Question

The equilibrium constants for dissolving calcium carbonate, silver nitrate, and silver chloride in water are \(2.8 \times 10^{-9}, 2.0 \times 10^{2},\) and \(1.8 \times 10^{-10},\) respectively. (a) Write the balanced dissociation reaction equation and the associated equilibrium constant expression for each process. (b) Which compound is most soluble? Explain your answer. (c) Which compound is least soluble? Explain your answer.

Short answer

AgNO3 is most soluble; AgCl is least soluble.

Step-by-step solution

Understand the Dissociation Reaction

First, identify and write the balanced chemical equation for the dissolution of each compound in water. For calcium carbonate (CaCO3), silver nitrate (AgNO3), and silver chloride (AgCl):1. **CaCO3 Dissolution**: \[ \text{CaCO}_3 (s) \rightleftharpoons \text{Ca}^{2+} (aq) + \text{CO}_3^{2-} (aq) \]2. **AgNO3 Dissolution**: \[ \text{AgNO}_3 (s) \rightleftharpoons \text{Ag}^{+} (aq) + \text{NO}_3^{-} (aq) \]3. **AgCl Dissolution**: \[ \text{AgCl} (s) \rightleftharpoons \text{Ag}^{+} (aq) + \text{Cl}^{-} (aq) \]

Write the Equilibrium Constant Expressions

Next, write the equilibrium constant expression for each dissociation based on the balanced equations. The equilibrium constants are derived from the concentration of the products:1. **For \( \, \text{CaCO}_3 \, \):** \( K_{eq} = [\text{Ca}^{2+}][\text{CO}_3^{2-}] \) Given \( K_{eq} = 2.8 \times 10^{-9} \)2. **For \( \, \text{AgNO}_3 \, \):** \( K_{eq} = [\text{Ag}^{+}][\text{NO}_3^{-}] \) Given \( K_{eq} = 2.0 \times 10^{2} \)3. **For \( \, \text{AgCl} \, \):** \( K_{eq} = [\text{Ag}^{+}][\text{Cl}^{-}] \) Given \( K_{eq} = 1.8 \times 10^{-10} \)

Determine the Most Soluble Compound

The compound with the largest equilibrium constant is the most soluble because it produces the greatest concentration of ions in solution. Compare the given equilibrium constants:- \( K_{eq}(\text{CaCO}_3) = 2.8 \times 10^{-9} \)- \( K_{eq}(\text{AgNO}_3) = 2.0 \times 10^{2} \)- \( K_{eq}(\text{AgCl}) = 1.8 \times 10^{-10} \)The largest \( K_{eq} \) is for AgNO3, meaning it is the most soluble compound.

Determine the Least Soluble Compound

The compound with the smallest equilibrium constant is the least soluble as it contributes the least amount of ions to the solution. Compare the equilibrium constants:- \( K_{eq}(\text{CaCO}_3) = 2.8 \times 10^{-9} \)- \( K_{eq}(\text{AgNO}_3) = 2.0 \times 10^{2} \)- \( K_{eq}(\text{AgCl}) = 1.8 \times 10^{-10} \)The smallest \( K_{eq} \) is for AgCl, indicating it is the least soluble compound.

Key concepts

Solubility Product

The solubility product (often symbolized as \( K_{sp} \)) is an equilibrium constant that applies to sparingly soluble salts. It reflects the extent to which a compound can dissolve in water. The greater the solubility product, the more the salt dissolves, creating ions in the solution. This value is represented as a specific type of equilibrium constant for dissolution reactions.

• The solubility product relies on the concentrations of the ions produced in the solution.
• It is unique for each compound and depends significantly on the temperature.
• A higher \( K_{sp} \) indicates a more soluble substance.

Consider calcium carbonate (CaCO\(_3\)), which has a \( K_{sp} \) of \( 2.8 \times 10^{-9} \). Compared to silver nitrate with a much larger value of \( 2.0 \times 10^{2} \), it implies that calcium carbonate dissolves less than silver nitrate. Understanding \( K_{sp} \) helps in predicting the solubility of salts in various environments.

Dissolution Reactions

Dissolution reactions describe the process through which an ionic solid dissolves in a solvent, usually water, to form ions. The basic unit or formula of the compound breaks apart to release its constituant ions into solution. It's the first step in understanding solubility and the role of equilibrium.

• Each ionic compound has a specific dissolution reaction that can be expressed chemically.
• Dissolution reactions are reversible and reach a dynamic equilibrium called solution equilibrium.

For example, when calcium carbonate (CaCO\(_3\)) is dissolved, it splits into calcium ions (Ca\(^{2+}\)) and carbonate ions (CO\(_3^{2-}\)). Each of these plays a role in maintaining the balance dictated by the \( K_{sp} \). Dissolution is essential for understanding how ions interact in solutions and measure their impact on chemical reactions.

Equilibrium Constant Expression

An equilibrium constant expression describes the balance between the reactants and products in a chemical reaction at equilibrium. In the context of dissolution, it refers to the concentrations of ions formed from a solid dissolving in solution.

• The expression involves the concentrations of products raised to the power of their coefficients in the balanced equation.
• In dissolution, it simplifies to the concentration of ions since the concentration of a pure solid is constant.

For a compound like silver chloride (AgCl), the equilibrium constant expression is given as \( K_{eq} = [\text{Ag}^+][\text{Cl}^-] \). Here, even though AgCl starts as a solid, its contributions to the equilibrium are expressed solely through its ions in the solution. The equilibrium constant tells us how far the dissolution goes and what quantities of ions are produced.