Question

For each compound, write an equation showing how the compound dissolves in water and write an expression for \(K_{\text {sp }}\). (a) \(\mathrm{Mg}(\mathrm{OH})_{2}\) (b) \(\mathrm{FeCO}_{3}\) (c) \(\mathrm{PbS}\) (d) \(\mathrm{PbSO}_{4}\)

Short answer

a) Mg(OH)2(s) ⇌ Mg2+(aq) + 2OH-(aq), Ksp = [Mg2+][OH-]^2; b) FeCO3(s) ⇌ Fe2+(aq) + CO32-(aq), Ksp = [Fe2+][CO32-]; c) PbS(s) ⇌ Pb2+(aq) + S2-(aq), Ksp = [Pb2+][S2-]; d) PbSO4(s) ⇌ Pb2+(aq) + SO42-(aq), Ksp = [Pb2+][SO42-].

Step-by-step solution

Write the Dissolution Equations

Write a balanced equation showing how each compound dissolves into its constituent ions in water.

Write the Solubility Product Constant Expressions

For each dissolution equation, write the expression for the solubility product constant, Ksp, which is the product of the concentrations of the ions raised to the power of their stoichiometric coefficients in the balanced equation.

Key concepts

Dissolution Equations

Dissolution equations are a representation of the process in which ionic compounds separate into their individual ions when dissolved in water. A fundamental principle in chemistry is that salts dissolve in water to form cations and anions. For instance, magnesium hydroxide (Mg(OH)₂) dissolves by dissociating into magnesium cations (Mg²⁺) and hydroxide anions (OH^-). The balanced dissolution equation for this reaction would be:

Mg(OH)₂(s) → Mg²⁺(aq) + 2OH^-(aq)

The 's' denotes a solid compound, while 'aq' signifies that the ions are in aqueous solution. When ionic compounds dissolve in water, it is crucial to balance the equation by ensuring that the number of each type of ion on both sides of the equation is equal. This reflects the conservation of mass and charge.

Ksp Expressions

The solubility product constant, abbreviated as Ksp, is a special type of equilibrium constant that describes the saturation level of a solute in solution. It is associated with the dissolved ionic compound's tendency to remain in the ionic form or to crystallize back into a solid. The Ksp expression is derived from the balanced dissolution equation. For example, if we consider the dissolution of lead(II) sulfide (PbS), the equation is as follows:

PbS(s) ⇌ Pb²⁺(aq) + S²⁻(aq)

The corresponding Ksp expression for this equilibrium would be the product of the concentrations of the resulting ions, each raised to the power of its coefficient in the balanced equation:

Ksp = [Pb²⁺][S²⁻]

In this equation, the square brackets represent the concentration of ions in moles per liter (M). The Ksp expression does not include solids or liquids since their concentration is constant.

Stoichiometry

Stoichiometry is based on the law of conservation of mass, where the total mass of reactants equals the total mass of products in a chemical reaction. In the context of dissolution equations and Ksp expressions, stoichiometry involves the relationships between the amounts of reactants and products. Consider iron(II) carbonate (FeCO₃) as it dissolves:

FeCO₃(s) ⇌ Fe²⁺(aq) + CO₃²⁻(aq)

Stoichiometric coefficients correspond to the number of moles of each ion produced. In this equation, one molecule of FeCO₃ dissociates into one mole of Fe²⁺ and one mole of CO₃²⁻. Hence, the stoichiometric coefficients in the Ksp expression are 1, maintaining the balance that the reaction stoichiometry provides, as reflected in the Ksp expression:

Ksp = [Fe²⁺][CO₃²⁻]

Understanding stoichiometry is vital because it allows us to predict the amount of product formed from a given amount of reactant and vice versa.

Ionic Compounds in Water

Ionic compounds in water are those that can dissociate into their constitutive ions due to the polar nature of water molecules. The dissolution of ionic compounds in water is governed by the interaction between the ions and water molecules. In this interaction, the water's partial negative charge (oxygen) is attracted to cations while its partial positive charge (hydrogen) is attracted to anions. Lead(II) sulfate (PbSO₄), for example, dissolves in water according to the equation:

PbSO₄(s) → Pb²⁺(aq) + SO₄²⁻(aq)

Not all ionic compounds are equally soluble. The solubility of an ionic compound is indicated by its Ksp value - a low Ksp value means the compound is less soluble. This process is dynamic, meaning at equilibrium, the rate at which the solid dissolves equals the rate at which the ions recombine to form a solid. This equilibrium between the solid phase and dissolved ions in solution is fundamental for understanding the solubility of different substances in water.