Chapter 16

. Definitions of Acids and Bases

Arrhenius Definition

  • Acid: A substance that dissociates in water to produce H⁺ (or H₃O⁺) ions.

    • Example: HCl → H⁺ + Cl⁻

  • Base: A substance that dissociates in water to produce OH⁻ ions.

    • Example: NaOH → Na⁺ + OH⁻

Limitations:

  • Only applies to aqueous solutions.

  • Does not account for bases like NH₃ (ammonia), which do not contain OH⁻.

Brønsted-Lowry Definition

  • Acid: A proton (H⁺) donor.

  • Base: A proton (H⁺) acceptor.

Key Points:

  • Focuses on the transfer of H⁺ ions.

  • Applies to reactions in any solvent, not just water.

  • Conjugate pairs: Every acid has a conjugate base (after losing H⁺), and every base has a conjugate acid (after gaining H⁺).

Example:

  • NH₃ (base) + H₂O (acid) ⇌ NH₄⁺ (conjugate acid) + OH⁻ (conjugate base)

Lewis Definition

  • Acid: An electron pair acceptor.

  • Base: An electron pair donor.

Key Points:

  • Broadest definition; includes all Brønsted-Lowry acids/bases and more.

  • Can explain acid-base reactions in non-protonic systems (e.g., BF₃ + NH₃ → BF₃NH₃).

Example:

  • BF₃ (Lewis acid) + NH₃ (Lewis base) → BF₃NH₃

2. Identifying Acids and Bases

Can a substance act as an Arrhenius, Brønsted-Lowry, and/or Lewis acid or base?

  • Arrhenius: Only if it produces H⁺ or OH⁻ in water.

  • Brønsted-Lowry: If it donates or accepts H⁺.

  • Lewis: If it accepts or donates an electron pair.

Examples:

Substance

Arrhenius

Brønsted-Lowry

Lewis

HCl

Acid

Acid

Acid

NaOH

Base

Base

Base

NH₃

—

Base

Base

BF₃

—

—

Acid

Conjugate Acid-Base Pairs

  • Conjugate acid: Formed when a base gains an H⁺.

  • Conjugate base: Formed when an acid loses an H⁺.

Example:

  • Acid: H₂O → Conjugate base: OH⁻

  • Base: NH₃ → Conjugate acid: NH₄⁺

Identifying Conjugate Pairs in an Equation:

  • Look for two species that differ by one H⁺.

  • Example:
    HNO₃ + H₂O ⇌ H₃O⁺ + NO₃⁻

    • Conjugate pairs:

      • HNO₃ (acid) and NO₃⁻ (conjugate base)

      • H₂O (base) and H₃O⁺ (conjugate acid)

3. Identifying Acid/Base Reactions

An equation represents an acid/base reaction if:

  1. H⁺ is transferred (Brønsted-Lowry).

  2. An electron pair is donated/accepted (Lewis).

  3. H⁺ or OH⁻ is produced (Arrhenius).

Examples:

  • Acid/base: HCl + NaOH → NaCl + H₂O (H⁺ transferred)

  • Not acid/base: NaCl → Na⁺ + Cl⁻ (no H⁺ or OH⁻ produced)

4. Amphoteric Substances

  • Definition: A substance that can act as both an acid and a base.

  • Examples:

    • Water (H₂O): Can donate H⁺ (acid) or accept H⁺ (base).

    • Amino acids, HSO₄⁻, Al₂O₃.

Example Reaction:

  • H₂O + H₂O ⇌ H₃O⁺ + OH⁻

    • One water molecule acts as an acid, the other as a base.

5. Favored Side of an Acid/Base Reaction

The reaction favors the side with:

  1. Weaker acid and weaker base (lower energy).

  2. Higher pKa (weaker acid) and higher pKb (weaker base).

Example:

  • HCl (strong acid) + H₂O → H₃O⁺ + Cl⁻

    • Reaction favors the right because HCl is a strong acid (fully dissociates).

6. pH, pOH, and the pH Equation

  • pH: Measure of H₃O⁺ concentration.

    • pH = -log[H₃O⁺]

  • pOH: Measure of OH⁻ concentration.

    • pOH = -log[OH⁻]

  • Relationship:

    • pH + pOH = 14 (at 25°C)

  • Determining Acidity/Basicity:

    • pH < 7: Acidic

    • pH = 7: Neutral

    • pH > 7: Basic

Example:

  • If [H₃O⁺] = 1 × 10⁻³ M, then pH = -log(1 × 10⁻³) = 3 (acidic).

7. Kw Equation

  • Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ (at 25°C)

  • Used to find [H₃O⁺] or [OH⁻] if one is known.

Example:

  • If [OH⁻] = 1 × 10⁻⁴ M, then [H₃O⁺] = Kw / [OH⁻] = 1 × 10⁻¹⁰ M.

8. Strong vs. Weak Acids and Bases

  • Strong acid/base: Fully dissociates in water.

