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. \(\operatorname{Cr}(\mathrm{OH})_{3}(s)\) c. \(\mathrm{Ba}(\mathrm{OH})_{2}(s)\) d. \(\operatorname{Sn}(O H)_{2}(s)\)

Short answer

The balanced chemical equations for the dissolution of metal hydroxides in water are: a. \( Cu(OH)_{2}(s) \rightleftharpoons Cu^{2+}(aq) + 2OH^-(aq) \) b. \( Cr(OH)_{3}(s) \rightleftharpoons Cr^{3+}(aq) + 3OH^-(aq) \) c. \( Ba(OH)_{2}(s) \rightleftharpoons Ba^{2+}(aq) + 2OH^-(aq) \) d. \( Sn(OH)_{2}(s) \rightleftharpoons Sn^{2+}(aq) + 2OH^-(aq) \) The expressions for \(K_{sp}\) for each process are: a. \( K_{sp} = [Cu^{2+}][OH^-]^2 \) b. \( K_{sp} = [Cr^{3+}][OH^-]^3 \) c. \( K_{sp} = [Ba^{2+}][OH^-]^2 \) d. \( K_{sp} = [Sn^{2+}][OH^-]^2 \)

Step-by-step solution

Write the balanced chemical equation for each metal hydroxide dissolving in water.

To write these equations, we need to remember that when the metal hydroxide dissolves in water, it dissociates into its corresponding metal cation and hydroxide anion. a. For Cu(OH)₂(s): \[ Cu(OH)_{2}(s) \rightleftharpoons Cu^{2+}(aq) + 2OH^-(aq) \] b. For Cr(OH)₃(s): \[ Cr(OH)_{3}(s) \rightleftharpoons Cr^{3+}(aq) + 3OH^-(aq) \] c. For Ba(OH)₂(s): \[ Ba(OH)_{2}(s) \rightleftharpoons Ba^{2+}(aq) + 2OH^-(aq) \] d. For Sn(OH)₂(s): \[ Sn(OH)_{2}(s) \rightleftharpoons Sn^{2+}(aq) + 2OH^-(aq) \]

Write the expressions for \(K_{sp}\) for each process.

To write the expressions for \(K_{sp}\), we will use the equilibrium concentrations of the metal cations and hydroxide anions in each case. Remember that the \(K_{sp}\) expression doesn't include the concentration of the solid metal hydroxide. a. For Cu(OH)₂(s): \[ K_{sp} = [Cu^{2+}][OH^-]^2 \] b. For Cr(OH)₃(s): \[ K_{sp} = [Cr^{3+}][OH^-]^3 \] c. For Ba(OH)₂(s): \[ K_{sp} = [Ba^{2+}][OH^-]^2 \] d. For Sn(OH)₂(s): \[ K_{sp} = [Sn^{2+}][OH^-]^2 \]

Key concepts

Chemical Equilibrium

In the realm of chemistry, equilibrium refers to a condition where reactants and products in a reversible reaction cease to change in concentration over time, leading to a state of balance. This occurs when the rate at which the reactants are converting into products is equal to the rate at which products are converting back into reactants. Understanding equilibrium is crucial when discussing solubility products, as it gives us insights into the solubility of compounds in solutions.

When we apply the concept of equilibrium to the dissolution of metal hydroxides, the sparingly soluble nature of these compounds comes into play. Instead of fully dissolving, these compounds reach a point where the dissolved ions in solution are in a dynamic equilibrium with the undissolved solid, a situation well captured by the equilibrium constant for this specific case: the solubility product constant (K_sp).

Dissolution of Metal Hydroxides

The process of dissolution of metal hydroxides occurs when these compounds interact with water. Most metal hydroxides have very low solubility in water, meaning they only dissolve to a small extent. When these sparingly soluble compounds do dissolve, they separate into metal cations and hydroxide anions in a process known as dissociation. The dissolution of metal hydroxides can be influenced by various factors including temperature and the presence of other ions in solution.

Dissolution is an important process in many areas of chemistry and environmental science because it determines the bioavailability of metal ions in water systems. The limited solubility of certain metal hydroxides is also made use of in analytical chemistry for precipitation reactions and titrations.

Writing Chemical Equations

To properly articulate the process of chemical reactions, scientists use chemical equations. These equations provide a symbolic representation of all involved reactants and products. Writing a chemical equation involves placing the reactants on the left side and the products on the right, separated by an arrow that indicates the direction of the reaction. When writing the dissolution of metal hydroxides, it is key to ensure that the equation is balanced, meaning that the number of atoms of each element is the same on both sides of the equation.

For the dissolution of metal hydroxides, the reactants are the solid metal hydroxide, and the products are the aqueous metal ions and hydroxide ions. Remember to balance the equation not only for mass, but also for charge, leading to a neutral overall system.

Ksp Expression

The solubility product constant, denoted as K_sp, is an equilibrium constant that applies to the dissolution of slightly soluble salts. The K_sp expression is deduced from the balanced chemical equation of the dissolving process. For each equilibrium, the product of the concentrations of the ions raised to the power of their coefficients in the balanced equation gives us the K_sp value.

To write the K_sp expression, we only consider the soluble ionic products, omitting the concentration of any pure solids or liquids. Through these expressions, K_sp helps us appreciate the extent to which a substance can dissolve under equilibrium conditions, paving the way for calculations related to concentration, precipitation, and ion product comparisons with K_sp for solubility predictions.