Lesson 7.6-7.7: Solubility Equilibria and the Solubility Product Constant (Ksp) (12 Chem)

Solubility Equilibria and the Solubility Product Constant

Solubility and Its Importance

Solubility refers to the quantity of a solute that dissolves in a given quantity of solvent at a particular temperature, forming a saturated solution. The solubility of ionic compounds is crucial in various applications, such as medical imaging and water treatment. For example, barium sulfate is used in X-ray imaging of the digestive tract due to its low solubility, which prevents toxic barium ions from entering the body while providing clear images.

• Solubility: The concentration of a saturated solution at a particular temperature.

• Saturated solution: Contains the maximum quantity of solute at a given temperature and pressure.

• Example: Calcium sulfate is more soluble in cold water than hot water, affecting plumbing systems.

Solubility Equilibria of Ionic Compounds

When an ionic compound dissolves in water, it forms a dynamic equilibrium between the solid and its dissolved ions. Water molecules surround the ions, pulling them from the crystal lattice into solution. The reverse process, precipitation, occurs when dissolved ions recombine to form the solid.

• Dynamic equilibrium: The rate of dissolution equals the rate of precipitation.

• Solubility equilibrium: A dynamic equilibrium between a solute and a solvent in a saturated solution.

• Example: Silver iodide dissolving and precipitating in water.

The Solubility Product Constant (Ksp)

The solubility product constant, Ksp, is the equilibrium constant for the solubility equilibrium of a solid ionic compound in water. It is calculated using the concentrations of the dissolved ions, omitting the solid's concentration since it remains constant.

• Ksp equation for AgI: $K_{sp} = [Ag^+][I^-]$

• Ksp equation for CaF2: $K_{sp} = [Ca^{2+}][F^-]^2$

• Ksp equation for Al2(SO4)3: $K_{sp} = [Al^{3+}]^2[SO_4^{2-}]^3$

• Ksp values are temperature-dependent and have no units.

Calculating Ksp and Molar Solubility

Ksp can be calculated from ion concentrations in a saturated solution, and vice versa. The relationship between Ksp and solubility depends on the stoichiometry of the dissolution reaction.

• Example: For Zn(OH)2, $K_{sp} = [Zn^{2+}][OH^-]^2$

• Sample calculation: If $[Zn^{2+}] = 2.7 \times 10^{-6}$ mol/L and $[OH^-] = 5.4 \times 10^{-6}$ mol/L, then $K_{sp} = (2.7 \times 10^{-6})(5.4 \times 10^{-6})^2 = 7.9 \times 10^{-17}$

Solubility vs. Solubility Product Constant

Solubility is the maximum amount of solute that dissolves in a solvent, while Ksp is the equilibrium constant for the dissolution process. Highly charged ions generally result in lower solubility due to stronger ionic bonds.

• Molar solubility: Maximum moles of solute that dissolve per liter of solvent.

• Ksp: Product of ion concentrations at equilibrium.

• Example: Lithium carbonate has a molar solubility of $1.8 \times 10^{-2}$ mol/L and a Ksp of $8.2 \times 10^{-4}$ at 25°C.

Converting Between Ksp and Solubility

Given the molar solubility, Ksp can be calculated, and vice versa. The process involves writing the balanced dissolution equation, determining ion concentrations, and substituting into the Ksp expression.

• Example: For CuBr, if molar solubility is $2.0 \times 10^{-4}$ mol/L, then $K_{sp} = (2.0 \times 10^{-4})^2 = 4.0 \times 10^{-8}$

• ICE tables are used to track changes in ion concentrations during dissolution.

  • NTS: Practice an example

Predicting Precipitation

When two solutions are mixed, a precipitate forms if the product of ion concentrations exceeds Ksp. The trial ion product, Q, is used to predict precipitation quantitatively.

• Q > Ksp: Precipitation occurs.

• Q < Ksp: No precipitation; more solid can dissolve.

• Q = Ksp: System is at equilibrium; no net change.

• Example: Mixing AgNO3 and KBr can form AgBr precipitate if Q exceeds Ksp.

Solubility Tables and Trends

Solubility tables summarize experimental results and help predict whether a compound will be soluble or form a precipitate. Nitrate salts are always soluble, while other ions may form insoluble compounds depending on their partners.

• Solubility rules: Used to qualitatively predict precipitation.

• Example: Silver chloride is insoluble, while sodium nitrate is soluble.

The Common Ion Effect

The common ion effect occurs when a solution already contains an ion present in the dissolving compound, reducing its solubility. Adding a common ion shifts the equilibrium toward the solid, causing precipitation.

• Le Châtelier’s principle: Adding a common ion shifts equilibrium to favor the solid.

• Example: Adding AgNO3 to Ag2CrO4 solution increases Ag+ concentration, causing more Ag2CrO4 to precipitate.

• Quantitative calculation: Use ICE tables and Ksp to determine new solubility.

Solubility Equilibrium in Nature

Solubility equilibria are observed in natural environments, such as the formation of stalactites and stalagmites in limestone caves. These structures form as a result of precipitation from saturated solutions, governed by Ksp and environmental conditions.

• Example: Stalactites and stalagmites form from calcium carbonate precipitation in caves.

Summary Table: Solubility vs. Ksp

Term	Definition	Example
Molar Solubility	Maximum moles of solute dissolved per liter	1.8 × 10-2 mol/L (Li2CO3)
Ksp	Product of ion concentrations at equilibrium	8.2 × 10-4 (Li2CO3)
Trial Ion Product (Q)	Product of initial ion concentrations	Used to predict precipitation
Common Ion Effect	Reduction in solubility due to presence of a common ion	AgNO3 added to Ag2CrO4 solution

Key Equations

• $K_{sp} = [A^+][B^-]$ (for AB)

• $K_{sp} = [A^{2+}][B^-]^2$ (for AB2)

• $Q = [A^+][B^-]$ (trial ion product)

• For dilution: $c_d = \frac{c_c V_c}{V_d}$

Summary Points

• A solubility equilibrium is a heterogeneous equilibrium system between a solid ionic compound and its ions dissolved in a saturated aqueous solution.

• The solubility product constant, Ksp, is the value of the equilibrium law equation for a solubility equilibrium and does not include the concentration of the solid.

• The trial ion product, Q, is the reaction quotient applied to the ion concentrations of a slightly soluble ionic compound.

• The common ion effect explains why the solubility of an ionic compound may decrease when a common ion is added to the equilibrium system.