Solubility Equilibrium

Introduction

Understanding solubility equilibrium is essential for grasping how ionic compounds, such as NaCl, react with solvents to form solutions. This equilibrium is achieved when the rate of solute dissolution matches the rate of precipitation, resulting in a stable concentration of dissolved ions.

• Solubility Equilibrium: The rate of solute dissolution is equal to the rate of precipitation.
• Dynamic Equilibrium: The processes of dissolving and recrystallising occur at equivalent rates.

Key Terms and Definitions

Dissolution Process of Ionic Compounds

Introduction to Dissolution

Dissolution is observed in daily activities, such as dissolving salt in water, and is vital to numerous chemical processes.

• Solute: A substance that dissolves within a solvent.
• Solvent: The medium in which the solute dissolves, with water being the most common.
• Dissociation: The process by which ionic compounds separate into ions in a solution.
• Hydration: Water molecules forming a surrounding layer around ions, providing stability.

Detailed Description of Ion Dissociation

When NaCl is introduced to water, it dissociates into ions facilitated by water's polar nature, creating hydration shells.

• NaCl Example:
  • Dissociates: NaCl → Na⁺ + Cl⁻
• CaCl₂ Example:
  • Dissociates: CaCl₂ → Ca²⁺ + 2 Cl⁻

Ion-Water Interaction Steps:

• Initial Contact: Ionic compound interacts with water.
• Dissociation: Separation into constituent ions.
• Hydration Shell Formation: Water molecules encase each ion.

Ion-Dipole Interactions and Solubility

Solubility: Defined as the capacity of a substance to dissolve, influenced by ion-dipole interactions.

• Enhanced ion-dipole interactions lead to increased solubility.
• Temperature Effect: An increase in temperature raises solubility by enhancing molecular motion.

Factors Affecting Dissolution

• Ion Size: Smaller ions exhibit stronger interactions.
• Ion Charge: Greater charges lead to enhanced interaction strength.
• Temperature: Raises dissolution rates by boosting molecular motion.

Temperature's Influence on Solubility

• Solids: Rising temperature generally improves solubility due to increased molecular motion.
• Gases: Their solubility decreases as temperature rises due to increased kinetic energy.

Examples:

• Sugar in Hot Tea: Rapid dissolution attributable to increased energy.
• Salt in Hot Water: Enhanced dissolution due to added energy facilitating motion.

Pressure's Role: Henry's Law in Gaseous Solubility

Henry's Law: The solubility of a gas is directly proportional to the pressure of the gas above the liquid. Formula:

$C = kP$

• Useful for predicting changes in oxygen solubility with varying pressure.

Overview of Thermodynamic Concepts in Dissolution

Thermodynamics: The study of energy transformations in processes such as dissolution.

• Enthalpy (ΔH): Reflects energy changes during dissolution.
• Entropy (ΔS): Represents disorder increase as substances dissolve.
• Gibbs Free Energy (ΔG): Establishes the spontaneity of reactions.

Enthalpy Changes (ΔH)

• Exothermic Process (-ΔH): Involves heat release, e.g., NaCl dissolving.
• Endothermic Process (+ΔH): Involves heat absorption, e.g., NH₄NO₃ dissolving.

Entropy (ΔS) Considerations

Entropy (ΔS): Corresponds to the increased disorder as dissolving occurs.

Gibbs Free Energy (ΔG) and Spontaneity

Equation:

$\Delta G = \Delta H - T\Delta S$

• Example: If ΔH = 10 kJ/mol, ΔS = 50 J/mol⋅K, and T = 298 K, then:

  $\Delta G = 10,000 - 298 \times 50 = -4,900 \text{ J/mol}$

• A negative ΔG indicates spontaneous dissolution.

Introduction to Ksp

Solubility Product Constant (Ksp): Measures the solubility of sparingly soluble ionic compounds. Higher Ksp values denote greater solubility.

• Derivation of Ksp Formula

  • For ionic compound AB:

    $AB_{(s)} \rightleftharpoons A^+_{(aq)} + B^-_{(aq)}$

    $K_{sp} = [A^+][B^-]$

  

Ksp and Equilibrium

• Real-life Applications of Le Chatelier's Principle: Adding ions influences solubility by shifting equilibrium. Utilise this principle to forecast solubility variations.

Worked Example: Calculating Solubility from Ksp

Problem: For a salt AB with Ksp = 4.0 × 10⁻⁵, calculate its solubility in mol/L.

Solution:

1. Write the equilibrium equation: AB(s) ⇌ A⁺(aq) + B⁻(aq)

2. Let's call the solubility 's' in mol/L:

   • When AB dissolves, it produces equal amounts of A⁺ and B⁻
   • [A⁺] = [B⁻] = s

3. Write the Ksp expression: Ksp = [A⁺][B⁻] = s × s = s²

4. Solve for s: s² = 4.0 × 10⁻⁵ s = √(4.0 × 10⁻⁵) = 6.3 × 10⁻³ mol/L

Therefore, the solubility of AB is 6.3 × 10⁻³ mol/L.

Problem: Determine if precipitation will occur when 100 mL of 0.02 M AgNO₃ is mixed with 200 mL of 0.01 M NaCl. (Ksp for AgCl = 1.8 × 10⁻¹⁰)

Solution:

1. Calculate diluted concentrations after mixing:

   • [Ag⁺] = (0.02 M × 100 mL) ÷ 300 mL = 0.0067 M
   • [Cl⁻] = (0.01 M × 200 mL) ÷ 300 mL = 0.0067 M

2. Calculate the ion product Q: Q = [Ag⁺][Cl⁻] = 0.0067 × 0.0067 = 4.5 × 10⁻⁵

3. Compare Q with Ksp: Q (4.5 × 10⁻⁵) > Ksp (1.8 × 10⁻¹⁰)

Since Q > Ksp, precipitation will occur.

Common Ion Effect

• Equilibrium Shift:
  • Introducing a common ion lowers solubility by causing an equilibrium shift.
  • Example: Adding NaCl to a PbCl₂ solution leads to the precipitation of PbCl₂.

Real-World Interplay of Factors

• Integrated Effects: Solubility is influenced by temperature, pressure, and common ions acting together.

• Case Study in Desalination:

  • Desalination employs temperature and pressure adjustments for effective water purification.

Addressing Common Misconceptions

• "Solutes disappear": In truth, they remain in dynamic equilibrium.
• "Unconscious limits": Visual aids help clarify solubility states.

Misconception Example: Solutes do not vanish; they maintain equilibrium in solution.

Conclusion

Grasping solubility equilibrium is fundamental for delving into more intricate chemical scenarios, spanning from pharmaceuticals to ecological systems. Utilise the provided diagrams and examples to visualise and reinforce these concepts.