Year 11 Chemistry Module 2 ⏱ ~40 min Lesson 10 of 20

Volumetric Analysis
& Titration

Every antacid tablet you've ever taken was tested by titration before it left the factory. Every blood pH reading, every wine acidity measurement, every batch of pharmaceutical drugs — titration is the technique that underpins quantitative chemistry in the real world. It's also the most commonly examined calculation type in NSW HSC Chemistry.

🧫
📐

The Titration Calculation Pathway

Known (standard)
c₁, V₁
n₁ = c₁ × V₁
Step 1
n(known)
mole ratio
Step 2
n(unknown)
c = n ÷ V₂
Answer
c₂ or m or %
⚠️ V must be in litres at all steps. The mole ratio comes from the balanced equation — don't skip it, even when it's 1:1.
📖 Know

Key Facts

  • Definitions: analyte, titrant, equivalence point, end point
  • Equipment: burette, pipette, volumetric flask, conical flask
  • Common indicators and their colour changes
  • The 4-step titration calculation method
💡 Understand

Concepts

  • Why a standard solution is needed as the titrant
  • Difference between equivalence point and end point
  • Why concordant titres are averaged
✅ Can Do

Skills

  • Describe the titration procedure with justifications
  • Apply the 4-step method to find concentration, mass, or purity
  • Calculate the average of concordant titres correctly

📚 Core Content

🧪

Key Terms and Equipment

Volumetric analysis (titration) determines the concentration of an unknown solution (the analyte) by reacting it with a solution of known concentration (the titrant). The titrant is added slowly from a burette until the reaction is exactly complete — this is the equivalence point.

Because you can't always see the equivalence point directly, an indicator is added — a chemical that changes colour near the equivalence point. The moment the colour change occurs is the end point. Ideally, the end point and equivalence point coincide.

01020304050
Burette
Contains titrant (standard solution). Read from top. Accurate to ±0.05 mL.
Pipette
Delivers exact volume of analyte to flask. Accurate to ±0.02 mL.
Conical Flask
Contains analyte + indicator. Swirled during titration.
EquipmentPurposeRead toWhy this piece?
Burette (50 mL)Delivers variable volumes of titrant with precision±0.05 mLOnly piece that can dispense continuously and be read mid-titration
Pipette (25 mL)Delivers a fixed, precise volume of analyte±0.02 mLMore accurate than measuring cylinder; delivers exact aliquot each time
Volumetric flaskPrepares standard solution to exact volume±0.1 mLNarrow neck allows precise reading of the calibration mark
Conical flaskHolds analyte during titrationNarrow neck prevents splashing; easy to swirl without spilling
White tilePlaced under conical flaskProvides contrast to see indicator colour change clearly

Indicators

Phenolphthalein

Acidic: colourless
Basic: pink/magenta
Range: pH 8.3–10.0
Use for strong acid–strong base or weak acid–strong base

Methyl Orange

Acidic: red/orange
Basic: yellow
Range: pH 3.1–4.4
Use for strong base–strong acid or weak base–strong acid

Universal Indicator

Acidic: red → orange
Basic: green → purple
Range: pH 1–14
Not precise — only for estimating pH, not for titrations

The Titration Procedure

1
Rinse and fill the burette with titrant
Rinse the burette with titrant solution (not water) before filling. Fill to just above the 0.00 mL mark, then drain to 0.00 mL, ensuring no air bubbles in the tip.
Why rinse with titrant: water left in the burette dilutes the titrant, changing its concentration and giving an incorrect result.
2
Pipette the analyte into a conical flask
Use a pipette to transfer the exact volume of analyte (e.g. 25.00 mL) into a clean conical flask. Rinse the pipette with analyte solution first.
Why rinse pipette: same reason — residual water changes the number of moles of analyte delivered.
3
Add indicator and perform a rough titration
Add 2–3 drops of indicator. Run a "rough" titration quickly to find the approximate end point volume. This rough titre is discarded.
Why rough first: gives a target so that subsequent accurate titrations can be slowed to drop-by-drop near the end point.
4
Perform accurate titrations until concordant
Run at least two, ideally three, accurate titrations. Add titrant drop-by-drop near the end point. Record the titre (volume added) for each run.
Why multiple runs: reduces the effect of random errors. Results within 0.10 mL of each other are "concordant".
5
Average the concordant titres
Calculate the mean of all concordant titres (those within 0.10 mL of each other). The rough titre is never included in this average.
Why average: reduces random error. More concordant readings = more reliable average.
Concordant titres: Two or more titres are concordant if they agree within 0.10 mL (some sources say 0.20 mL). Only concordant titres are averaged. If your first two accurate titres are 24.35 and 24.28 mL, they are concordant (difference = 0.07 mL) and you average them: (24.35 + 24.28) ÷ 2 = 24.32 mL.
🧮

The 4-Step Calculation Method

Every titration calculation, regardless of complexity, follows the same four steps. Memorise this sequence — it will never fail you.

Step 1: Calculate moles of the known/standard solution: n = c × V (V in litres)
Step 2: Use the mole ratio from the balanced equation to find moles of the unknown
Step 3: Calculate the concentration of the unknown: c = n ÷ V (V in litres)
Step 4: If required, convert to mass or percentage
The mole ratio is not always 1:1. For example, H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O gives a 1:2 ratio (1 mol H₂SO₄ reacts with 2 mol NaOH). If you assume 1:1 when it's 1:2, your answer will be exactly double the correct value. Always write the balanced equation first.

🧮 Worked Examples

Worked Example 1 — Finding concentration of NaOH (1:1 ratio)

Standard Titration
25.00 mL of NaOH solution is titrated against 0.1000 mol L⁻¹ HCl. Three concordant titres of 18.45, 18.50 and 18.48 mL are recorded. Calculate the concentration of the NaOH solution.
  1. 1
    Average the concordant titres and write equation
    V(HCl) = (18.45 + 18.50 + 18.48) ÷ 3 = 18.48 mL = 0.01848 L
    HCl + NaOH → NaCl + H₂O   (1:1 ratio)
  2. 2
    Step 1 — n(HCl) from standard solution
    n(HCl) = c × V = 0.1000 × 0.01848 = 1.848 × 10⁻³ mol
  3. 3
    Step 2 — mole ratio → n(NaOH)
    1 mol HCl : 1 mol NaOH
    n(NaOH) = 1.848 × 10⁻³ mol
  4. 4
    Step 3 — c(NaOH)
    V(NaOH) = 25.00 mL = 0.02500 L
    c(NaOH) = 1.848 × 10⁻³ ÷ 0.02500 = 0.07392 mol L⁻¹
✓ Answerc(NaOH) = 0.0739 mol L⁻¹

Worked Example 2 — Non-1:1 ratio: H₂SO₄ vs NaOH

Non-trivial Ratio
20.00 mL of 0.2500 mol L⁻¹ NaOH is titrated against H₂SO₄ solution. The average titre is 12.50 mL. Calculate the concentration of H₂SO₄.
  1. 1
    Write equation — identify mole ratio carefully
    H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O
    Mole ratio: 1 mol H₂SO₄ : 2 mol NaOH
  2. 2
    Step 1 — n(NaOH) from standard
    n(NaOH) = 0.2500 × 0.02000 = 5.000 × 10⁻³ mol
  3. 3
    Step 2 — mole ratio → n(H₂SO₄)
    n(H₂SO₄) = n(NaOH) × (1/2) = 5.000 × 10⁻³ ÷ 2 = 2.500 × 10⁻³ mol
    ⚠️ Divide by 2 — the ratio is 1:2, not 1:1
  4. 4
    Step 3 — c(H₂SO₄)
    V(H₂SO₄) = 12.50 mL = 0.01250 L
    c(H₂SO₄) = 2.500 × 10⁻³ ÷ 0.01250 = 0.2000 mol L⁻¹
✓ Answerc(H₂SO₄) = 0.2000 mol L⁻¹

Worked Example 3 — Finding mass and purity from titration

Multi-Step Applied
An antacid tablet is dissolved and made up to 250.0 mL. A 25.00 mL aliquot is titrated against 0.1000 mol L⁻¹ HCl. The average titre is 22.40 mL. The active ingredient is Mg(OH)₂. Calculate (a) the moles of Mg(OH)₂ in the aliquot, (b) the mass of Mg(OH)₂ in the whole tablet, and (c) the % purity if the tablet mass is 1.500 g. (Mg = 24.305, O = 15.999, H = 1.008)
  1. 1
    Equation and ratio
    Mg(OH)₂ + 2HCl → MgCl₂ + 2H₂O
    Ratio: 1 mol Mg(OH)₂ : 2 mol HCl
  2. 2
    n(HCl) used in titration
    n(HCl) = 0.1000 × 0.02240 = 2.240 × 10⁻³ mol
  3. 3
    (a) n(Mg(OH)₂) in 25 mL aliquot
    n(Mg(OH)₂) = 2.240 × 10⁻³ ÷ 2 = 1.120 × 10⁻³ mol
  4. 4
    (b) Scale up to whole tablet — 250 mL total
    n(Mg(OH)₂) whole = 1.120 × 10⁻³ × (250.0 ÷ 25.00) = 1.120 × 10⁻² mol
    MM(Mg(OH)₂) = 24.305 + 2(15.999 + 1.008) = 58.320 g mol⁻¹
    m = 1.120 × 10⁻² × 58.320 = 0.6532 g
  5. 5
    (c) Percentage purity
    % purity = (0.6532 ÷ 1.500) × 100 = 43.5%
✓ Answer(a) 1.12 × 10⁻³ mol  |  (b) 0.653 g  |  (c) 43.5%
⚠️

Common Mistakes

Assuming 1:1 mole ratio without checking
H₂SO₄ reacts with 2 NaOH. H₃PO₄ reacts with 3 NaOH. Na₂CO₃ reacts with 2 HCl. If you blindly apply 1:1, you will get answers that are exactly 2× or 3× off — a classic sign of this error.
✓ Fix: Write the balanced equation before every titration calculation. Circle the coefficients. Write "ratio: X:Y" explicitly.
Forgetting to convert mL to L
With two volumes in a titration problem (burette volume and pipette volume), there are two opportunities to forget the conversion. Students often convert one but not the other.
✓ Fix: Convert both volumes immediately after reading them. Write V₁ = ___ mL = ___ L and V₂ = ___ mL = ___ L as two separate lines before substituting anything.
Including the rough titre in the average
The rough titre is always larger than accurate titres (you overshoot intentionally). Including it inflates the average and gives too high a titre, leading to too low a calculated concentration.
✓ Fix: Identify concordant titres first (within 0.10 mL of each other). Average only those. Never include the rough titre.
Using the wrong volume when scaling up
When a tablet is dissolved in 250 mL and a 25 mL aliquot is titrated, the titration gives results for just that aliquot. To find the total in the tablet, multiply moles by (250÷25) = 10. Students often forget this scaling step.
✓ Fix: After finding n in the aliquot, always ask: "Was the whole sample titrated, or just a portion?" If a portion, scale up: n(total) = n(aliquot) × (total volume ÷ aliquot volume).

📓 Copy Into Your Books

📖 Key Terms

  • Analyte: unknown solution in flask
  • Titrant: standard solution in burette
  • Equivalence point: stoichiometric completion
  • End point: indicator colour change
  • Concordant: titres within 0.10 mL

🧮 4-Step Calculation

  • 1. n(known) = c × V (V in L)
  • 2. n(unknown) = n(known) × mole ratio
  • 3. c(unknown) = n ÷ V (V in L)
  • 4. Convert to mass or % if needed

🎨 Indicators

  • Phenolphthalein: colourless → pink (pH 8.3–10)
  • Methyl orange: red → yellow (pH 3.1–4.4)
  • Strong acid + strong base: either indicator
  • Weak acid + strong base: phenolphthalein

⚠️ Key Habits

  • Rinse burette with titrant, pipette with analyte
  • Always write balanced equation + ratio
  • Both volumes → convert to L immediately
  • Scale up if only aliquot was titrated
  • Never include rough titre in average

📝 How are you completing this lesson?

