What is the solubility product expression for calcium phosphate?

The solubility product expression for calcium phosphate, Ca3(PO4)2, is given by the product of the concentrations of its constituent ions, each raised to the power of its stoichiometric coefficient: Ksp = [Ca²⁺]³[PO₄³⁻]².

Understanding Solubility Product (Ksp)

The solubility product constant (Ksp) is a specific type of equilibrium constant that describes the equilibrium between a sparingly soluble ionic solid and its ions in a saturated solution. It quantifies the extent to which a solid compound dissolves in water. A smaller Ksp value indicates lower solubility, while a larger Ksp value suggests higher solubility.

Deriving the Solubility Product Expression for Calcium Phosphate

To derive the Ksp expression for calcium phosphate, Ca3(PO4)2, we first write its dissolution equilibrium in water and then formulate the equilibrium constant expression.

Dissolution Equilibrium

Calcium phosphate is an ionic compound that dissociates into calcium ions (Ca²⁺) and phosphate ions (PO₄³⁻) when it dissolves in water. The balanced chemical equation for this dissolution is:

Ca₃(PO₄)₂ (s) ⇌ 3Ca²⁺ (aq) + 2PO₄³⁻ (aq)

This equation shows that for every one mole of solid calcium phosphate that dissolves, three moles of calcium ions and two moles of phosphate ions are produced in the solution.

Ksp Expression in Terms of Ion Concentrations

Based on the balanced dissolution equilibrium, the solubility product expression (Ksp) is written as the product of the molar concentrations of the dissolved ions, with each concentration raised to the power of its stoichiometric coefficient from the balanced equation. Solids are not included in the Ksp expression.

For Ca3(PO4)2:
Ksp = [Ca²⁺]³[PO₄³⁻]²

Here, [Ca²⁺] represents the molar concentration of calcium ions, and [PO₄³⁻] represents the molar concentration of phosphate ions in a saturated solution.

Relating Ksp to Molar Solubility (S)

Molar solubility (S) is defined as the number of moles of solute that dissolve to form one liter of a saturated solution. We can relate the Ksp expression to the molar solubility:

1. Let 'S' be the molar solubility of Ca3(PO4)2.
2. From the balanced equation, if 'S' moles of Ca3(PO4)2 dissolve, they produce:
   • 3S moles of Ca²⁺ ions, so [Ca²⁺] = 3S
   • 2S moles of PO₄³⁻ ions, so [PO₄³⁻] = 2S
3. Substitute these concentrations into the Ksp expression:
   Ksp = (3S)³ (2S)²
   Ksp = (27S³) (4S²)
   Ksp = 108S⁵

This relationship allows us to calculate the molar solubility of calcium phosphate if its Ksp value is known, or vice versa.

Common Misconceptions and Variations

It is crucial to correctly apply stoichiometric coefficients when deriving Ksp expressions. While some sources or problem sets might present expressions such as 27S⁵, 16S⁴, or 81S⁴ as options for the solubility product of Ca3(PO4)2, the chemically accurate solubility product in terms of molar solubility for calcium phosphate (Ca3(PO4)2) is consistently derived as 108S⁵, based on its dissociation into 3 Ca²⁺ ions and 2 PO₄³⁻ ions.

Importance and Applications of Ksp

The Ksp value is a fundamental property of sparingly soluble ionic compounds and has several important applications in chemistry:

• Predicting Precipitation: Ksp can be used to predict whether a precipitate will form when two solutions are mixed. If the ion product (Qsp) is greater than Ksp, precipitation will occur.
• Calculating Solubility: Ksp allows for the calculation of the molar solubility and mass solubility of a compound in various conditions, including in pure water or in the presence of a common ion.
• Comparing Solubilities: While not always straightforward, Ksp values can sometimes be used to compare the relative solubilities of different compounds under similar conditions.

The following table illustrates general Ksp expressions for different types of ionic compounds, highlighting the pattern of derivation: