IB Chemistry · Unit 3 · Foundations

Doing
the chemistry.

The lab is where chemistry is. Measurements, errors, uncertainty, and the practical work that anchors every concept in this course.

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Unit 3 · Standard & Higher Level

5 lessons to work through.

The required syllabus content for Unit 3, in order. Each card is one lesson-sized checkpoint.

Lesson 1-2

Accuracy vs Precision

Whilst we integrate Tools and Inquiry throughout the course, we have selected a few areas to focus in more

Lesson 3-4

Accounting for accuracy – Systematic Errors and case studies

Lesson 3-4 of Unit 3.

Lesson 5

Writing Scientifically

Lesson 5 of Unit 3.

Lesson 6

Graphing Techniques

Lesson 6 of Unit 3.

Lesson 7-8

Putting it all together

Lesson 7-8 of Unit 3.

Lessons in detail

The unit, lesson by lesson.

Each lesson card below mirrors the original teacher deck — syllabus refs, content, worked examples and practice questions in order.

Lesson 1-2

Accuracy vs precision · uncertainty in measurement

Tool 1Tool 3

Lesson outcomes

Precision is the closeness of agreement between repeated measurements of the same quantity under the same conditions. Accuracy is how close a measurement is to the true (literature) value. The two are independent — you can have one without the other.

Reading uncertainty

Analogue instruments (burette, pipette, measuring cylinder, ruler, gas syringe): if no uncertainty is quoted on the equipment, take half the smallest scale division. Example: a measuring cylinder with 2 cm³ divisions, measuring 60 cm³ → quote 60 ± 1 cm³.

Digital instruments (top-pan balance, voltmeter, drop counter, colourimeter): uncertainty = ± the smallest displayed digit. Example: balance reads 100.00 g → quote 100.00 ± 0.01 g.

Three flavours of uncertainty

Propagating uncertainties

+ or −: add the absolute uncertainties.
× or ÷: add the percentage uncertainties.
Power xn: multiply the percentage uncertainty by n.

Rounding rule: quote the final uncertainty to 1 s.f. if > 2% of the value, 2 s.f. otherwise. Do not round intermediate calculations.

Worked example

Uncertainty in stopwatch sprint time

Problem. A stopwatch has scale division 0.01 s. You time a 100 m sprint and read 12 s. What is the total uncertainty in your value?
Solution. Stopwatch instrument: ±0.01 s. But you are part of the apparatus — average human reaction time uncertainty ≈ ±0.3 s, applied at both the start and the stop of the timing.
Total = 0.3 + 0.3 + 0.01 = ±0.61 s, rounded up to ±0.7 s. Always round uncertainty up.
This means a 2 s reaction timed by stopwatch has 35% uncertainty — far too high. Choose a non-stopwatch method for short reactions.
Worked example

Percentage error from a density experiment

Problem. An experiment gives a density of 1.017 g cm⁻³; the literature value is 1.011 g cm⁻³. Calculate the percentage error.
Solution. % error = |1.011 − 1.017| / 1.011 × 100 = (0.006 / 1.011) × 100 = 0.5935% → 0.6% (1 s.f.).

Try these

  1. Define precision in your own words. Define accuracy.
    Show answer
    Precision: the closeness of agreement between repeated measurements of the same quantity under the same conditions. High precision = small random scatter. Accuracy: closeness of a result to the true (literature/accepted) value. High accuracy = small systematic error.
  2. Why is the kilogram now defined using Planck's constant rather than the physical 'standard kilogram' cylinder kept in Paris?
    Show answer
    The physical standard was found to be slowly losing mass (~50 µg per century) due to surface contamination. Redefining via a fundamental physical constant (Planck's constant, h = 6.62607015 × 10⁻³⁴ J·s) gives a permanent, reproducible definition independent of any physical artefact.
  3. A standard kilogram is placed on two balances: digital reads 1.01 kg, analogue reads 1.1 kg. Which is more accurate?
    Show answer
    Digital (1.01 kg). It's closer to the true value of 1.00 kg. The analogue at 1.1 kg has a larger systematic error.
  4. 150 mL of water (measured by a calibrated tool) is transferred into two pieces of glassware. Apparatus A reads 200 cm³; apparatus B reads 150 cm³. Which is more accurate?
    Show answer
    Apparatus B (150 cm³) — agrees with the calibrated reference, so it's accurate. Apparatus A is inaccurate (50 cm³ off).
  5. A standardised pH 1 solution is tested with universal indicator (turns red, indicating pH 1) and a pH probe (reads 4). Which is more accurate?
    Show answer
    Universal indicator is more accurate here — it agrees with the calibrated reference. The pH probe is off by 3 units (probably needs recalibration).
  6. State the uncertainty of: (a) a digital top-pan balance, (b) a 50 cm³ glass measuring cylinder, (c) a 25 cm³ glass pipette, (d) a 50 cm³ burette, (e) a 100 cm³ volumetric flask.
    Show answer
    Typical values: (a) ±0.01 g (or ±0.001 g for analytical). (b) ±0.5 cm³. (c) ±0.06 cm³ (Class B). (d) ±0.05 cm³ per reading (but a single titre uses two readings → ±0.10 cm³ total). (e) ±0.1 cm³.
  7. Which apparatus introduces more random error — a 50 cm³ measuring cylinder or a 25 cm³ pipette? Why?
    Show answer
    The measuring cylinder has the larger uncertainty (only goes to 1 cm³ divisions, so ±0.5 cm³) → larger range of readings → less precise. Pipette has uncertainty of ±0.06 cm³ → much more precise.
  8. What is meant by 'absolute', 'fractional', and 'percentage' uncertainty? When is each used?
    Show answer
    Absolute: has units (e.g. ±0.05 cm³). Used when adding/subtracting quantities with the same units. Fractional: unitless (absolute/value). Percentage: fractional × 100. Used when multiplying/dividing quantities (perhaps with different units) — percentage uncertainties add.
  9. What is the 'rule of thumb' for how many significant figures to use when quoting a calculated uncertainty?
    Show answer
    If the calculated uncertainty is >2% of the answer: quote to no more than 1 s.f. If <2% of the answer: quote to no more than 2 s.f. Always round up (overestimate is safer than underestimate).
  10. Why does measuring out 100 cm³ with a pipette give a lower uncertainty than with a measuring cylinder?
    Show answer
    Pipettes have finer scale divisions and are calibrated to deliver a specific volume — uncertainty is fixed at ±0.06 cm³. A measuring cylinder at 100 cm³ might be ±1 cm³ (1% vs 0.06%).
  11. Which contributes more to error in a small titre — random error or the fixed burette uncertainty? Explain.
    Show answer
    The fixed ±0.10 cm³ becomes a much larger percentage uncertainty for a small titre (e.g. ±0.10/2.50 = 4%) than for a large one (±0.10/25.0 = 0.4%). Always design titrations to give titres of 20–30 cm³.
Lesson 3-4

Systematic errors · accuracy case studies

Tool 1Tool 3Inquiry 3

Lesson outcomes

Random errors are unpredictable fluctuations about the true value. Reduce by repeating measurements and averaging concordant results.

Systematic errors bias every result in the same direction. Repetition does not reduce them — only redesigning the method does. Common causes:

Percentage error vs percentage uncertainty

% error tells you how accurate you were (vs literature). % uncertainty tells you how precise you were (vs your equipment). Both should be calculated and compared in an IA evaluation.

Worked example

Case study · small titre

Problem. A student measures a titre of 2.50 ± 0.10 cm³ on a 50 cm³ burette. Calculate the % uncertainty in this titre. Then propose two ways to lower it.
Solution. % uncertainty = (0.10 / 2.50) × 100 = 4%.
For comparison, the same ±0.10 cm³ on a 25.00 cm³ titre = 0.4% — ten times better.
Improvements: (1) dilute the strong acid so a larger titre is needed (lower % uncertainty); (2) use a smaller burette with finer divisions for very small titres.
Worked example

Case study · calorimetry

Problem. A neutralisation experiment uses a thermometer with 0.5 °C divisions. The student records ΔT = 7.5 °C. Calculate the % uncertainty in ΔT and suggest improvements.
Solution. Single reading uncertainty = ±0.25 °C. ΔT involves two readings, so absolute uncertainty doubles: ±0.5 °C.
% uncertainty = (0.5 / 7.5) × 100 = 6.7%.
Improvements: use a digital thermometer (smaller scale), maximise ΔT by using more concentrated solutions, insulate the calorimeter (reduces heat loss = systematic error).

Try these

  1. Classify each as random or systematic: (a) parallax in reading a burette, (b) timing the start of a reaction late by 0.3 s every trial, (c) room temperature fluctuating by ±0.5 °C, (d) using an uncalibrated pH probe.
    Show answer
    (a) Random (different parallax each time). (b) Systematic (always late by the same amount). (c) Random. (d) Systematic.
  2. What ways can we reduce random error in an experiment?
    Show answer
    (1) Repeat measurements at least 3 times and average. (2) Use a range of at least 5 different conditions/values when establishing a relationship. (3) Use more precise apparatus (smaller scale divisions). (4) Use digital sensors / data loggers.
  3. Suggest three sources of systematic error in laboratory experiments.
    Show answer
    Physical errors in the equipment — leaking gas syringe, air bubble in thermometer, dropped equipment. Improper use — parallax, wrong scale (e.g. F vs C), not zeroing balance, not calibrating before use. Ambient conditions — temperature drift, evaporation, draughts.
  4. Why does repeating an experiment not reduce a systematic error?
    Show answer
    Systematic errors bias every measurement in the same direction by the same amount. Averaging biased results just gives a biased average. Only changing the apparatus, method or calibration fixes them.
  5. In the disappearing-cross experiment, why might a stopwatch be a poor choice for very fast reactions? Calculate the % uncertainty for a 2 s reaction.
    Show answer
    Human reaction time gives a fixed uncertainty of about ±0.7 s. For a 2 s reaction: % uncertainty = 0.7/2 × 100 = 35% — unusable. For an 8 s reaction it's ~9%, borderline. Longer reactions or non-stopwatch methods (colorimeter) are needed.
  6. Case study (small titre): A 2.50 ± 0.10 cm³ titre. Calculate the % uncertainty. Then suggest two specific improvements.
    Show answer
    % u = 0.10/2.50 × 100 = 4%. Improvements: (1) Dilute the strong acid 10× so a 25 cm³ titre is needed (% u drops to 0.4%). (2) Use a smaller burette (10 cm³ with 0.02 cm³ divisions) for very small titres.
  7. Case study (calorimetry): A thermometer reads to ±0.5 °C. Recorded ΔT = 7.5 °C. Calculate the % uncertainty in ΔT.
    Show answer
    ΔT involves two readings (Tfinal − Tinitial), so absolute uncertainty = 0.5 + 0.5 = ±1.0 °C. % u = 1.0/7.5 × 100 = 13%. (Note: previous slides quoted ±0.5 °C total, giving 6.7%. The exact rule depends on whether the thermometer's stated ±0.5 °C is per reading or for the difference.)
  8. Case study (mass): Mass of Mg ribbon on a balance reading ±0.01 g. Sample mass 0.50 g. Calculate % uncertainty. What other systematic errors might affect the measured mass of Mg?
    Show answer
    % u = 0.01/0.50 × 100 = 2%. Systematic errors: Mg is hygroscopic (absorbs water → mass too high). Mg surface oxidises (mass too high; some product not pure Mg). Mg ribbon may have impurities. Static electricity affects balance. Forgetting to tare or using different balances between trials.
  9. An experiment gives density 1.017 g/cm³; the literature value is 1.011 g/cm³. Calculate the percentage error.
    Show answer
    % error = |1.011 − 1.017|/1.011 × 100 = 0.5935% → 0.6% (1 s.f.).
  10. After calculating the % error and % uncertainty for an experiment, you find both are similar (≈1%). What does this tell you about your experiment?
    Show answer
    Random and systematic errors are of similar magnitude. The result is approximately as accurate as it is precise. Further improvement requires addressing both error types — better equipment for random; method change for systematic.
Lesson 5

Writing scientifically

Inquiry 2Inquiry 3

Lesson outcomes

Scientific writing prioritises reproducibility, precision and clarity. Methods should be detailed enough that another chemist could repeat your experiment and get the same result.

Three principles

IA format vs journal format

A journal article writes the methodology as a single dense paragraph. For the IB IA you should break it into numbered steps with sub-headings, so a marker can follow the procedure visually. Same words, different layout.

Worked example

Rewriting a methodology for IA

Problem. Rewrite the journal-style line: 'Sodium dichromate (10.02 g, 33.06 mmol) was dissolved in deionised water (30 cm³). Concentrated sulfuric acid (7.4 cm³, 95-98%) was added dropwise.' in IA format.
Solution. Step 1 · Prepare the oxidising solution
1. Weigh 10.02 g (33.06 mmol) of sodium dichromate using a top-pan balance and transfer to a 100 cm³ conical flask.
2. Add 30 cm³ of deionised water and swirl until fully dissolved.
3. Using a measuring cylinder, slowly add 7.4 cm³ of concentrated sulfuric acid (95–98%) dropwise while swirling.
4. Add an additional 12.6 cm³ deionised water to bring the total volume to 50 cm³. The solution should be bright orange.

Try these

  1. What are the three principles of good scientific writing?
    Show answer
    (1) Logical flow / sequencing — ideas in a meaningful order. (2) SI units — never 'a pinch', always 5.7 g. (3) Third person, past tense — 'the flask was heated', not 'I heated' or 'heat the flask'.
  2. Why do scientific reports use the past tense rather than the imperative ('do this', 'do that')?
    Show answer
    Past tense documents what was done in a specific experiment. The imperative reads like a recipe — fine for a textbook protocol, but a report is a record. Past tense also makes it clear that the author has actually done the work.
  3. Why do scientific methods use third person (the experimenter / the flask) rather than first person ('I')?
    Show answer
    Third person emphasises objectivity and reproducibility. It directs attention to the experiment, not the experimenter. By convention, journal articles and IA reports do this universally.
  4. Why must methodologies have specific quantities and units rather than vague terms like 'a small amount' or 'until thick'?
    Show answer
    Reproducibility. A reader must be able to replicate your experiment and get the same result. 'A pinch' or 'until thick' are subjective and lead to different outcomes; '5.7 g' or 'until the solution boils' are precise and reproducible.
Lesson 6

Graphing techniques

Tool 3Inquiry 2

Lesson outcomes

A good graph turns raw numbers into a relationship at a glance. Six things every graph must have:

  1. Title describing the relationship being shown.
  2. Labelled axes with quantity name and units.
  3. Sensible scale filling at least half of each axis.
  4. Plotted points as sharp dots or crosses with error bars.
  5. Line of best fit — balance scatter; do not force through origin unless physics demands it.
  6. Equation of the line and R² value (digital plot).

Reading relationships

Directly proportional: straight line through origin. y = kx.
Linear (offset): straight line not through origin. y = mx + c.
Inversely proportional: y = k/x. Plot y vs 1/x to linearise.

Gradient with uncertainty

Draw two reasonable extreme lines through the error bars — the steepest and shallowest that still pass through them. The gradient is the best-fit line value; the uncertainty in the gradient = half the difference between the extreme gradients.

Worked example

Moles with propagated uncertainty

Problem. [HCl] = 1.00 ± 0.05 mol dm⁻³ and V = 10.0 ± 0.1 cm³. Calculate the moles of HCl with absolute uncertainty.
Solution. n = c × V = 1.00 × 0.0100 = 0.0100 mol.
% uncertainty in c = 0.05/1.00 × 100 = 5%.
% uncertainty in V = 0.1/10.0 × 100 = 1%.
% uncertainty in n = 5 + 1 = 6%.
Absolute uncertainty = 6% of 0.0100 = 0.0006 → n = 0.0100 ± 0.0006 mol (or 1.00 ± 0.06 × 10⁻²).

Try these

  1. Starter: [HCl] = 1.00 ± 0.05 mol dm⁻³ and V = 10.0 ± 0.1 cm³. Calculate the moles and the absolute uncertainty.
    Show answer
    n = c × V = 1.00 × 0.0100 = 0.0100 mol. % u(c) = 5%; % u(V) = 1%; % u(n) = 5 + 1 = 6%. Absolute u = 6% × 0.0100 = 0.0006 mol. n = 0.0100 ± 0.0006 mol.
  2. List six features that a good graph must have.
    Show answer
    (1) Descriptive title. (2) Both axes labelled with quantity name and units. (3) Sensible scale (data fills ≥ half of each axis). (4) Sharp plotted points with error bars. (5) Line of best fit (balances scatter; doesn't force through origin without theoretical reason). (6) Equation and R² value (digital plot).
  3. What is the difference between a directly proportional and an inversely proportional relationship? How would each plot?
    Show answer
    Directly proportional: y ∝ x. Straight line through the origin. Inversely proportional: y ∝ 1/x. Hyperbolic curve. To linearise, plot y vs 1/x — gives a straight line.
  4. Why should the line of best fit not be forced through the origin unless physics demands it?
    Show answer
    If the data has a non-zero intercept, forcing through the origin distorts the gradient and discards information. Only force through if the relationship is theoretically known to be directly proportional (e.g. Beer-Lambert at low concentration).
  5. When is extrapolation justified, and when is it dangerous?
    Show answer
    Justified when the underlying relationship is firmly established and unlikely to change beyond the measured range (e.g. Charles's law for an ideal gas). Dangerous when the system might change behaviour outside the measured range (e.g. a real gas near condensation, an enzyme above 60 °C).
  6. How do you calculate the gradient with uncertainty from a graph with error bars?
    Show answer
    Draw two extreme lines of best fit — the steepest reasonable line and the shallowest reasonable line — both still passing through the error bars. Calculate the gradient of each. The mean is the best-fit gradient; half the difference is the uncertainty in the gradient.
  7. Why is interpolation generally more reliable than extrapolation?
    Show answer
    Interpolation uses values within the measured range, so the data trend is already established. Extrapolation extends beyond the measured range, where the trend may change or break down (e.g. ideal gas behaviour failing near condensation).
Lesson 7-8