🧪 Activities

📊 Activity 1 — Titration Calculation Drill

The 4-Step Method in Action

Four problems with increasing complexity. Write out all four steps before revealing each answer.

  1. 1 25.00 mL of NaOH is titrated against 0.0500 mol L⁻¹ HCl. The concordant titres are 20.10 mL and 20.15 mL. Calculate c(NaOH).
    HCl + NaOH → NaCl + H₂O

    V(HCl) = (20.10 + 20.15) ÷ 2 = 20.13 mL = 0.02013 Ln(HCl) = 0.0500 × 0.02013 = 1.007 × 10⁻³ moln(NaOH) = 1.007 × 10⁻³ mol (1:1)c(NaOH) = 1.007 × 10⁻³ ÷ 0.02500 = 0.0402 mol L⁻¹
  2. 2 20.00 mL of Na₂CO₃ (0.1500 mol L⁻¹) is titrated against HCl. The average titre is 30.00 mL. Calculate c(HCl).
    Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂

    n(Na₂CO₃) = 0.1500 × 0.02000 = 3.000 × 10⁻³ moln(HCl) = 3.000 × 10⁻³ × 2 = 6.000 × 10⁻³ mol (1:2 ratio)c(HCl) = 6.000 × 10⁻³ ÷ 0.03000 = 0.2000 mol L⁻¹
  3. 3 25.00 mL of H₂SO₄ is titrated against 0.1200 mol L⁻¹ NaOH, using an average titre of 24.00 mL. Calculate c(H₂SO₄).
    H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O

    n(NaOH) = 0.1200 × 0.02400 = 2.880 × 10⁻³ moln(H₂SO₄) = 2.880 × 10⁻³ ÷ 2 = 1.440 × 10⁻³ molc(H₂SO₄) = 1.440 × 10⁻³ ÷ 0.02500 = 0.0576 mol L⁻¹
  4. 4 A vinegar sample is diluted to 100.0 mL. A 20.00 mL aliquot is titrated against 0.1000 mol L⁻¹ NaOH. The average titre is 16.80 mL. Calculate the mass of acetic acid (CH₃COOH) in the original 100 mL sample. (MM = 60.05 g mol⁻¹)
    CH₃COOH + NaOH → CH₃COONa + H₂O

    n(NaOH) = 0.1000 × 0.01680 = 1.680 × 10⁻³ mol = n(CH₃COOH) in aliquotn(total) = 1.680 × 10⁻³ × (100.0 ÷ 20.00) = 8.400 × 10⁻³ molm = 8.400 × 10⁻³ × 60.05 = 0.5044 g

Show full 4-step working for each problem:

Complete in your workbook.

✏️ Complete all 4 steps per problem in your workbook

❓ Multiple Choice

🎯

Test Your Knowledge

1. Why is the burette rinsed with titrant solution before filling?

A
To sterilise the burette for safety
B
To prevent the titrant from being diluted by residual water
C
To increase the reaction rate during titration
D
To lubricate the burette stopcock

2. In a titration, 25.00 mL of 0.200 mol L⁻¹ NaOH reacts with HCl. The average titre is 20.00 mL. Using HCl + NaOH → NaCl + H₂O, what is c(HCl)?

A
0.160 mol L⁻¹
B
0.200 mol L⁻¹
C
0.250 mol L⁻¹
D
0.400 mol L⁻¹

3. What is the difference between the equivalence point and the end point?

A
The equivalence point is when stoichiometrically equal amounts have reacted; the end point is the indicator colour change
B
The equivalence point is when the indicator changes colour; the end point is when the solution reaches pH 7
C
They are the same — both refer to when neutralisation is complete
D
The end point comes before the equivalence point in every titration

4. Titres of 24.50 mL (rough), 23.80 mL, 23.75 mL, and 23.82 mL are recorded. What volume should be used for calculations?

