Measuring Solubility

Solution equilibria involve the balance between dissolved ions in a saturated solution. Understanding these principles is critical for mastering the behaviour of chemical solutions.

Introduction

• Saturated Solutions: Solutions that contain the maximum concentration of ions at a given temperature.
• Ionic Compounds: Consist of charged ions.
  • Example: Table salt (NaCl).
• Solubility Product ($K_{\mathrm{sp}}$): Indicates the maximum solubility level of ionic compounds. Knowing $K_{\mathrm{sp}}$ is essential to predict the solubility of compounds.

Key Concepts

• Dynamic Equilibrium:

  • Occurs when the rate of dissolution equals the rate of precipitation.
  • Maintains a stable concentration of ions.

• Solubility Product ($K_{\mathrm{sp}}$):

  • An equilibrium constant that indicates solubility level.
  • A higher $K_{\mathrm{sp}}$ implies greater solubility.

• Heterogeneous Equilibrium:

  • Reactions involving different phases, such as solid and liquid.

Visual Illustrations

• Diagram Explanation: Displays ion balance in the solution.

• Solubility Curve Explanation: Illustrates the temperature dependence of solubility.

Steps to Derive Equilibrium Expressions

1. Identify the Dissociation Reaction

• Dissociation Equation Example:
  • $\mathrm{CaCO}_3 (s) \rightleftharpoons \mathrm{Ca}^{2+} (aq) + \mathrm{CO}_3^{2-} (aq)$
  • Note: Only dissolved ions appear in expressions.

2. Expression Formation Using $K_{\mathrm{sp}}$

• Expression Format:

  • General Formula:
    $K_{\mathrm{sp}} = [A^+]^m [B^-]^n$

• Example Using Silver Chloride:

  • Dissociation: $\mathrm{AgCl} (s) \rightleftharpoons \mathrm{Ag}^+ (aq) + \mathrm{Cl}^- (aq)$
  • Ksp Expression: $K_{\mathrm{sp}} = [\mathrm{Ag}^+][\mathrm{Cl}^-]$

Solubility and $K_{\mathrm{sp}}$ Calculations

Step-by-Step Calculation Example Using $\mathrm{AgCl}$:

• Write Dissociation Equation: $\mathrm{AgCl (s)} \rightleftharpoons \mathrm{Ag}^+ (aq) + \mathrm{Cl}^- (aq)$

• Formulate $K_{\mathrm{sp}}$:
  $K_{\mathrm{sp}} = [\mathrm{Ag}^+][\mathrm{Cl}^-]$

• Calculate Solubility:

  • If we define solubility as $s$ mol/L, then $[\mathrm{Ag}^+] = [\mathrm{Cl}^-] = s$
  • Therefore: $K_{\mathrm{sp}} = s \times s = s^2$

• Solving for $s$ (Given $K_{\mathrm{sp}} = 1.8 \times 10^{-10}$): $s = \sqrt{1.8 \times 10^{-10}} = 1.34 \times 10^{-5}\text{ mol/L}$

Challenges and Strategies

Understanding $K_{\mathrm{sp}}$ and $Q_{\mathrm{sp}}$

• Key Conditions:

  • Unsaturated: $Q_{\mathrm{sp}} < K_{\mathrm{sp}}$

  • Saturated at equilibrium: $Q_{\mathrm{sp}} = K_{\mathrm{sp}}$

  • Supersaturated: $Q_{\mathrm{sp}} > K_{\mathrm{sp}}$

pH and Common Ion Effect

• pH Impact: Influences solubility, with calcium carbonate dissolving more as pH decreases.

Exam Tips

• Practise with various ionic compounds.
• Verify understanding of stoichiometry and $K_{\mathrm{sp}}$.
• Regularly solve problems to reinforce concepts.