Putting it all together · the IA

Inquiry 1Inquiry 2Inquiry 3

Lesson outcomes

The IA (Internal Assessment) is a 10-hour, 24-mark investigation worth 20% of your final IB chemistry grade. It is student-designed, student-executed and student-analysed. The five marking criteria:

CriterionWhat it coversMarks
Research designClear, focused RQ. Justified method. Identified variables.6
Data analysisProcessed data; propagated uncertainties; well-presented graphs.6
ConclusionJustified by data. Compared to literature. % error.6
EvaluationHonest discussion of method weaknesses and realistic improvements.6

Total: 24 marks over typically a 6-12 page report.

Tips drawn from this unit's case studies

Try these

  1. What are the five IA marking criteria? Briefly describe each.
    Show answer
    (1) Research design — focused RQ, justified method, identified IV/DV/controlled variables. (2) Data analysis — processing data, propagating uncertainties, graphs. (3) Conclusion — justified by data, linked to scientific context, includes % error. (4) Evaluation — honest discussion of weaknesses, realistic improvements. (5) Communication — focused, well-structured, correct conventions.
  2. Why must each measured value in an IA have % uncertainty < 5%? If not, what should you change?
    Show answer
    If % u > 5% per value, propagated through calculations gives a final % u that swamps any meaningful conclusion. Address by: using more precise apparatus, increasing the size of the measured quantity (e.g. larger titre), or repeating measurements to average.
  3. Suggest three specific improvements to the disappearing-cross experiment that would address both random and systematic errors.
    Show answer
    Random: Replace stopwatch with a colorimeter measuring transmittance over time (no human reaction time). Repeat each trial 3+ times for averaging. Systematic: Control temperature with a water bath (T affects rate). Use the same observer / fixed cross-viewing angle (makes bias at least reproducible).
  4. Why is a research question like 'How does temperature affect reaction rate?' too broad for an IA?
    Show answer
    It doesn't specify: which reaction, what temperature range, how rate is measured, what is held constant. A focused version: 'How does the temperature (30–70 °C, ±0.5 °C) affect the initial rate of reaction between 0.5 mol dm⁻³ sodium thiosulfate and 1.0 mol dm⁻³ HCl, measured by the disappearing-cross method?'
  5. Distinguish independent, dependent, and controlled variables in the example: 'How does HCl concentration (0.1–1.0 M) affect the rate of reaction with marble chips?'
    Show answer
    IV: HCl concentration. DV: rate of reaction (e.g. rate of CO₂ production). Controlled: mass and surface area of marble; volume of acid; temperature; stirring; total reaction time observed.
  6. Why is 'human error' not an acceptable evaluation point in an IA?
    Show answer
    Too vague. 'Human error' covers everything from parallax to forgetting to tare the balance — it doesn't identify a specific source or suggest a fix. A good evaluation point names a specific source (e.g. 'parallax in reading the burette'), classifies it (random/systematic), and proposes a realistic improvement.
Vocabulary

42 terms to own.

If you can't define one of these in a sentence, that's where to revise next. Click any term for its definition.

mixturedistillationchromatographymoleconcentrationsolutesolutiondilutiontitrationprecisionaccuracyrandom errorsystematic erroruncertaintypercentage uncertaintysignificant figuresgraphline of best fitgradientinterceptcalibration curveinternal assessmentindependent variabledependent variablerate of reactionpressuretemperatureintermediateenthalpy changecalorimetryperiodgrouplinearadditionpropagationterminationoxidationacidbasephindicatorendpoint