Notes on Solubility and Ksp

Solubility Concept

• Refers to the maximum amount of a substance that dissolves in a solvent at a given temperature.

Ksp: Solubility-Product Constant

• Introduced by Walther Nernst in 1899.
• Relevant for solid substances considered insoluble in water.
• Key aspects:
  • Some solid dissolves, although minimally.
  • Dissociation occurs upon dissolving.
  • Equilibrium exists between undissolved solid and solvated ions.

Dissociation Example

• Silver chloride (AgCl(s)
• Equilibrium expression: K_c = \frac{[Ag^+][Cl^-]}{[AgCl]}
  • [AgCl] is constant and represents the molar concentration of solid AgCl.
• Rewrite as:
  K_{sp} = [Ag^+][Cl^-]

Calculating Ksp

• Can be measured or calculated from experimental data.
• Example Ksp expressions:
  • Sn(OH)2 (s) {sp} = [Sn^{2+}][OH^{-}]^2
  • Ag2CrO4 (s)
  • Fe(OH)3 (s) {sp} = [Fe^{3+}][OH^{-}]^3

Writing Ksp Expressions

• Each concentration in the Ksp expression is raised to the power of its coefficient in the balanced equation.

Solubility Equilibrium Calculations

• Example: Ksp of Ag2S, solubility = 3.4 \times 10^{-17}
  • For ions: [Ag^+] = 2x and [S^{2-}] = x
  • Ksp calculated as follows:
    K_{sp} = [Ag^+]^2[S^{2-}] = (2x)^2(x) = 4x^3
  • Solving yields K_{sp} = 1.6 \times 10^{-49}

Common Ion Effect on Solubility

• Example with SrF_2 (Ksp = 7.9 \times 10^{-10} ):
  • Examine solubility in pure water vs. ionic solutions.
• LeChâtelier’s Principle predicts solubility decreases with the presence of a common ion.

Precipitation Predictions Using Q Value

• Q (reaction quotient) compares initial concentrations to Ksp:
  • If Q < K_{sp} → No precipitate.
  • If Q = K_{sp} → Saturated, at equilibrium.
  • If Q > K_{sp} → Precipitate forms.

Example Calculations

• Ksp determination using solubility data:

  • 2.57 \times 10^{-2} grams of MgF2 in 1.0 L: calculate Ksp.
  • Determine precipitation order when Na2CrO4 is added to a mixed solution of Pb(NO3)2 and Ba(NO3)2, using respective Ksp values.

• Understanding ion concentrations in relation to pH buffers and Ksp values for different compounds is essential for solubility calculations and predictions.