Problem 52 - Chemistry The Central Science In Si Units

Question

(a) True or false: "solubility" and "solubility-product constant" are the same number for a given compound. (b) Write the expression for the solubility- product constant for each of the following ionic compounds: \(\mathrm{MnCO}_{3}, \mathrm{Hg}(\mathrm{OH})_{2},\) and \(\mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Step-by-Step Solution

Answer

(a) False; solubility and solubility-product constant are different. (b) MnCO_3: K_{sp} = [Mn^{2+}][CO_{3}^{2-}] , Hg(OH)_2: K_{sp} = [Hg^{2+}][OH^{-}]^{2} , Cu_3(PO_4)_2: K_{sp} = [Cu^{2+}]^{3}[PO_{4}^{3-}]^{2} .

Step 1: Understanding Solubility vs. Solubility-Product Constant

Solubility refers to the maximum amount of solute that can dissolve in a solvent at a given temperature to form a saturated solution, usually expressed in moles per liter (mol/L). The solubility-product constant ( K_{sp} ) is an equilibrium constant for the dissolution of an ionic compound into its constituent ions, representing the saturated solution's equilibrium condition. Thus, true or false? The statement 'solubility' and 'solubility-product constant' are the same number is false because they represent different concepts and are expressed with different units.

Step 2: Expression for the Solubility-Product Constant of MnCO₃

To express the solubility-product constant, K_{sp} , for MnCO_{3} dissolving, consider its dissociation in water: MnCO_{3 (s)} ightarrow Mn^{2+}_{(aq)} + CO_{3}^{2-}_{(aq)} . The K_{sp} expression is the product of the concentrations of the ions at equilibrium: K_{sp} = [Mn^{2+}][CO_{3}^{2-}] .

Step 3: Expression for the Solubility-Product Constant of Hg(OH)₂

Starting with the dissociation reaction for Hg(OH)_{2} : Hg(OH)_{2 (s)} ightarrow Hg^{2+}_{(aq)} + 2OH^{-}_{(aq)} . The K_{sp} expression is thus the product of the concentrations of the ions, each raised to the power of their coefficients: K_{sp} = [Hg^{2+}][OH^{-}]^{2} .

Step 4: Expression for the Solubility-Product Constant of Cu₃(PO₄)₂

Lastly, for Cu_{3}(PO_{4})_{2} dissolving in water, the dissociation is: Cu_{3}(PO_{4})_{2 (s)} ightarrow 3Cu^{2+}_{(aq)} + 2PO_{4}^{3-}_{(aq)} . The K_{sp} expression will be: K_{sp} = [Cu^{2+}]^{3}[PO_{4}^{3-}]^{2} , accounting for the stoichiometry of the reaction.

Key Concepts

Ionic Compounds

Ionic compounds are substances made up of charged particles called ions. These ions form when atoms gain or lose electrons, creating positive ions (cations) and negative ions (anions). Ionic compounds typically form a structured lattice arrangement that helps in stabilizing the charges.

• Cations are positively charged ions. Common examples are sodium ions (\( \text{Na}^+ \)) and magnesium ions (\( \text{Mg}^{2+} \)).
• Anions are negatively charged ions. Chloride (\( \text{Cl}^- \)) and sulfate (\( \text{SO}_{4}^{2-} \)) are examples.

The strength and stability of ionic compounds are mostly due to the strong electrostatic forces between oppositely charged ions.
Ionic compounds readily dissolve in water, creating a solution of ions that is capable of conducting electricity. These dissolved ions are crucial in reaction processes, such as those involving equilibrium constants.

Equilibrium Constant

The equilibrium constant is a number that expresses the balance between products and reactants in a chemical reaction at a set condition of temperature and pressure. In the context of ionic compounds and solubility, this constant refers to the solubility-product constant, \( K_{sp} \).
It quantifies the point at which the dissolution and precipitation of a compound are in balance. At this point, the rate at which the compound dissolves equals the rate at which it forms a solid again.

• A larger \( K_{sp} \) indicates a compound is more soluble.
• A smaller \( K_{sp} \) means less solubility.

This value is significant when predicting or calculating how much of a compound will dissolve in a solution and at what concentration.

Dissolution Reaction

A dissolution reaction occurs when an ionic compound breaks apart into its individual ions in a solvent, usually water. During this process, the solid compound becomes part of the solution:
For example, when calcium chloride (\( \text{CaCl}_2 \)) dissolves in water, it dissociates into calcium ions (\( \text{Ca}^{2+} \)) and chloride ions (\( \text{Cl}^- \)).
These ions are then free to interact with other substances in the solution or remain as they are:
The dissolution reaction can be influenced by several factors:

• Temperature: Usually, solubility increases with temperature.
• The nature of solvent: Polar solvents, like water, are particularly effective at dissolving ionic compounds.
• Pressure: Usually effects gas solubility, but solid solubility is mostly unaffected by pressure changes.

Understanding the nature of dissolution is key in fields ranging from chemistry to environmental science, as it explains how substances interact in a solution.