L4 - Dissolution and Precipitation

Solution and Precipitation Reactions

Introduction: Salt in Water Experiment

  • Simple experiment: Adding salt (NaCl) to water.

  • Observation: Salt disappears, forming a solution.

  • Saturation: Point where no more salt dissolves.

Representation

  • Plotting concentration of Na^+ or Cl^- ions vs. time.

  • Two phases:

  • Dissolution: Salt dissociates into ions.

    • Saturation: Equilibrium between solid salt and ions.

Dissolution Reaction

  • NaCl(s) \rightarrow Na^+(aq) + Cl^-(aq)

  • aq indicates aqueous species.

Saturation

  • Equilibrium between solid NaCl and Na^+ and Cl^- ions in solution.

  • NaCl(s) \rightleftharpoons Na^+(aq) + Cl^-(aq)

Solubility

  • Concentration of substance in solution at saturation.

  • Function of pressure and temperature.

Formal Representation of Solid Dissolution

Solid composed of p atoms of cation B and n atoms of anion A:

  • B_pA_n

Dissolution (non-equilibrium):

  • B_pA_n(s) \rightarrow pB^{n+}(aq) + nA^{p-}(aq)

At equilibrium:

  • B_pA_n(s) \rightleftharpoons pB^{n+}(aq) + nA^{p-}(aq)

Solubility Definition

  • Concentration of cation or anion at saturation, normalized by stoichiometric coefficient.

  • Units: mol/L or mol/kg.

Solubility Product (Ksp)

  • Equilibrium constant for dissolution equilibrium.

Law of Mass Action:

  • K_{sp} = \frac{a_{B^{n+}}^p a_{A^{p-}}^n}{a_{B_pA_n}}=a^p_{B^{n+}(eq)} \cdot a^n_{a^{p-}(eq)} because the activity of a pure solid is 1

  • K_{sp} is a product of ion activities at saturation and is called the solubility product.

  • Temperature and pressure dependent.

Ion Activity Product (IAP)

  • Reaction quotient (Q) for dissolution reaction.

  • Same expression as K_{sp}, but not necessarily at equilibrium.

Example: Calcium Carbonate Dissolution

  • CaCO_3(s) \rightleftharpoons Ca^{2+}(aq) + CO_3^{2-}(aq)

IAP expression:

  • IAP = a_{Ca^{2+}} \cdot a_{CO_3^{2-}}

Saturation Index (SI)

  • Measure of saturation state.

  • SI = log(\frac{IAP}{K_{sp}})

    • SI = 0: Solution is saturated (equilibrium).

    • SI > 0: Solution is supersaturated (precipitation).

    • SI < 0: Solution is undersaturated (dissolution).

Example Problem: Calcium Sulfate (Anhydrite)

  • Given: Concentrations of Ca^{2+} and SO_4^{2-}, K_{sp} of anhydrite.

  • [Ca^{2+}] = 5 \cdot 10^{-2} \text M

  • [SO_4^{2-}] = 7 \cdot 10^{-3} \text{M}

  • K_{sp(anhydrite)}=10^{-4.59}

  • Question 1: Is the solution supersaturated?

  • Question 2: How much mineral precipitates to reach equilibrium?

Assumptions

  • Activity coefficients = 1 (dilute solutions).

Solution

Kinetics vs. Thermodynamics

  • Thermodynamics predicts stable state (minimum Gibbs free energy), but the actual dissolution or precipitation in the appropriate saturation will depend on kinetic factors.

  • Seawater: Supersaturated with CaCO_3, but slow precipitation. The formation of CaCO_3 is kinetically inhibited.

  • Calcite in pure water: Undersaturated, but slow dissolution.

Metastability

  • System in non-equilibrium state due to slow kinetics.

  • Several supersaturated mineral phases may exist.

  • Unstable precursor phase: Precipitates faster, but not thermodynamically stable.

  • Example: calcite often precipitates via an amorphous calcium carbonate (ACC) precursor that is metastable.

  • Biomineralization: Organisms use metastable precursors for skeleton formation.

Metastable Zone

  • Solution supersaturated, but no precipitation due to slow reaction.

  • Homogeneous (spontaneous) nucleation: Direct precipitation in solution.

  • Heterogeneous nucleation: Precipitation on a seed crystal (lower activation energy).

Stability Diagrams

  • Predict mineral precipitation based on solution composition.

  • Two-dimensional representation of stability fields.

Example: Magnesium-containing Solution

  • Minerals: Brucite (Mg(OH)_2) and Magnesite (MgCO_3).

  • Axes: pH and log[Mg^{2+}].

Steps to Build Diagram

  1. Write dissolution reactions.

  2. Express [Mg^{2+}] as a function of pH.

Brucite Stability

Mg(OH)_2(s) \rightleftharpoons Mg^{2+}(aq) + 2OH^-(aq)

K_{sp,Bru} = [Mg^{2+}][OH^-]^2=10^{-11.6}

[Mg^{2+}] = \frac{K_{sp,Bru}}{[OH^-]^2}

Using K_w = [H^+][OH^-], [OH^-] = \frac{K_w}{[H^+]}:

[Mg^{2+}] = \frac{K_{sp,Bru}[H^+]^2}{Kw^2}

log[Mg^{2+}] = log(K_{sp,Bru}) + 2log[H^+] - 2log(K_w)

log[Mg^{2+}] = 16.4 - 2pH

Magnesite Stability

MgCO_3(s) \rightleftharpoons Mg^{2+}(aq) + CO_3^{2-}(aq)

K_{sp,Mag}=[Mg^{2+}][CO_3^{2-}]=10^{-7.5}

  • Carbonate system considerations (DIC, pH).

  • Three pH domains:

    1. High pH (pH > pK_{a_2}): [CO_3^{2-}] \approx DIC

    2. Intermediate pH (pK_{a_1} < pH < pK_{a_2}): [HCO_3^-] \approx DIC

    3. Low pH (pH < pK_{a_1}): [H_2CO_3] \approx DIC

  • Using appropriate carbonate equilibrium constants to relate [CO_3^{2-}] to DIC and pH.

High pH

K_{sp,Mag}=\left\lbrack Mg^{2+}\right\rbrack\left\lbrack CO_{3^{}}^{2-}\right\rbrack=\left\lbrack Mg^{2+}\right\rbrack\sum CO_2

\log\left\lbrack Mg^{2+}\right\rbrack=\log K_{sp,Mag}-\log\sum CO_2=-pK_{sp,Mag}+p\sum CO_2

log[Mg^{2+}] = log(\frac{K_{sp}}{DIC})

log[Mg^{2+}] = -5

  • Horizontal line.

Intermediate pH

Low pH

Overlapping Stability Fields

  • Stable mineral is the one with lowest solubility (lowest line on diagram).

Applications of Stability Diagrams

  • Predicting mineral dissolution/precipitation in natural waters.

  • Weathering processes.

  • Impact of CO_2$$ on Ocean Acidification and the effect on production of calcium carbonate skeletal material by some marine organisms. Increasing acidity reduces the saturation index of calcium carbonate.