Acids and Bases

Core Review

Three Acid-Base Theories

Arrhenius: Acid produces H⁺ in water; base produces OH⁻ in water. Limited — only applies to aqueous solutions. HCl → H⁺ + Cl⁻; NaOH → Na⁺ + OH⁻.

Brønsted-Lowry: Acid is a proton (H⁺) donor; base is a proton acceptor. Broader — applies to any solvent. In every proton transfer, the acid donates H⁺ to the base.

HCl + H₂O → H₃O⁺ + Cl⁻
(acid) (base) (conjugate acid) (conjugate base)

Lewis: Acid is an electron-pair acceptor; base is an electron-pair donor. Most general — includes species without protons (BF₃, AlCl₃). NH₃ donates a lone pair to BF₃ → H₃N–BF₃.

Strong vs. Weak Acids and Bases

The six strong acids (memorize these):

1. HCl — hydrochloric acid
2. HBr — hydrobromic acid
3. HI — hydroiodic acid
4. HNO₃ — nitric acid
5. H₂SO₄ — sulfuric acid (diprotic; first proton is strong)
6. HClO₄ — perchloric acid

Strong acids dissociate completely in water — K_a is effectively infinite. Weak acids dissociate partially; equilibrium lies far to the left. For a strong acid, [H⁺] = initial acid concentration (for monoprotic).

Strong bases: Group 1 hydroxides (NaOH, KOH) and heavy Group 2 hydroxides — Ca(OH)₂, Sr(OH)₂, Ba(OH)₂. Mg(OH)₂ and Be(OH)₂ are weak.

Acid strength trends for binary acids: Across a period: H–F < H–Cl < H–Br < H–I. Bond strength matters — weaker H–X bond = stronger acid. Down a group: larger atom, weaker bond, stronger acid.

Oxyacid trends: More electronegative central atom or more oxygen atoms = stronger acid. HClO₄ > HClO₃ > HClO₂ > HClO.

pH, pOH, and K_w

pH = −log[H⁺]           pOH = −log[OH⁻]
pH + pOH = 14.00 (at 25°C)
K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ (at 25°C)

Worked Example: Calculate the pH of 0.025 M HCl (strong monoprotic acid).

• [H⁺] = 0.025 M
• pH = −log(0.025) = −(−1.60) = 1.60

Worked Example: Calculate [H⁺] when pH = 8.40.

• [H⁺] = 10^(−8.40) = 4.0 × 10⁻⁹ M

K_a and K_b — Weak Acid/Base Equilibria

For a weak acid HA: HA ⇌ H⁺ + A⁻

K_a = [H⁺][A⁻] / [HA]

Larger K_a = stronger acid. pK_a = −log(K_a). Smaller pK_a = stronger acid.

For a weak base B: B + H₂O ⇌ BH⁺ + OH⁻

K_b = [BH⁺][OH⁻] / [B]

Relationship between K_a and K_b for conjugate pairs:

K_a × K_b = K_w = 1.0 × 10⁻¹⁴
pK_a + pK_b = 14.00

The stronger the acid, the weaker its conjugate base (and vice versa).

Worked Example: K_a for acetic acid (CH₃COOH) = 1.8 × 10⁻⁵. What is the pH of 0.100 M acetic acid?

• Use ICE table: K_a = x² / (0.100 − x) ≈ x² / 0.100 (assumption valid if K_a is small)
• x² = 1.8 × 10⁻⁵ × 0.100 = 1.8 × 10⁻⁶
• x = [H⁺] = 1.34 × 10⁻³ M
• pH = −log(1.34 × 10⁻³) = 2.87

Conjugate Acid-Base Pairs

In an acid-base reaction, the acid donates H⁺ to become its conjugate base; the base accepts H⁺ to become its conjugate acid. The pair differs by exactly one H⁺:

• HCl / Cl⁻
• H₂O / OH⁻ (water as acid) or H₃O⁺ / H₂O (water as base)
• NH₄⁺ / NH₃
• CH₃COOH / CH₃COO⁻

Amphoteric (amphiprotic) species can act as either acid or base: H₂O, HCO₃⁻, HSO₄⁻, H₂PO₄⁻.

Strong ≠ Concentrated

"Strong" describes extent of dissociation (thermodynamics); "concentrated" describes amount dissolved (kinetics/amount). A 12 M solution of weak acetic acid is concentrated but weak; a 0.001 M solution of HCl is dilute but strong — dissociation in the latter is 100%.

Key Equations

Common Traps

• HF is NOT a strong acid (fluorine's high electronegativity makes the H–F bond very strong).
• H₂SO₄'s first proton is strong; the second (HSO₄⁻ → SO₄²⁻) is weak (K_a2 = 1.2 × 10⁻²).
• "Concentrated weak acid" ≠ "strong acid."
• Polyprotic acids have multiple K_a values — successive K_a values are always smaller.
• The conjugate base of a weak acid produces basic solutions (salt hydrolysis).