1 Definitions
Arrhenius Definitions
The Arrhenius model is the simplest: it defines acids and bases by what they release into water.
- Acid — produces H⁺ ions in water (e.g., HCl → H⁺ + Cl⁻)
- Base — produces OH⁻ ions in water (e.g., NaOH → Na⁺ + OH⁻)
Brønsted-Lowry Definitions
A more general model based on proton (H⁺) transfer — works for reactions outside water too.
- Acid — H⁺ donor (gives away a proton)
- Base — H⁺ acceptor (receives a proton)
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Every Brønsted-Lowry acid-base reaction creates a conjugate acid-base pair. When an acid donates H⁺, it becomes a conjugate base; when a base accepts H⁺, it becomes a conjugate acid.
Example: CH₃COOH + H₂O ⇌ CH₃COO⁻ + H₃O⁺
CH₃COOH/CH₃COO⁻ is one conjugate pair; H₂O/H₃O⁺ is the other.
Example: CH₃COOH + H₂O ⇌ CH₃COO⁻ + H₃O⁺
CH₃COOH/CH₃COO⁻ is one conjugate pair; H₂O/H₃O⁺ is the other.
2 Strong vs Weak Acids/Bases
Strong Acids — Fully Dissociate (memorise these)
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The 6 strong acids: HCl, HNO₃, H₂SO₄, HBr, HI, HClO₄
"strong" means 100% dissociation — every molecule releases all its H⁺ ions.
"strong" means 100% dissociation — every molecule releases all its H⁺ ions.
Strong Bases
- NaOH, KOH, LiOH, Ba(OH)₂, Ca(OH)₂ — fully dissociate in water
Weak Acids — Partially Dissociate
- CH₃COOH (acetic acid), H₂CO₃ (carbonic acid), HF (hydrofluoric), H₂S, HNO₂
- Only a small fraction of molecules donate H⁺ — an equilibrium exists
Weak Base
- NH₃ (ammonia) — partially accepts H⁺ from water to form NH₄⁺ and OH⁻
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Weak acid ≠ dilute acid. "Strength" refers to degree of dissociation, not concentration. A concentrated solution of a weak acid still only partially dissociates; a dilute solution of a strong acid still fully dissociates.
3 pH and pOH
Definitions
pH
pH = −log[H⁺]
[H⁺] from pH
[H⁺] = 10^(−pH)
pOH
pOH = −log[OH⁻]
Relationship
pH + pOH = 14 (at 25°C)
Water constant Kw
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ (at 25°C)
pH Scale
| pH Range | Nature of Solution | [H⁺] vs [OH⁻] |
|---|---|---|
| pH < 7 | Acidic | [H⁺] > [OH⁻] |
| pH = 7 | Neutral | [H⁺] = [OH⁻] = 10⁻⁷ M |
| pH > 7 | Basic (alkaline) | [H⁺] < [OH⁻] |
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Logarithmic scale: each pH unit represents a 10× change in [H⁺]. pH 3 has 100× more H⁺ than pH 5. As pH increases, [H⁺] decreases — they move in opposite directions.
4 Strong Acid/Base Calculations
Because strong acids fully dissociate, [H⁺] equals the acid concentration (times number of H⁺ per molecule). No equilibrium calculation needed.
