Uncertainty analysis in the Chemistry IA means identifying the limits of measured data, propagating those limits through calculations, and explaining how they affect the conclusion. A strong investigation does not merely attach ± values to a table. It uses uncertainty to judge precision, compare results, interpret graphs, and propose justified improvements.
Under the current course, first assessed in 2025, the IA is officially called the scientific investigation. It contributes 20% of the final Chemistry grade and is assessed through Research design, Data analysis, Conclusion, and Evaluation, each worth six marks. The Data analysis criterion expects uncertainty treatment to be appropriate and consistent with the methodology, rather than following a universal checklist for every experiment.
What uncertainty means in a Chemistry IA
A measurement such as 25.00 ± 0.03 cm³ communicates both a measured value and a plausible range. Here, the volume is reported as 25.00 cm³, while the actual value is expected to lie within the stated uncertainty under the assumptions used.
Uncertainty is not the same as a mistake. It describes the unavoidable limitation of measurement. An error, in scientific usage, is the difference between a measured value and the true or accepted value, although the true value is often unknown.
| Concept | Meaning | Typical IA treatment |
|---|---|---|
| Random error | Unpredictable variation that moves results above and below a central value | Repeat trials, calculate a mean, examine spread |
| Systematic error | A consistent bias that shifts results in one direction | Identify its source and improve calibration or method |
| Absolute uncertainty | Uncertainty expressed in the same unit as the measurement | Report as value ± uncertainty |
| Percentage uncertainty | Uncertainty relative to the size of the measurement | Use when comparing precision or propagating products and quotients |
Repeating measurements can reduce the effect of random variation on a mean, but it does not remove systematic bias. For example, repeating a titration ten times will not correct a burette that is consistently miscalibrated.
Establishing absolute uncertainty
Use the manufacturer’s tolerance or calibration information when it is available. If no value is supplied, the current IB supporting material gives the common convention of using the smallest displayed increment for digital equipment and half the smallest scale division for an analogue reading.
Examples include:
- Digital balance reading to 0.01 g: commonly ±0.01 g, unless the manufacturer specifies otherwise.
- Analogue thermometer marked every 1 °C: commonly ±0.5 °C per reading.
- Volumetric pipette labelled 25.00 ± 0.03 cm³: use the printed ±0.03 cm³ tolerance.
- Burette reading with ±0.05 cm³ per reading: a titre calculated from two readings has ±0.10 cm³ under the conservative addition rule.
Place units and uncertainty in the table heading, such as Mass / g (±0.01 g). Record every value from the same instrument to consistent decimal places. The RevisionDojo guide to Chemistry IA data analysis provides additional table and graph examples.
Absolute versus percentage uncertainty
Absolute uncertainty gives the size of the uncertainty in the measurement’s original unit:
measured value ± absolute uncertainty
Percentage uncertainty describes its relative size:
percentage uncertainty = (absolute uncertainty ÷ measured value) × 100
Suppose a balance records 0.50 ± 0.01 g:
Percentage uncertainty = (0.01 ÷ 0.50) × 100 = 2%
For 10.00 ± 0.01 g, the percentage uncertainty is only 0.10%. Both measurements use the same balance, but the larger mass has a smaller relative uncertainty. This is why measuring larger quantities, where safe and practical, can improve the precision of an investigation.
Propagating uncertainty through calculations
The current IB Chemistry supporting material uses conservative propagation rules in which component uncertainties are added. Apply only the uncertainties belonging to measured quantities that actually influence the calculated result.
| Calculation | Practical propagation rule |
|---|---|
| Addition or subtraction | Add absolute uncertainties |
| Multiplication or division | Add percentage uncertainties |
| Quantity raised to a power, xⁿ | Multiply the percentage uncertainty by ** |
| Multiplication by an exact constant | Do not add uncertainty for the exact constant |
More advanced analytical chemistry sometimes combines independent uncertainties using a root-sum-square method. Do not switch methods without explanation. For an IB investigation, follow the convention taught by your course and apply it consistently, unless the statistical model of your investigation clearly justifies another approach.
Worked example 1: temperature change
A temperature change is calculated from two thermometer readings:
- Initial temperature = 20.4 ± 0.1 °C
- Final temperature = 27.8 ± 0.1 °C
The temperature change is:
ΔT = 27.8 - 20.4 = 7.4 °C
Because this is subtraction, add the absolute uncertainties:
uncertainty in ΔT = 0.1 + 0.1 = 0.2 °C
Report the result as ΔT = 7.4 ± 0.2 °C. Its percentage uncertainty is approximately 2.7%.
