Solubility Product Constant (Ksp)
Equilibrium of dissolution for sparingly soluble salts
Understanding Solubility Product Constant (Ksp)
The solubility product constant (Ksp) is a special type of equilibrium constant that describes the dissolution equilibrium of sparingly soluble ionic compounds. When an ionic solid like silver chloride (AgCl) is placed in water, it establishes an equilibrium between the solid phase and dissolved ions: AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq). The Ksp expression includes only the dissolved ions, not the solid, because the activity of a pure solid is defined as unity. This concept is fundamental to analytical chemistry, environmental chemistry, geochemistry, and pharmaceutical science where controlling precipitation and dissolution is essential.
The magnitude of Ksp indicates relative solubility: smaller Ksp values correspond to less soluble compounds. For example, AgCl has Ksp = 1.8 × 10⁻¹⁰, making it quite insoluble, while PbCl₂ has Ksp = 1.7 × 10⁻⁵, making it moderately soluble. However, comparing Ksp values directly only works for compounds with the same stoichiometry (same number of ions). A compound like Ag₂CrO₄ (Ksp = 1.1 × 10⁻¹²) might seem more soluble than AgCl based on Ksp alone, but calculating actual molar solubility reveals the truth.
Ksp calculations have numerous practical applications: predicting whether precipitation will occur when solutions are mixed (compare reaction quotient Q to Ksp), optimizing conditions for quantitative precipitation in gravimetric analysis, understanding scale formation in pipes and boilers, predicting mineral dissolution in natural waters, designing drug formulations where solubility affects bioavailability, and treating heavy metal contamination by inducing controlled precipitation. The common ion effect—where adding an ion already present in the equilibrium decreases solubility—is a key principle in analytical separations and water treatment processes.
Definition
For a salt A_aB_b ⇌ a A⁺ + b B⁻, Ksp = [A⁺]^a [B⁻]^b at equilibrium. Activity may be used for high ionic strength.
Ksp = Π [ion]^stoichiometric coefficient
Detailed Example: PbCl₂ Solubility
Problem: Calculate the molar solubility of PbCl₂ if Ksp = 1.7 × 10⁻⁵.
Step 1: Write dissolution equation
PbCl₂(s) ⇌ Pb²⁺(aq) + 2Cl⁻(aq)
Step 2: Write Ksp expression
Ksp = [Pb²⁺][Cl⁻]²
Step 3: Define solubility (s)
If s moles of PbCl₂ dissolve per liter:
[Pb²⁺] = s and [Cl⁻] = 2s
Step 4: Substitute and solve
1.7 × 10⁻⁵ = (s)(2s)² = 4s³
s³ = (1.7 × 10⁻⁵)/4 = 4.25 × 10⁻⁶
s = ∛(4.25 × 10⁻⁶) ≈ 1.62 × 10⁻² M
Answer: Molar solubility of PbCl₂ ≈ 0.0162 M or 16.2 mM
Key Concepts
Common Ion Effect
Adding a common ion decreases solubility. For AgCl, adding NaCl (source of Cl⁻) shifts equilibrium left, reducing [Ag⁺] and precipitating more AgCl. Used in analytical separations.
Precipitation Predictions
Calculate Q (reaction quotient) from initial concentrations. If Q > Ksp, precipitation occurs; if Q < Ksp, more solid can dissolve; if Q = Ksp, system is at equilibrium.
pH Effects on Solubility
Sparingly soluble hydroxides (Mg(OH)₂) become more soluble as pH decreases because H⁺ reacts with OH⁻, shifting equilibrium. Carbonates and sulfides also show pH-dependent solubility.
Common Mistakes
Comparing Ksp values with different stoichiometry
Ksp alone doesn't determine relative solubility unless compounds have same ion ratio. Must calculate actual molar solubility.
Forgetting stoichiometric coefficients
In PbCl₂: [Cl⁻] = 2s, not s. The coefficient matters both in concentration and in the exponent of Ksp.
Including solid in Ksp expression
Pure solids have activity = 1 and don't appear in equilibrium expressions.
Notes
- Common ion effect reduces solubility: presence of shared ions shifts equilibrium.
- Complexation and pH changes can alter apparent solubility.
- Use activities for concentrated solutions; γ < 1 lowers effective concentration.
Related Calculators
Solubility Product Calculator
Calculate Ksp and solubility
Equilibrium Constant Calculator
Calculate K from concentrations
Common Ion Effect
Shared ions affect solubility
Equilibrium Constant Formula
K expression and calculations
All Chemical Equilibrium Calculators
Explore all equilibrium tools and calculators