    • Example: HCl, HNO₃, NaOH.

  • Weak acid/base: Partially dissociates in water.

    • Example: CH₃COOH, NH₃.

Property Defining Strength:

  • Ka or Kb value: Larger Ka/Kb = stronger acid/base.

9. Calculating pH/pOH for Strong Acids/Bases

  • For strong acids/bases, the concentration of H₃O⁺ or OH⁻ is equal to the initial concentration of the acid/base.

Example:

  • 0.1 M HCl → [H₃O⁺] = 0.1 M → pH = -log(0.1) = 1.

  • 0.1 M NaOH → [OH⁻] = 0.1 M → pOH = 1 → pH = 13.

10. Calculations for Weak Acids/Bases

Use the Ka or Kb and an ICE table (Initial, Change, Equilibrium) to find [H₃O⁺] or [OH⁻].

Example:

  • For a weak acid HA with Ka = 1.8 × 10⁻⁵ and concentration 0.1 M:

    • HA ⇌ H⁺ + A⁻

    • Ka = [H⁺][A⁻] / [HA] = x² / (0.1 - x) ≈ x² / 0.1

    • Solve for x: [H⁺] = √(Ka × 0.1) = √(1.8 × 10⁻⁶) ≈ 1.34 × 10⁻³ M

    • pH = -log(1.34 × 10⁻³) ≈ 2.87

11. Ranking Acids/Bases Using Ka/Kb

  • Larger Ka = stronger acid.

  • Larger Kb = stronger base.

Example:

  • Rank the following acids in order of increasing strength:

    • HCN (Ka = 4.9 × 10⁻¹⁰)

    • CH₃COOH (Ka = 1.8 × 10⁻⁵)

    • HF (Ka = 6.8 × 10⁻⁴)

  • Order: HCN < CH₃COOH < HF

12. Polyprotic Acids

  • Definition: Acids with multiple dissociable H⁺ ions.

  • Examples: H₂SO₄, H₂CO₃, H₃PO₄.

Why Ka1 > Ka2 > Ka3?

  • The first H⁺ is easier to remove due to weaker electrostatic attraction after the first dissociation.

Step-wise Dissociation:

  • H₂SO₄ ⇌ H⁺ + HSO₄⁻ (Ka1)

  • HSO₄⁻ ⇌ H⁺ + SO₄²⁻ (Ka2)

13. Relationship Between Ka and Kb for Conjugate Pairs

  • Ka × Kb = Kw = 1.0 × 10⁻¹⁴ (at 25°C)

  • Used to find Ka or Kb if one is known.

Example:

  • For NH₄⁺ (conjugate acid of NH₃), Kb of NH₃ = 1.8 × 10⁻⁵.

  • Ka of NH₄⁺ = Kw / Kb = 1.0 × 10⁻¹⁴ / 1.8 × 10⁻⁵ ≈ 5.6 × 10⁻¹⁰.

14. Hydrolysis of Ions

  • Definition: Reaction of an ion with water to produce H₃O⁺ or OH⁻.

  • Cations: Small, highly charged cations (e.g., Al³⁺, Fe³⁺) hydrolyze to produce acidic solutions.

  • Anions: Anions of weak acids (e.g., CH₃COO⁻, CO₃²⁻) hydrolyze to produce basic solutions.

Example:

  • CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻ (basic solution)

15. Salt Solutions: Acidic, Basic, or Neutral?

  • Neutral salts: From strong acid + strong base (e.g., NaCl).

  • Acidic salts: From strong acid + weak base (e.g., NH₄Cl).

  • Basic salts: From weak acid + strong base (e.g., CH₃COONa).

Example:

  • Na₂CO₃ (basic): CO₃²⁻ + H₂O ⇌ HCO₃⁻ + OH⁻

16. Calculating pH of a Salt Solution

  1. Identify the ions in the salt.

  2. Determine if either ion hydrolyzes.

  3. Calculate the pH based on the hydrolysis reaction.

Example:

  • For 0.1 M NH₄Cl:

    • NH₄⁺ hydrolyzes: NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺

    • Ka of NH₄⁺ = Kw / Kb of NH₃ = 5.6 × 10⁻¹⁰

    • Use Ka to find [H₃O⁺] and pH.

17. Acid Strength and Molecular Structure

Binary Acids (HX)

  • Trend: Acid strength increases down a group (H-F < H-Cl < H-Br < H-I).

  • Reason: Bond strength decreases, making H⁺ easier to release.

Oxoacids with Same Central Atom, Varying Oxygens

  • Trend: More oxygens = stronger acid.

  • Reason: Additional oxygens stabilize the conjugate base by delocalizing charge.

Example:

  • HClO < HClO₂ < HClO₃ < HClO₄

Oxoacids with Same Number of Oxygens, Different Central Atoms

  • Trend: More electronegative central atom = stronger acid.

  • Reason: Pulls electron density away from the O-H bond, making H⁺ easier to release.

Example:

  • HClO > HBrO > HIO