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: Kc=[Ag+][Cl−][AgCl]K_c = \frac{[Ag^+][Cl^-]}{[AgCl]}
    • [AgCl] is constant and represents the molar concentration of solid AgCl.
  • Rewrite as:
    Ksp=[Ag+][Cl−]K_{sp} = [Ag^+][Cl^-]

Calculating Ksp

  • Can be measured or calculated from experimental data.
  • Example Ksp expressions:
    • Sn(OH)<em>2(s)<===>Sn2+(aq)+2OH−(aq), K</em>sp=[Sn2+][OH−]2Sn(OH)<em>2 (s) <===> Sn^{2+} (aq) + 2 OH^{-} (aq), \, K</em>{sp} = [Sn^{2+}][OH^{-}]^2
    • Ag<em>2CrO</em>4(s)<===>2Ag+(aq)+CrO<em>42−(aq), K</em>sp=[Ag+]2[CrO42−]Ag<em>2CrO</em>4 (s) <===> 2 Ag^+ (aq) + CrO<em>4^{2-} (aq), \, K</em>{sp} = [Ag^+]^2[CrO_4^{2-}]
    • Fe(OH)<em>3(s)<===>Fe3+(aq)+3OH−(aq), K</em>sp=[Fe3+][OH−]3Fe(OH)<em>3 (s) <===> Fe^{3+} (aq) + 3 OH^{-} (aq), \, K</em>{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 = 3.4×10−173.4 \times 10^{-17}
    • For ions: [Ag+]=2x[Ag^+] = 2x and [S2−]=x[S^{2-}] = x
    • Ksp calculated as follows:
      Ksp=[Ag+]2[S2−]=(2x)2(x)=4x3K_{sp} = [Ag^+]^2[S^{2-}] = (2x)^2(x) = 4x^3
    • Solving yields Ksp=1.6×10−49K_{sp} = 1.6 \times 10^{-49}

Common Ion Effect on Solubility

  • Example with SrF2SrF_2 (Ksp = 7.9×10−107.9 \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=KspQ = K_{sp} → Saturated, at equilibrium.
    • If Q > K_{sp} → Precipitate forms.

Example Calculations

  • Ksp determination using solubility data:

    • 2.57×10−22.57 \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.