91Ó°ÊÓ

The solubility product constant, often abbreviated as \( K_{sp} \), is crucial in predicting the solubility of ionic compounds in water. It specifically applies to sparingly soluble salts, such as \( \text{Ag}_2\text{S} \) in the given exercise.

The formula for the solubility product of a salt \( ext{A} ext{B} ightleftharpoons ext{A}^{+} + ext{B}^{-} \) is given by: \[ K_{sp} = [A^+]^a[B^-]^b \] where \([A^+]\) and \([B^-]\) are the molar concentrations of the ions in the solution at equilibrium and \(a\) and \(b\) are the stoichiometric coefficients.

For \( \text{Ag}_2\text{S} \), which dissociates in water according to: \[ \text{Ag}_2\text{S}(s) \rightleftharpoons 2\text{Ag}^{+}(aq) + \text{S}^{2-}(aq) \] The \( K_{sp} \) expression will be: \[ K_{sp} = [Ag^+]^2[S^{2-}] \] Understanding \( K_{sp} \) helps us determine the extent to which this salt will dissolve in a solution under specified conditions.

The acid dissociation constant, represented as \( K_{a} \), measures the strength of an acid in terms of its ability to donate protons (\( H^+ \)) in an aqueous solution.

For a general acid \( HA\) dissociating as: \[ HA(aq) \rightleftharpoons H^+(aq) + A^-(aq) \] The expression for \( K_a \) is: \[ K_{a} = \frac{[H^+][A^-]}{[HA]} \]

In the original problem, \( \text{H}_2\text{S} \) is considered with two dissociation steps and corresponding constants \( K_{a1} \) and \( K_{a2} \):

• \( \text{H}_2\text{S} \rightleftharpoons H^+ + \text{HS}^- \), described by \( K_{a1} \)
• \( \text{HS}^- \rightleftharpoons H^+ + \text{S}^{2-} \), described by \( K_{a2} \)

Each \( K_{a} \) value informs us how readily the proton dissociation occurs, with a higher value indicating a stronger acid.

The formation constant, known as \( K_{f} \), describes the stability of complex ions in solution. Specifically, it refers to the equilibrium between the ions that form a complex ion.

For a reaction where a complex ion \( \text{ML}_n \) is formed: \[ M^{+} + nL^{-} \rightleftharpoons ML_n \] the formation constant expression is: \[ K_{f} = \frac{[ML_n]}{[M^+][L^-]^n} \]
In the problem at hand, the reaction involves forming \( \text{AgCl}_2^- \) from \( \text{Ag}^+ \) and \( \text{Cl}^- \). The given \( K_{f} = 1.1 \times 10^5 \) reveals the high stability and likelihood of this complex ion to form in solution.

Stronger complex formation results in larger \( K_{f} \) values, which indicates that even at low reactant concentrations, the complex ion forms readily.