Ionization of Acids and Bases

Full Notes

Ionization of Acids and Bases

This section explores how acids and bases behave in water by donating or accepting protons – a process known as ionization. These reactions establish an equilibrium, which we describe using equilibrium constants.

When an acid donates a proton (H⁺), it forms its conjugate base – the species that can potentially accept a proton. Similarly, when a base accepts a proton, it forms its conjugate acid – the species that can later donate a proton. Understanding these conjugate pairs is key to following acid–base equilibrium.

The Ionization Constant of Water and Its Ionic Product

In any aqueous solution, water molecules are constantly undergoing self-ionization, forming H⁺ and OH⁻ ions:

The equilibrium lies far to the left – meaning only a tiny amount of water actually ionizes. Even pure water contains equal and very small concentrations of H⁺ and OH⁻ ions.

• If [H⁺] > [OH⁻], the solution is acidic.
• If [OH⁻] > [H⁺], the solution is basic (alkaline).

This is a reversible process, and an equilibrium is established. The equilibrium constant is:

Because each water molecule forms H⁺ and OH⁻ in a 1:1 ratio, pure water has: [H⁺] = [OH⁻] = 1 × 10⁻⁷ mol L⁻¹ at 298 K.

The pH Scale

Since [H⁺] indicates acidity/basicity, we use a logarithmic scale – the pH scale – to express wide-ranging values more simply.

• A lower pH indicates a higher concentration of hydrogen ions (i.e. a more acidic solution).
• At 298 K:
  • Neutral solution: pH = 7
  • Acidic: pH < 7
  • Basic: pH > 7

• Neutral solution: pH = 7
• Acidic: pH < 7
• Basic: pH > 7

Meaning, at 298 K pH + pOH = 14. This logarithmic scale is widely used to monitor acidity/basicity in chemistry and biology.

Ionization Constants of Weak Acids

A weak acid only partially ionizes in water. Only a small fraction of acid molecules donate protons, so [H⁺] is much lower than the initial [HA].

An equilibrium is established between:

• Undissociated acid molecules (HA)
• Conjugate base ions (A⁻)
• H⁺ ions

Where HA = weak acid, A⁻ = conjugate base ion, H⁺ = hydrogen ion.

For Example:

• Ethanoic acid (CH₃COOH):

CH₃COOH ⇌ H₃O⁺ + CH₃COO⁻

Only a small proportion of CH₃COOH molecules ionize, so the solution contains an equilibrium mixture of all three species.

Acid Dissociation Constant, K_a:

Because weak acids form an equilibrium system, we use an equilibrium constant, K_a, to quantify the extent of ionization:

• Smaller K_a = weaker acid
• Larger pK_a = weaker acid

Percent ionization of a weak acid: % ionization = ([H₃O⁺] at equilibrium / initial [HA]) × 100

Ionization of Weak Bases

Weak bases accept protons from water, forming their conjugate acids and OH⁻ ions. They ionize only partially and establish equilibrium.

• B is the weak base.
• BH⁺ is the conjugate acid formed when the base accepts a proton.
• OH⁻ is the hydroxide ion released into solution, increasing basicity.

The position of this equilibrium depends on how effectively the base accepts protons from water (its base strength).

Base Dissociation Constant, K_b:

As with weak acids, the strength of a weak base is described by an equilibrium constant:

• Smaller K_b = weaker base
• Larger pK_b = weaker base
• The majority of the base remains unreacted in solution.

Percent ionization of a weak base: % ionization
= ([OH⁻] at equilibrium / initial [B]) × 100

Relation Between K_a and K_b

Acids and bases exist in conjugate pairs. The strength of one determines the strength of the other:

Key Relationship:
K_a × K_b = K_w
 pK_a + pK_b = pK_w

At 25 °C: K_w = 1.0 × 10⁻¹⁴  (pK_w = 14.00)

This allows interconversion between K_a and K_b (or pK_a and pK_b) for any conjugate pair.

Deriving the Relationship

and

Multiplying these together:

Di- and Polybasic Acids and Di- and Polyacidic Bases

Some acids and bases can donate or accept more than one proton — this occurs in steps, each with its own equilibrium constant.

Example: H₂SO₄

• H₂SO₄ → H⁺ + HSO₄⁻ (K_a1 = large)
• HSO₄⁻ ⇌ H⁺ + SO₄²⁻ (K_a2 = smaller)

Each successive ionization is harder, so K_a decreases with each step due to increased negative charge.

Factors Affecting Acid Strength

Several factors contribute to affect acid strength:

• Bond polarity (more polar = stronger acid)
• Bond strength (weaker bonds = easier to ionize)
• Size of atom (larger X in H–X → easier dissociation)
• Electronegativity (inductive effects)
• Solvation/hydration (more solvation stabilizes ions)

Example:
In halogen acids, acid strength increases from HF < HCl < HBr < HI due to bond strength.

Common Ion Effect in the Ionization of Acids and Bases

When a salt is added to a solution that already contains one of its own ions, its solubility decreases. This is known as the common-ion effect.

For Example:

• In a solution of CH₃COOH + CH₃COONa:
  • Addition of CH₃COO⁻ from salt shifts equilibrium left:
    CH₃COOH ⇌ CH₃COO⁻ + H⁺
  • This reduces [H⁺] and hence increases pH. It's used in buffer solutions.

Hydrolysis of Salts and the pH of Their Solutions

When salts dissolve in water, their ions may react with water (hydrolysis), affecting pH.

• Strong acid + strong base → neutral salt
  Example: NaCl → pH ≈ 7
• Strong acid + weak base → acidic salt
  Example: NH₄Cl NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺ → pH < 7
• Weak acid + strong base → basic salt
  Example: CH₃COONa CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻ → pH > 7
• Weak acid + weak base → acidic, basic or neutral salt
  Depends on relative K_a and K_b values.

Common Ions and Their pH Effects

• NH₄⁺ (ammonium)
  NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺ → acidic
• RCOO⁻ (carboxylate)
  RCOO⁻ + H₂O ⇌ RCOOH + OH⁻ → basic
• CO₃²⁻ (carbonate)
  CO₃²⁻ + H₂O ⇌ HCO₃⁻ + OH⁻ → basic
• HCO₃⁻ (hydrogencarbonate)
  Amphiprotic:
  • As acid: HCO₃⁻ + H₂O ⇌ CO₃²⁻ + H₃O⁺
  • As base: HCO₃⁻ + H₂O ⇌ H₂CO₃ + OH⁻

Summary

• K_a and K_b quantify ionization of weak acids and bases in water.
• K_w at 298 K equals 1 × 10⁻¹⁴ and pH + pOH equals 14.
• For conjugate pairs K_a × K_b equals K_w and pK_a + pK_b equals pK_w.
• Common ion effect suppresses ionization and salt hydrolysis controls solution pH.