At the equivalence point of a titration, the moles of the analyte and titrant are equal, resulting in the formation of a precipitate that exists in equilibrium with its constituent ions. To determine the concentration of the analyte, the solubility product constant (Ksp) of the precipitate, such as silver chloride (AgCl), is utilized. The dissociation of silver chloride can be represented as follows:\[\text{AgCl (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^- (aq)\]In this equilibrium, the solid AgCl is ignored in the Ksp expression, which focuses solely on the aqueous ions. The Ksp expression for silver chloride is given by:\[K_{sp} = [\text{Ag}^+][\text{Cl}^-]\]Assuming that at equilibrium, the concentrations of silver ions and chloride ions are both equal to \(x\), the Ksp can be expressed as:\[K_{sp} = x \cdot x = x^2\]If the stoichiometry were different, such as having two chloride ions for every silver ion, the expression would adjust accordingly:\[K_{sp} = [\text{Ag}^+][\text{Cl}^-]^2 = x \cdot (2x)^2 = 4x^3\]To find the concentration of chloride ions, \(x\), one would take the square root of the Ksp value:\[x = \sqrt{K_{sp}}\]For example, if \(K_{sp} = 1.8 \times 10^{-10}\), then:\[x = \sqrt{1.8 \times 10^{-10}} \approx 1.34 \times 10^{-5} \text{ M}\]This value represents the concentration of chloride ions. The pCl, which is the negative logarithm of the chloride ion concentration, can be calculated as:\[pCl = -\log[\text{Cl}^-] = -\log(1.34 \times 10^{-5}) \approx 4.87\]As titrant is added, the pCl value increases, reflecting the changes in chloride ion concentration. After reaching the equivalence point, further analysis is required to determine the final pCl, which will depend on the excess titrant present.