Worked example 2: titration concentration
Assume a 25.00 ± 0.03 cm³ sample is titrated with 0.1000 ± 0.0005 mol dm⁻³ solution. The titre is 18.60 ± 0.10 cm³, and the reacting mole ratio is 1:1.
c(sample) = (0.1000 × 18.60) ÷ 25.00 = 0.07440 mol dm⁻³
Calculate each percentage uncertainty:
- Standard concentration: (0.0005 ÷ 0.1000) × 100 = 0.50%
- Titre: (0.10 ÷ 18.60) × 100 = 0.54%
- Pipetted volume: (0.03 ÷ 25.00) × 100 = 0.12%
Total percentage uncertainty = 0.50 + 0.54 + 0.12 = 1.16%, reported as 1.2%. The absolute uncertainty is 0.07440 × 0.012 = 0.00089 mol dm⁻³, which rounds to 0.0009 mol dm⁻³. The final result is therefore 0.0744 ± 0.0009 mol dm⁻³.
Significant figures and decimal places
Do calculations using unrounded values, then round only the final result. Premature rounding can create avoidable differences, especially when several processing stages are involved.
A practical reporting sequence is:
- Calculate the final value and uncertainty using full calculator precision.
- If the final percentage uncertainty is 2% or greater, report it to one significant figure.
- If it is below 2%, report no more than two significant figures.
- Round the measured or calculated value to the same decimal place as its absolute uncertainty.
For example, 12.376 ± 0.428 g should not remain in that form. It would normally become 12.4 ± 0.4 g. Writing 12.376 ± 0.4 g falsely implies that the final digits are meaningful.
Error bars and what they show
Error bars, also called uncertainty bars, show the upper and lower range associated with each plotted point. They may be applied to the x-axis, y-axis, or both, depending on which variables have meaningful uncertainties.
The value used for an error bar must be identified. It might represent:
- propagated instrumental uncertainty in a calculated value
- standard deviation from repeated trials
- half the range of repeats, if justified
- another confidence or uncertainty interval appropriate to the method
These quantities are not interchangeable. Instrument uncertainty describes measurement resolution, while standard deviation describes observed variation among repeats. A graph caption should state what the bars represent.
Substantial overlap may suggest that an apparent difference is not clearly resolved by the precision of the experiment, but overlap alone is not a formal significance test. Conversely, a best-fit line passing outside one error bar does not automatically make that point an outlier. Interpret the pattern alongside scatter, chemical theory, residuals, and any statistical analysis.
Turning uncertainty into evaluation
The strongest evaluation identifies the dominant uncertainty and explains its effect. A generic claim such as “human error affected the result” is too vague because it neither identifies a mechanism nor establishes direction or magnitude.
A more useful evaluation might state that heat loss made the measured temperature change systematically too small, causing the calculated enthalpy magnitude to be underestimated. The improvement should then address that mechanism, perhaps through better insulation, a lid, temperature logging, or extrapolation to the mixing time.
Use percentage uncertainty to prioritize improvements. Replacing an apparatus item contributing 4% uncertainty is more valuable than replacing one contributing 0.1%. The Chemistry IA guide, data presentation guide, and Chemistry IA exemplars can help you compare your treatment with complete investigations.
Common mistakes to avoid
- Confusing percentage uncertainty with percentage error.
- Giving every instrument the same arbitrary uncertainty.
- Forgetting that a difference may involve two readings.
- Propagating an uncertainty from a controlled variable that is not in the calculation.
- Using standard deviation error bars without repeated measurements.
- Reporting more decimal places than the uncertainty supports.
- Listing limitations without explaining their direction or effect on the conclusion.
- Claiming that more repeats will eliminate a systematic error.
For exam preparation, practise calculations through the uncertainties and errors Questionbank. Before submission, the Chemistry IA Grader can provide criterion-linked feedback through Jojo AI, although your teacher remains responsible for official assessment guidance.
Conclusion
Effective IB Chemistry IA uncertainty analysis connects apparatus precision, calculations, graphs, and evaluation. Record defensible absolute uncertainties, convert them to percentages when needed, propagate them consistently, round results honestly, and explain exactly what error bars represent.
Most importantly, use uncertainty to interpret the chemistry. RevisionDojo’s Chemistry IA guide, Questionbank, exemplars, and Jojo AI feedback tools can help you check both the calculations and the quality of the reasoning built around them.
Sources and referenced URLs
- Official IB Chemistry subject brief, first assessment 2025
- Official IB Chemistry curriculum updates
- IB Mathematics in DP Chemistry supporting material
- IB Chemistry data booklet, first assessment 2025 document mirror
- RevisionDojo IB Chemistry IA guide
- RevisionDojo Chemistry IA data analysis guide
- RevisionDojo uncertainties and errors Questionbank
- RevisionDojo IA data and results best practices
- RevisionDojo Chemistry IA exemplars
- RevisionDojo Chemistry IA Grader
