Problem 48 - Chemistry The Molecular Science

Question

The equilibrium constants for dissolving silver sulfate and silver sulfide in water are \(1.7 \times 10^{-5}\) and \(6 \times 10^{-30}\), respectively. (a) Write the balanced dissociation reaction equation and the associated equilibrium constant expression for each process. (b) Which compound is more soluble? Explain your answer. (c) Which compound is less soluble? Explain your answer.

Step-by-Step Solution

Answer

Silver sulfate is more soluble than silver sulfide, as it has a higher Ksp value.

Step 1: Determine Dissociation Equations

For silver sulfate, the chemical formula is \( \text{Ag}_2\text{SO}_4 \). Its dissociation in water is:\[\text{Ag}_2\text{SO}_4 (s) \rightleftharpoons 2\text{Ag}^+ (aq) + \text{SO}_4^{2-} (aq)\]For silver sulfide, the chemical formula is \( \text{Ag}_2\text{S} \). Its dissociation in water is:\[\text{Ag}_2\text{S} (s) \rightleftharpoons 2\text{Ag}^+ (aq) + \text{S}^{2-} (aq)\]

Step 2: Write Equilibrium Constant Expressions

For silver sulfate, the equilibrium constant expression \( K_{sp} \) is:\[K_{sp} = [\text{Ag}^+]^2[\text{SO}_4^{2-}]\]For silver sulfide, the equilibrium constant expression \( K_{sp} \) is:\[K_{sp} = [\text{Ag}^+]^2[\text{S}^{2-}]\]

Step 3: Analyze Solubility Based on Ksp

The compound with the larger equilibrium constant \( K_{sp} \), which is silver sulfate with \(1.7 \times 10^{-5}\), is more soluble in water compared to silver sulfide with a \( K_{sp} \) of \(6 \times 10^{-30}\). This is because a larger \( K_{sp} \) value indicates higher solubility.

Step 4: Conclude Less Soluble Compound

Since silver sulfide has a much smaller \( K_{sp} \) value of \(6 \times 10^{-30}\), it dissociates less in water, making it the less soluble compound out of the two.

Key Concepts

Solubility Product Constant

The solubility product constant, often denoted as \(K_{sp}\), is a crucial concept in chemistry, especially in understanding the solubility and dissolution behavior of sparingly soluble salts in water. It represents the equilibrium constant for a solid substance dissolving in an aqueous solution. In simpler terms, \(K_{sp}\) equals the product of the concentrations of the ions formed when the substance dissociates in water, each raised to the power of its coefficient in the balanced equation.

• A high \(K_{sp}\) value indicates high solubility, as it signifies that more ions are present in the solution.
• A low \(K_{sp}\) value suggests low solubility, indicating fewer ions in the solution.

Understanding \(K_{sp}\) allows chemists to predict whether a precipitate will form in a mixture or whether a solid will dissolve in a solution.

Dissociation Reaction

A dissociation reaction occurs when a compound splits into its ions in a solution. This is a type of equilibrium reaction, meaning it can proceed in both forward (dissociation) and backward (association) directions. The dissociation of silver sulfate and silver sulfide can be represented as:

• Silver sulfate: \(\text{Ag}_2\text{SO}_4(s) \rightleftharpoons 2\text{Ag}^+(aq) + \text{SO}_4^{2-}(aq)\)
• Silver sulfide: \(\text{Ag}_2\text{S}(s) \rightleftharpoons 2\text{Ag}^+(aq) + \text{S}^{2-}(aq)\)

In these equations, the solid compounds break down into positive and negative ions when they dissolve in water. The ions in solution are essential in determining the solubility product because their concentrations are used in calculating \(K_{sp}\). The concentration of these ions in equilibrium will define the solubility of the compound.

Silver Sulfate

Silver sulfate, with the chemical formula \(\text{Ag}_2\text{SO}_4\), is a compound that can dissolve in water to some extent. When it dissolves, it dissociates into silver ions \((\text{Ag}^+)\) and sulfate ions \((\text{SO}_4^{2-})\). The equation for its dissociation is:\[ \text{Ag}_2\text{SO}_4(s) \rightleftharpoons 2\text{Ag}^+(aq) + \text{SO}_4^{2-}(aq)\]The solubility product expression for silver sulfate is:\[ K_{sp} = [\text{Ag}^+]^2[\text{SO}_4^{2-}]\]In this equation, \(K_{sp}\) depends on the concentrations of the ions. For silver sulfate, \(K_{sp} = 1.7 \times 10^{-5}\). This relatively higher \(K_{sp}\) value suggests that silver sulfate is more soluble than compounds with lower \(K_{sp}\) values.The solubility of silver sulfate is a significant focus in analytical chemistry, often influencing the preparation and reaction conditions in various chemical processes.

Silver Sulfide

Silver sulfide, represented chemically as \(\text{Ag}_2\text{S}\), is a compound known for its low solubility in water. Upon dissociation, silver sulfide forms silver ions \((\text{Ag}^+)\) and sulfide ions \((\text{S}^{2-})\).The dissociation reaction can be written as:\[ \text{Ag}_2\text{S}(s) \rightleftharpoons 2\text{Ag}^+(aq) + \text{S}^{2-}(aq)\]The solubility product expression for this compound is:\[ K_{sp} = [\text{Ag}^+]^2[\text{S}^{2-}]\]In the case of silver sulfide, \(K_{sp} = 6 \times 10^{-30}\), which is extremely small. This low value reflects the poor solubility of silver sulfide, meaning it dissociates very little to release ions into the solution.Silver sulfide's low solubility is an important characteristic, often considered in the formation of silver tarnish and in various industrial processes where silver compounds are involved.