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Understanding how silver sulfide (Ag\(_2\)S) dissolves is key to solving solubility product problems. Silver sulfide is a compound composed of silver and sulfur. When it dissolves in water, it breaks down into its ions:

• 2 Ag\(^+\) ions
• 1 S\(^{2-}\) ion

This reaction is represented by the chemical equilibrium equation: \[\text{Ag}_2\text{S} (s) \rightleftharpoons 2 \text{Ag}^+ (aq) + \text{S}^{2-} (aq)\]This equation shows how solid silver sulfide dissociates into silver ions and sulfide ions in an aqueous solution. The dissolution occurs at a molecular level where the solid compound interacts with water molecules.
Understanding dissolution on this basic level aids in understanding how concentration changes impact equilibrium.

The equilibrium expression for the dissolution of silver sulfide involves balancing the concentrations of the dissolved ions. The silver sulfide solubility product, or \(K_{sp}\), is an indicator of its solubility in water and is derived from the concentrations of the ions at equilibrium.The general expression for the solubility product of silver sulfide, Ag\(_2\)S, can be expressed as:\[K_{sp} = [\text{Ag}^+]^2 [\text{S}^{2-}]\]This expression shows that the solubility product is dependent on the concentration of silver ions \([\text{Ag}^+]\) squared (because 2 moles of silver ions are produced per mole of silver sulfide) and the concentration of sulfide ions \([\text{S}^{2-}]\).
For the given problem, substitution of the known concentrations into this expression allows for the calculation of the dissolved silver sulfide's concentration. An understanding of how equilibrium expressions work is crucial as it describes the balance in reversible reactions.

To convert moles of a substance into grams, calculating its molar mass is essential. The molar mass is the mass of one mole of a chemical compound, reported in grams per mole (g/mol).For silver sulfide (Ag\(_2\)S), the molar mass is calculated by summing the atomic masses of its constituent elements:

• Silver (Ag) has an atomic mass of approximately 107.87 g/mol. For two silver atoms: 2 脳 107.87 g/mol = 215.74 g/mol.
• Sulfur (S) has an atomic mass of approximately 32.06 g/mol.
• Adding these, Ag\(_2\)S has a molar mass of 247.80 g/mol.

This calculation is significant as it allows conversion from moles to grams, providing the actual mass of silver sulfide that can dissolve in a given volume of solution.
Ensuring accurate molar mass calculation is a critical step in solving chemical quantity problems.

Stoichiometry is the calculation of reactants and products in chemical reactions. In the context of silver sulfide dissolution, it helps us understand the mole-to-mole relationships between reactants and products.As represented in the dissolution equation, for every mole of Ag\(_2\)S that dissolves:

• 2 moles of Ag\(^+\) ions are generated.
• 1 mole of S\(^{2-}\) ions is produced.

This ratio is derived from the balanced chemical equation:\[\text{Ag}_2\text{S} (s) \rightleftharpoons 2 \text{Ag}^+ (aq) + \text{S}^{2-} (aq)\]Understanding stoichiometry allows you to calculate the amount of product versus reactant consumed or produced in reactions.
In this exercise, stoichiometry facilitated the step from calculating ionic concentrations to predicting the mass of dissolved silver sulfide, illustrating its practical application in real-world scenarios.