Question

Devise as many ways as you can to experimentally determine the \(K_{\mathrm{sp}}\) value of a solid. Explain why each of these would work.

Short answer

There are three experimental methods to determine the Ksp value of a solid: 1. Direct Measurement of Saturated Solution Concentration: Prepare a saturated solution of the sparingly soluble salt, dissolve it in water, and analyze the supernatant liquid using titration. Determine the equilibrium concentration of ions and calculate the Ksp using the ion concentrations. 2. Precipitation Titration: Prepare a saturated solution of the sparingly soluble salt and titrate it with a standard solution of a reactant that forms a precipitate with one of the ions of the soluble salt. Determine the equivalence point and calculate the concentration of the ions in the saturated solution. Calculate the Ksp using the ion concentrations. 3. Conductivity Measurement: Prepare a saturated solution of the sparingly soluble salt and measure its conductivity. Use a standard curve to determine the equilibrium concentration of the ions in the solution and calculate the Ksp using the ion concentrations. Each method works by obtaining the ion concentrations of the saturated solution, allowing for the calculation of the Ksp value representing the solubility of the salt in question.

Step-by-step solution

Method 1: Direct Measurement of Saturated Solution Concentration

For this method, prepare a saturated solution of the sparingly soluble salt by dissolving it in water and allowing it to reach equilibrium. Filter the excess solid from the mixture and analyze the supernatant liquid using a method such as titration. Determine the equilibrium concentration of each of the ions present in the saturated solution, and then use the ion concentrations to find the Ksp value for the solid in the given reaction. For example, if the solid is AB(s) ⇌ A⁺(aq) + B⁻(aq), determine the concentrations of A⁺ and B⁻ in the saturated solution, represented by [A⁺] and [B⁻], respectively. The Ksp for the solid AB would be calculated as follows: \[ K_{sp} = [A^{+}] [B^{-}] \]

Method 2: Precipitation Titration

In precipitation titration, prepare a saturated solution of the sparingly soluble salt and titrate it with a standard solution of a reactant that forms a precipitate with one of the ions of the soluble salt. Determine the equivalence point at which the precipitate forms, and calculate the concentration of the ions in the saturated solution accordingly. By knowing the ion concentrations, the Ksp value can be calculated. For example, if the solid is AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq), titrate a saturated AgCl solution with a standard solution of KCl. At the equivalence point, use the volume and concentration of KCl to determine the concentration of Cl⁻ ions, which is equal to the equilibrium concentration of Ag⁺ ions in the solution. The Ksp can then be calculated using the equilibrium concentrations: \[ K_{sp} = [Ag^{+}] [Cl^{-}] \]

Method 3: Conductivity Measurement

Prepare a saturated solution of the sparingly soluble salt and measure its conductivity. The conductivity of a solution depends on the concentration of ions present in the solution. Use a standard curve to correlate the conductivity values with ion concentrations, and calculate the equilibrium concentrations of the ions in the solution. With the ion concentrations, the Ksp value can be determined. For example, if the solid is CaF₂(s) ⇌ Ca²⁺(aq) + 2F⁻(aq), measure the conductivity of a saturated CaF₂ solution and use a standard curve to find the equilibrium concentrations of Ca²⁺ and F⁻ ions. The Ksp value can then be calculated as follows: \[ K_{sp} = [Ca^{2+}] [F^{-}]^2 \] These are three experimental methods to determine the solubility product constant of a solid. Each of these methods works by ultimately obtaining the ion concentrations of the saturated solution, which allows for the calculation of the Ksp value representing the solubility of the salt in question.