The solubility product (Ksp) is a fundamental equilibrium constant that quantifies the extent to which a sparingly soluble ionic compound dissolves in water. It is determined by multiplying the equilibrium concentrations of the ions produced from the dissolution, each raised to the power of its stoichiometric coefficient in the balanced chemical equation.
Understanding the Solubility Product (Ksp)
The solubility product, denoted as Ksp, is a specific type of equilibrium constant applicable to the dissolution of ionic solids that are only slightly soluble in water. It represents the product of the concentrations of the constituent ions in a saturated solution, where the solid solute is in equilibrium with its dissolved ions.
According to the definition, the solubility product is equal to the product of the concentrations of the ions involved in the equilibrium, each raised to the power of its stoichiometric coefficient in the equilibrium equation.
Steps to Determine Solubility Product (Ksp)
Determining the solubility product involves understanding the dissolution equilibrium and often requires experimental measurement of ion concentrations.
1. Write the Dissolution Equilibrium Equation
For a generic sparingly soluble ionic compound, M_x_Ay, the dissolution equilibrium can be represented as:
M_x_Ay(s) ⇌ xM^(y+)(aq) + yA^(x-)(aq)
Here:
- M_x_Ay(s) represents the solid ionic compound.
- M^(y+)(aq) represents the cation with charge y+.
- A^(x-)(aq) represents the anion with charge x-.
- 'x' and 'y' are the stoichiometric coefficients of the ions in the balanced equation.
2. Formulate the Ksp Expression
Based on the equilibrium equation, the Ksp expression is written by taking the product of the molar concentrations of the dissolved ions, with each concentration raised to the power of its stoichiometric coefficient. Solid reactants are not included in the expression.
For M_x_Ay(s):
Ksp = [M^(y+)]^x [A^(x-)]^y
3. Relate Ion Concentrations to Molar Solubility (s)
Molar solubility (s) is defined as the number of moles of the compound that dissolve to form one liter of a saturated solution. By stoichiometry, the concentrations of the ions at equilibrium can be expressed in terms of 's':
- If 's' is the molar solubility of M_x_Ay, then:
- [M^(y+)] = x * s
- [A^(x-)] = y * s
4. Calculate Ksp Using Molar Solubility
Substitute the ion concentrations in terms of 's' into the Ksp expression:
Ksp = (x s)^x (y * s)^y
Practical Determination of Ksp
In a laboratory setting, Ksp is determined by measuring the molar solubility (s) of the compound. This typically involves:
- Preparing a Saturated Solution: Dissolve the sparingly soluble salt in water until no more solid dissolves, ensuring equilibrium is reached.
- Measuring Ion Concentration: Determine the concentration of one of the ions in the saturated solution using an analytical technique. Common methods include:
- Spectrophotometry: For ions that absorb light at specific wavelengths.
- Atomic Absorption Spectroscopy (AAS): For metal ions.
- Conductivity Measurements: For solutions containing ions.
- Gravimetric Analysis: Precipitating and weighing an ion.
- Titration: For ions that can react with a known standard solution.
- Calculating Molar Solubility (s): Use the measured ion concentration and the stoichiometry of the dissociation reaction to calculate the molar solubility 's' of the entire salt.
- Calculating Ksp: Plug the calculated molar solubility 's' into the derived Ksp expression for that specific compound.
Examples of Ksp Determination
Let's illustrate with common types of sparingly soluble salts.
Example 1: AB Type (e.g., Silver Chloride, AgCl)
- Dissolution Equilibrium:
AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq) - Ksp Expression:
Ksp = [Ag⁺][Cl⁻] - In Terms of Molar Solubility (s):
If 's' is the molar solubility of AgCl, then [Ag⁺] = s and [Cl⁻] = s.
Ksp = (s)(s) = s² - Practical Insight: If you experimentally determine that the molar solubility of AgCl is 1.3 x 10⁻⁵ mol/L, then Ksp = (1.3 x 10⁻⁵)² = 1.69 x 10⁻¹⁰.
Example 2: AB₂ or A₂B Type (e.g., Lead(II) Iodide, PbI₂)
- Dissolution Equilibrium:
PbI₂(s) ⇌ Pb²⁺(aq) + 2I⁻(aq) - Ksp Expression:
Ksp = [Pb²⁺][I⁻]² - In Terms of Molar Solubility (s):
If 's' is the molar solubility of PbI₂, then [Pb²⁺] = s and [I⁻] = 2s.
Ksp = (s)(2s)² = s(4s²) = 4s³ - Practical Insight: If the experimentally determined molar solubility of PbI₂ is 1.2 x 10⁻³ mol/L, then Ksp = 4(1.2 x 10⁻³ )³ = 4(1.728 x 10⁻⁹) = 6.9 x 10⁻⁹.
Example 3: A₃B₂ Type (e.g., Calcium Phosphate, Ca₃(PO₄)₂)
- Dissolution Equilibrium:
Ca₃(PO₄)₂(s) ⇌ 3Ca²⁺(aq) + 2PO₄³⁻(aq) - Ksp Expression:
Ksp = [Ca²⁺]³[PO₄³⁻]² - In Terms of Molar Solubility (s):
If 's' is the molar solubility of Ca₃(PO₄)₂, then [Ca²⁺] = 3s and [PO₄³⁻] = 2s.
Ksp = (3s)³(2s)² = (27s³)(4s²) = 108s⁵
Summary Table of Ksp Expressions
| Compound Type | General Formula | Equilibrium | Ksp Expression | Ksp in terms of Molar Solubility (s) |
|---|---|---|---|---|
| AB | MX | MX(s) ⇌ M⁺(aq) + X⁻(aq) | [M⁺][X⁻] | s² |
| AB₂ | MX₂ | MX₂(s) ⇌ M²⁺(aq) + 2X⁻(aq) | [M²⁺][X⁻]² | 4s³ |
| A₂B | M₂X | M₂X(s) ⇌ 2M⁺(aq) + X²⁻(aq) | [M⁺]²[X²⁻] | 4s³ |
| A₃B₂ | M₃X₂ | M₃X₂(s) ⇌ 3M²⁺(aq) + 2X³⁻(aq) | [M²⁺]³[X³⁻]² | 108s⁵ |
Significance of Ksp
The determined Ksp value is crucial for:
- Predicting Precipitation: By comparing the ion product (Qsp) with Ksp, one can predict whether a precipitate will form. If Qsp > Ksp, precipitation occurs.
- Comparing Solubilities: A smaller Ksp generally indicates lower solubility for compounds of the same stoichiometric type.
- Understanding Common Ion Effect: Ksp is used to calculate how the solubility of a sparingly soluble salt changes when a common ion is added to the solution.
Solubility Equilibrium