A
23.97 mL (mean of all four)
B
23.80 mL (first accurate titre)
C
23.79 mL (mean of three accurate titres)
D
23.79 mL (mean of the three concordant accurate titres)

5. In the reaction H₂SO₄ + 2KOH → K₂SO₄ + 2H₂O, if 0.0100 mol of H₂SO₄ reacts, how many moles of KOH are needed?

A
0.0050 mol
B
0.0200 mol
C
0.0100 mol
D
0.0400 mol

✍️ Short Answer

📝

Extended Questions

6. A student titrates 25.00 mL of a Na₂CO₃ solution against 0.1000 mol L⁻¹ HCl, using methyl orange as an indicator. The titration results are: rough = 26.50 mL, accurate = 25.30 mL, 25.25 mL, 25.80 mL. (a) Select the concordant titres and calculate the average. (b) Calculate c(Na₂CO₃). Equation: Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂. 5 MARKS

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Answer in workbook.

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7. A student dissolves a sample of impure oxalic acid (H₂C₂O₄) in water and makes up to 250.0 mL. A 25.00 mL aliquot is titrated against 0.1000 mol L⁻¹ NaOH. The average titre is 18.60 mL. Equation: H₂C₂O₄ + 2NaOH → Na₂C₂O₄ + 2H₂O. (a) Calculate the moles of H₂C₂O₄ in the aliquot. (b) Calculate the mass of H₂C₂O₄ in the original 250 mL solution. (c) If the original sample had a mass of 0.400 g, calculate the percentage purity. (MM of H₂C₂O₄ = 90.03 g mol⁻¹) 6 MARKS

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✅ Comprehensive Answers

❓ Multiple Choice

1. B — Residual water in the burette dilutes the titrant, reducing its concentration and causing more to be used than expected — making the unknown appear more concentrated than it is.

2. C — n(NaOH) = 0.200 × 0.02500 = 5.00 × 10⁻³ mol. 1:1 ratio → n(HCl) = 5.00 × 10⁻³. c(HCl) = 5.00 × 10⁻³ ÷ 0.02000 = 0.250 mol L⁻¹.

3. A — The equivalence point is a stoichiometric concept (equal moles reacted); the end point is an experimental observation (indicator colour change). A good indicator choice makes them nearly coincide.

4. D — Rough titre (24.50) excluded. Accurate titres: 23.80, 23.75, 23.82. Check concordance: 23.82 − 23.75 = 0.07 ✓. Average = (23.80 + 23.75 + 23.82) ÷ 3 = 23.79 mL.

5. B — The ratio is 1:2 (H₂SO₄:KOH), so 0.0100 × 2 = 0.0200 mol KOH.

📝 Short Answer Model Answers

Q6 (5 marks):

(a) Concordant: 25.30 and 25.25 mL (diff = 0.05 mL ✓). 25.80 excluded (diff from 25.30 = 0.50 mL ✗). Average = (25.30 + 25.25) ÷ 2 = 25.28 mL = 0.02528 L (b) n(HCl) = 0.1000 × 0.02528 = 2.528 × 10⁻³ mol n(Na₂CO₃) = 2.528 × 10⁻³ ÷ 2 = 1.264 × 10⁻³ mol c(Na₂CO₃) = 1.264 × 10⁻³ ÷ 0.02500 = 0.05056 mol L⁻¹ ≈ 0.0506 mol L⁻¹

Q7 (6 marks):

(a) n(NaOH) = 0.1000 × 0.01860 = 1.860 × 10⁻³ mol n(H₂C₂O₄) in aliquot = 1.860 × 10⁻³ ÷ 2 = 9.300 × 10⁻⁴ mol (b) n(total) = 9.300 × 10⁻⁴ × (250.0 ÷ 25.00) = 9.300 × 10⁻³ mol m = 9.300 × 10⁻³ × 90.03 = 0.8373 g (c) % purity = (0.8373 ÷ 0.400) × 100 = 209%

Note: A purity >100% is physically impossible and indicates an error in the given data (sample mass too small, or titre too large). In an exam, present the calculation correctly and note the anomaly.

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Tick when you've finished all activities and checked your answers.

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