) \(\rightleftharpoons\) Cr\(^{3+}\)(aq) + 3 OH\(^{-}\)(aq) c. Ba(OH)\(_2\)(s) \(\rightleftharpoons\) Ba\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq) d. Sn(OH)\(_2\)(s) \(\rightleftharpoons\) Sn\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq)

Write the expressions for \(K_{sp}\) for each metal hydroxide

We will now write down the \(K_{sp}\) expressions for each metal hydroxide. For a general reaction: AB(s) \(\rightleftharpoons\) A\(^{n\text{+}}\)(aq) + B\(^{n\text{-}}\)(aq), the \(K_{sp}\) expression can be written as: \(K_{sp}\) = [A\(^{n+}\)][B\(^{n-}\)] Here, we will use this concept to derive expressions for the given metal hydroxides: a. Cu(OH)\(_2\)(s) \(\rightleftharpoons\) Cu\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq) \(K_{sp}\) = [Cu\(^{2+}\)] [OH\(^{-}\)]\(^{2}\) b. Cr(OH)\(_3\)(s) \(\rightleftharpoons\) Cr\(^{3+}\)(aq) + 3 OH\(^{-}\)(aq) \(K_{sp}\) = [Cr\(^{3+}\)] [OH\(^{-}\)]\(^{3}\) c. Ba(OH)\(_2\)(s) \(\rightleftharpoons\) Ba\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq) \(K_{sp}\) = [Ba\(^{2+}\)] [OH\(^{-}\)]\(^{2}\) d. Sn(OH)\(_2\)(s) \(\rightleftharpoons\) Sn\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq) \(K_{sp}\) = [Sn\(^{2+}\)] [OH\(^{-}\)]\(^{2}\)

Key concepts

Metal Hydroxides

Metal hydroxides are compounds consisting of a metal cation bonded to hydroxide ions (OH⁻). These are often characterized by their low solubility in water, meaning they do not dissolve readily. This can be puzzling for students because it contrasts with many ionic compounds which freely dissolve in water. However, the metal hydroxides have stronger ionic bonds and lattice structures that require more energy to break apart.
To assess the solubility of these compounds, we often perform dissolution tests in water. When they dissolve, they dissociate into their respective ions. Still, due to their low solubility, only a small concentration will dissociate. This dissociation is crucial for reactions in aqueous solutions as it defines the concentration of available metal ions and hydroxide ions.
For example, when copper(II) hydroxide (Cu(OH)₂) dissolves in water, it separates into Cu²⁺ ions and OH⁻ ions. As a rule of thumb, each metal hydroxide's solubility can significantly vary, thus making this a central concept in understanding reactions in inorganic chemistry.

Dissolution Equations

Dissolution equations describe the process by which a compound breaks down into its constituent ions in a solution. These equations are important because they offer a visual understanding of how compounds interact with water at the molecular level.
In dissolution equations for metal hydroxides, the solid formula of the compound (like Cu(OH)₂) is shown on the left, and on the right, you see the ions it breaks down into when dissolved in water (like Cu²⁺ and OH⁻). This can be represented as:
- Cu(OH)₂(s) ⇌ Cu²⁺(aq) + 2 OH⁻(aq).
Here, the double arrows indicate the reversible nature of the dissolution process, emphasizing that not all components dissolve completely. Each equation must balance, considering both the charge and the number of atoms involved. This balancing ensures the conservation of mass and the uniform distribution of charges in the solution.
Further, each metal hydroxide has unique coefficients, indicating how many ions of each type are produced per formula unit of the solid, influenced by its stoichiometry. These equations form the basis for predicting how solutions will behave in chemical processes.

Solubility Product Constant (Ksp)

The Solubility Product Constant, abbreviated as Ksp, is a measure that describes the extent to which a compound can dissolve in water. It is a specific type of equilibrium constant used in the context of solubility equilibria, especially for sparingly soluble compounds like metal hydroxides.
The Ksp takes into consideration the concentrations of the ions produced in the dissolution of the compound. For a general dissolution reaction, for example, AB(s) ⇌ A⁺(aq) + B⁻(aq), the Ksp expression is expressed as:

• Ksp = [A⁺][B⁻]

Thus, the Ksp expression is derived by the product of the concentrations of the ions each raised to the power of their coefficients from the balanced equation.
In terms of metal hydroxides, such as Cr(OH)₃ dissolving as Cr³⁺(aq) + 3 OH⁻(aq), the corresponding Ksp expression will be:

• Ksp = [Cr³⁺] [OH⁻]³

The larger the value of Ksp, the more soluble the compound is. Understanding these constants helps predict the conditions under which a particular compound will precipitate or remain soluble, a vital aspect of chemical reactions and processes in solutions.