A Level Chemistry - How to Solve: Acid-Base Titrations & Back Titrations (pH Curves, Indicators)

How to Solve: Acid-Base Titrations & Back Titrations (pH Curves, Indicators)

Complete Guide For GCSE/A-Level Chemistry (Edexcel, AQA, OCR, IB)

Introduction

"Mastering titrations unlocks 10–15% of your GCSE/A-Level Chemistry exam—think buffer calculations, drug purity tests, and even how your stomach neutralises acid. One wrong step? You lose 4–6 marks. Today, we’ll turn this into a 100% predictable process."

WHAT YOU NEED TO KNOW FIRST

1. Moles & Concentration: n = c × V (moles = concentration × volume in dm³).
2. pH Scale: Acids (pH < 7), bases (pH > 7), neutral (pH = 7).
3. Strong vs. Weak Acids/Bases: Strong = fully dissociates (e.g., HCl, NaOH); weak = partially dissociates (e.g., CH₃COOH, NH₃).

KEY TERMS & FORMULAS

Terms

Formulas

1. Moles (n) = concentration (c) × volume (V)
2. c = mol/dm³, V = dm³ (MEMORISE THIS).

3. If volume is in cm³, divide by 1000 first.

4. Dilution: c₁V₁ = c₂V₂

5. Used when diluting solutions (MEMORISE THIS).

6. % Purity = (mass of pure substance / mass of impure sample) × 100

7. Used in back titrations (MEMORISE THIS).

8. pH = -log[H⁺]

9. For strong acids only (given on exam sheet).

STEP-BY-STEP METHOD

Part 1: Standard Titration (Direct)

Goal: Find unknown concentration of acid/base.

1. Write the balanced equation (e.g., HCl + NaOH → NaCl + H₂O).
2. Calculate moles of known solution (use n = c × V).
3. V must be in dm³ (divide cm³ by 1000).
4. Use mole ratio to find moles of unknown.
5. E.g., 1:1 ratio → moles of acid = moles of base.
6. Calculate unknown concentration (use c = n / V).
7. Check units: Answer must be in mol/dm³.

Part 2: Back Titration

Goal: Find % purity or concentration when direct titration is impossible (e.g., insoluble sample).

1. Write two balanced equations:
2. Reaction of sample with excess acid/base.
3. Titration of leftover acid/base.
4. Calculate moles of titrant used (e.g., NaOH in burette).
5. Find moles of leftover acid/base (use mole ratio from 2nd equation).
6. Find moles of acid/base that reacted with sample (initial moles – leftover moles).
7. Use 1st equation’s mole ratio to find moles of sample.
8. Calculate mass or % purity (use mass = n × Mᵣ).

Part 3: Choosing Indicators

1. Identify equivalence point pH from pH curve:
2. Strong acid + strong base → pH 7.
3. Weak acid + strong base → pH > 7.
4. Strong acid + weak base → pH < 7.
5. Pick indicator with pH range overlapping equivalence point:
6. Methyl orange: pH 3.1–4.4 (strong acid + weak base).
7. Phenolphthalein: pH 8.3–10.0 (weak acid + strong base).

WORKED EXAMPLES

Example 1 – Basic Titration

Question: 25.0 cm³ of NaOH neutralises 20.0 cm³ of 0.100 mol/dm³ HCl. Find [NaOH].

Steps:
1. Balanced equation: HCl + NaOH → NaCl + H₂O (1:1 ratio).
2. Moles HCl = 0.100 × (20.0/1000) = 0.00200 mol.
3. Moles NaOH = 0.00200 mol (1:1 ratio).
4. [NaOH] = 0.00200 / (25.0/1000) = 0.0800 mol/dm³.

What we did and why: - Used n = c × V to find moles of HCl. - 1:1 ratio → moles NaOH = moles HCl. - Rearranged c = n / V to find [NaOH].

