For the salt AgCl, which dissociates as AgCl(s) ⇌ Ag^+(aq) + Cl^-(aq), how can the solubility product constant (K_{sp}) be expressed in terms of the molar solubility (s)?

• A. K_{sp} = s^2
• B. K_{sp} = s^3
• C. K_{sp} = s
• D. K_{sp} = 2s

Answer: (A)

Verified step by step guidance

1. Identify the dissociation equation for AgCl: \(\mathrm{AgCl(s) \rightleftharpoons Ag^{+}(aq) + Cl^{-}(aq)}\).
2. Define the molar solubility \(s\) as the concentration of \(\mathrm{Ag^{+}}\) ions in solution at equilibrium, which is also equal to the concentration of \(\mathrm{Cl^{-}}\) ions because they dissociate in a 1:1 ratio.
3. Write the expression for the solubility product constant \(K_{sp}\) in terms of the ion concentrations: \(K_{sp} = [\mathrm{Ag^{+}}][\mathrm{Cl^{-}}]\).
4. Substitute the molar solubility \(s\) into the expression, since \([\mathrm{Ag^{+}}] = s\) and \([\mathrm{Cl^{-}}] = s\), so \(K_{sp} = s \times s\).
5. Simplify the expression to get \(K_{sp} = s^{2}\), which relates the solubility product constant to the molar solubility.