Aqueous Equilibria: Buffers, Titrations, and Solubility (GOB Chemistry Study Notes)

Additional Aspects of Aqueous Equilibria

Introduction

This chapter explores advanced concepts in aqueous equilibria, focusing on the common-ion effect, buffer solutions, acid-base titrations, solubility equilibria, and the factors affecting solubility. These topics are essential for understanding chemical reactions in solution, especially in biological and environmental contexts.

The Common-Ion Effect

Definition and Principle

• Common-Ion Effect: The suppression of the ionization of a weak electrolyte when a strong electrolyte containing a common ion is added to the solution.

• When a solution contains two substances that share a common ion, the equilibrium shifts to reduce the ionization of the weak electrolyte (Le Chatelier’s Principle).

• Example: Adding sodium acetate (CH3COONa) to acetic acid (CH3COOH) increases the concentration of acetate ions (CH3COO−), shifting the equilibrium to the left and decreasing [H+].

Key Equation:

$\mathrm{CH_3COOH(aq) + H_2O(l) \rightleftharpoons CH_3COO^-(aq) + H_3O^+(aq)}$

Result: The solution becomes less acidic (higher pH).

Buffer Solutions

Composition and Action

• Buffer Solution: A solution that resists changes in pH when small amounts of acid or base are added.

• Composed of a weak acid and its conjugate base, or a weak base and its conjugate acid.

• Buffers are crucial in biological systems (e.g., blood pH) and industrial processes.

How Buffers Work

• When a strong acid is added, the conjugate base neutralizes the added H+.

• When a strong base is added, the weak acid neutralizes the added OH−.

• The pH remains nearly constant as long as the buffer components are present in sufficient amounts.

Example: Acetate buffer (CH3COOH/CH3COO−)

Buffer Preparation

• Mix a weak acid with a salt of its conjugate base, or a weak base with a salt of its conjugate acid.

• Alternatively, partially neutralize a weak acid with a strong base (or vice versa).

Buffer Capacity and pH Range

• Buffer Capacity: The amount of acid or base a buffer can neutralize before the pH changes significantly.

• Effective Buffer Range: Typically within ±1 pH unit of the buffer’s pKa.

• Buffer capacity increases with the concentration of buffer components.

Calculating Buffer pH: Henderson-Hasselbalch Equation

• The pH of a buffer can be calculated using the Henderson-Hasselbalch equation:

$\mathrm{pH = pK_a + \log \left( \frac{[\text{base}]}{[\text{acid}]} \right)}$

• If [base] = [acid], then pH = pKa.

• If [base] > [acid], then pH > pKa.

• If [base] < [acid], then pH < pKa.

Addition of Strong Acids and Bases to Buffers

• When a strong acid or base is added, first perform a stoichiometric calculation to determine the new concentrations of buffer components.

• Then, use the Henderson-Hasselbalch equation to find the new pH.

Acid-Base Titrations

Principles and Setup

• Titration: A quantitative technique to determine the concentration of an unknown acid or base by neutralization with a standard solution.

• Equivalence Point: The point at which moles of acid equal moles of base.

• Endpoint: The point at which the indicator changes color, ideally close to the equivalence point.

Indicators

• Indicators are weak acids or bases that change color at a specific pH range.

• The color change occurs when [HIn] = [In−], i.e., pH = pKa of the indicator.

• Choose an indicator whose color change interval brackets the equivalence point pH.

Titration Curves

• Strong Acid–Strong Base: pH rises slowly, then rapidly near equivalence (pH = 7 at equivalence).

• Weak Acid–Strong Base: Initial pH is higher, buffer region present, pH at equivalence > 7.

• Polyprotic Acids: Multiple equivalence points, each corresponding to the loss of a proton.

Solubility Equilibria

The Solubility-Product Constant (Ksp)

• Ksp: The equilibrium constant for the dissolution of a sparingly soluble salt.

• For a salt AB: $\mathrm{AB(s) \rightleftharpoons A^+(aq) + B^-(aq)}$

• $\mathrm{K_{sp} = [A^+][B^-]}$

• For a salt with formula AxBy: $\mathrm{K_{sp} = [A^{n+}]^x [B^{m-}]^y}$

Solubility vs. Solubility Product

• Solubility: The amount of solute that dissolves to form a saturated solution (g/L or mol/L).

• Ksp: Depends on the equilibrium concentrations of the ions.

• Solubility and Ksp are related but not identical; Ksp is used for calculations involving ionic equilibria.

Predicting Precipitation: The Ion Product (Q)

• Ion Product (Q): Calculated like Ksp but with initial concentrations.

• If Q < Ksp: No precipitate forms (unsaturated solution).

• If Q = Ksp: Solution is saturated (at equilibrium).

• If Q > Ksp: Precipitate forms (supersaturated solution).

Factors Affecting Solubility

Common-Ion Effect

• The presence of a common ion decreases the solubility of a salt due to Le Chatelier’s Principle.

• Example: Adding NaF to a solution of CaF2 decreases the solubility of CaF2.

Effect of pH

• Salts containing basic anions are more soluble in acidic solutions.

• Buffers can control pH and thus influence solubility equilibria.

Precipitation and Separation of Ions

Selective Precipitation

• Ions can be separated from mixtures by adding reagents that selectively precipitate the least soluble salts first.

• Comparing Ksp values allows prediction of the order of precipitation.

Qualitative Analysis for Metallic Elements

Application of Solubility Rules

• Differences in solubility are used to identify and separate metal ions in solution.

• This is a foundational technique in qualitative inorganic analysis.

Summary Table: Key Concepts in Aqueous Equilibria

Concept	Definition	Key Equation
Common-Ion Effect	Suppression of ionization by a common ion	$\mathrm{HA \rightleftharpoons H^+ + A^-}$
Buffer Solution	Resists pH change	$\mathrm{pH = pK_a + \log \left( \frac{[\text{base}]}{[\text{acid}]} \right)}$
Titration	Determines unknown concentration	$\mathrm{n_{acid} = n_{base}}$
Ksp	Solubility product constant	$\mathrm{K_{sp} = [A^+]^x [B^-]^y}$
Ion Product (Q)	Predicts precipitation	Compare Q to Ksp