Strong Acid
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Example: 0.01 M HCl
HCl is a strong acid (monoprotic) → [H⁺] = 0.01 M = 10⁻² M
pH = −log(0.01) = −log(10⁻²) = 2
HCl is a strong acid (monoprotic) → [H⁺] = 0.01 M = 10⁻² M
pH = −log(0.01) = −log(10⁻²) = 2
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Diprotic example: 0.05 M H₂SO₄
H₂SO₄ is diprotic → [H⁺] = 2 × 0.05 = 0.10 M
pH = −log(0.10) = 1
H₂SO₄ is diprotic → [H⁺] = 2 × 0.05 = 0.10 M
pH = −log(0.10) = 1
Strong Base
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Example: 0.001 M NaOH
NaOH fully dissociates → [OH⁻] = 0.001 M = 10⁻³ M
pOH = −log(0.001) = 3
pH = 14 − 3 = 11
NaOH fully dissociates → [OH⁻] = 0.001 M = 10⁻³ M
pOH = −log(0.001) = 3
pH = 14 − 3 = 11
General rule — strong acid
[H⁺] = C × n_H (n_H = H⁺ per formula unit)
General rule — strong base
[OH⁻] = C × n_OH (n_OH = OH⁻ per formula unit)
5 Ka and Kb
Acid Dissociation Constant Ka
For a weak acid HA dissociating: HA ⇌ H⁺ + A⁻
Ka expression
Ka = [H⁺][A⁻] / [HA]
A larger Ka means more dissociation — a stronger weak acid. Ka values are typically small (e.g., Ka for acetic acid = 1.8 × 10⁻⁵).
ICE Table Method
Use an ICE (Initial, Change, Equilibrium) table to find [H⁺] from Ka and initial concentration C.
| HA | H⁺ | A⁻ | |
|---|---|---|---|
| Initial | C | 0 | 0 |
| Change | −x | +x | +x |
| Equilibrium | C − x | x | x |
Ka from ICE
Ka = x² / (C − x)
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5% approximation: if Ka is small, C − x ≈ C, so x ≈ √(Ka × C). This is valid when x/C < 5%.
6 Neutralization
A neutralization reaction occurs when an acid and a base react to form a salt and water.
General
acid + base → salt + water
Net ionic
H⁺(aq) + OH⁻(aq) → H₂O(l)
pH at Equivalence
| Combination | Salt formed | pH at equivalence |
|---|---|---|
| Strong acid + strong base | Neutral salt | pH = 7 |
| Strong acid + weak base | Acidic salt | pH < 7 |
| Weak acid + strong base | Basic salt | pH > 7 |
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At the equivalence point, moles of H⁺ equal moles of OH⁻. For diprotic acids, you must supply 2 moles of base per mole of acid.
7 Titration
Titration is a technique to determine the unknown concentration of an acid or base by adding a solution of known concentration (the titrant) until the reaction is complete.
- Equivalence point — moles of H⁺ exactly equal moles of OH⁻
- Endpoint — the point where the indicator changes colour (ideally matches equivalence point)
- Indicator — a substance that changes colour at a specific pH range
Titration Calculation
1:1 reaction (monoprotic)
CₐVₐ = CᵦVᵦ
General formula
nₐ × Cₐ × Vₐ = nᵦ × Cᵦ × Vᵦ
nₐ and nᵦ are the moles of H⁺ and OH⁻ per formula unit, respectively.
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Example: 25.0 mL of unknown HCl titrated to equivalence with 31.5 mL of 0.100 M NaOH.
CₐVₐ = CᵦVᵦ → Cₐ = (0.100 × 31.5) / 25.0 = 0.126 M
CₐVₐ = CᵦVᵦ → Cₐ = (0.100 × 31.5) / 25.0 = 0.126 M
8 Common Mistakes to Avoid
| Mistake | What to do instead |
|---|---|
| Treating weak acid as having [H⁺] = C | Weak acids partially dissociate — use Ka and ICE table, not direct concentration. |
| Forgetting H₂SO₄ is diprotic | 0.1 M H₂SO₄ gives [H⁺] = 0.2 M (2 H⁺ per molecule). Always check the formula. |
| Thinking higher pH = more acidic | pH increases as [H⁺] decreases. pH 2 is more acidic than pH 5. |
| Using pH + pOH = 7 or pH − pOH = 14 | pH + pOH = 14 (at 25°C). Not plus-minus: always add to get 14. |
| Using CₐVₐ = CᵦVᵦ for diprotic acid | Use nₐCₐVₐ = nᵦCᵦVᵦ. For H₂SO₄ vs NaOH, nₐ = 2 (two H⁺ per molecule). |
| Weak acid = dilute acid | Strength = degree of dissociation. Concentration (dilute/concentrated) is separate. |