Example 2 – Medium (Back Titration)

Question: 2.50 g of impure CaCO₃ is reacted with 50.0 cm³ of 1.00 mol/dm³ HCl. Excess HCl requires 25.0 cm³ of 0.500 mol/dm³ NaOH for neutralisation. Find % purity of CaCO₃.

Steps:
1. Equations: - CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂ - HCl + NaOH → NaCl + H₂O
2. Moles NaOH = 0.500 × (25.0/1000) = 0.0125 mol.
3. Moles excess HCl = 0.0125 mol (1:1 ratio).
4. Initial moles HCl = 1.00 × (50.0/1000) = 0.0500 mol.
5. Moles HCl reacted with CaCO₃ = 0.0500 – 0.0125 = 0.0375 mol.
6. Moles CaCO₃ = 0.0375 / 2 = 0.01875 mol (1:2 ratio).
7. Mass CaCO₃ = 0.01875 × 100.1 = 1.877 g.
8. % purity = (1.877 / 2.50) × 100 = 75.1%.

What we did and why: - Used back titration to find moles of HCl that reacted with CaCO₃. - 1:2 ratio → moles CaCO₃ = ½ moles HCl. - Calculated mass and % purity.

Example 3 – Exam-Style (pH Curve + Indicator)

Question: A student titrates 0.100 mol/dm³ CH₃COOH with 0.100 mol/dm³ NaOH. Sketch the pH curve and choose the best indicator.

Steps:
1. pH curve features: - Starts at pH ~3 (weak acid). - Equivalence point at pH ~8.5 (weak acid + strong base). - Gradual rise, then sharp jump at equivalence point.
2. Indicator choice: - Phenolphthalein (pH 8.3–10.0) overlaps equivalence point. - Methyl orange (pH 3.1–4.4) is wrong (too low).

What we did and why: - Weak acid + strong base → equivalence point > pH 7. - Phenolphthalein matches the pH jump.

COMMON MISTAKES

1. MISTAKE: Using cm³ directly in n = c × V. WHY IT HAPPENS: Forgetting to convert to dm³. CORRECT APPROACH: Divide cm³ by 1000 first.

2. MISTAKE: Ignoring mole ratios. WHY IT HAPPENS: Assuming 1:1 ratio for all reactions. CORRECT APPROACH: Write balanced equation first.

3. MISTAKE: Choosing wrong indicator. WHY IT HAPPENS: Not checking equivalence point pH. CORRECT APPROACH: Match indicator range to equivalence point.

4. MISTAKE: Misreading burette. WHY IT HAPPENS: Reading from top instead of bottom of meniscus. CORRECT APPROACH: Always read at eye level, bottom of meniscus.

5. MISTAKE: Not rinsing pipette/burette. WHY IT HAPPENS: Contamination from previous solutions. CORRECT APPROACH: Rinse with solution to be used.

EXAM TRAPS

1. TRAP: Back titration with two different mole ratios. HOW TO SPOT IT: Two equations given (e.g., 1:1 and 1:2). HOW TO AVOID IT: Label each step clearly.

2. TRAP: Dilution before titration. HOW TO SPOT IT: "25 cm³ of solution was diluted to 250 cm³". HOW TO AVOID IT: Use c₁V₁ = c₂V₂ to find new concentration.

3. TRAP: pH curve with two equivalence points. HOW TO SPOT IT: Diprotic acid (e.g., H₂SO₄) or carbonate (CO₃²⁻). HOW TO AVOID IT: Identify all possible reactions.

1-MINUTE RECAP

"Here’s the night-before cheat sheet:
1. Direct titration: Write equation → find moles of known → use ratio → find unknown concentration.
2. Back titration: Two equations → find leftover moles → subtract → use ratio → find purity.
3. Indicators: Strong acid + strong base = pH 7 (any indicator). Weak acid + strong base = pH > 7 (phenolphthalein). Strong acid + weak base = pH < 7 (methyl orange).
4. pH curves: Sketch the jump—sharp for strong, gradual for weak.
5. Units: Always dm³ for volume in n = c × V. Now go ace that exam!"