7.3.3Additional lessons
Processing Uncertainties in Chemistry — IB Chemistry HL Revision Notes & Topical Questions
5 min read 6 parts Lesson 165 of 172
Part 1 of 6Types of Uncertainty
Every measurement is only an estimate, and uncertainty states how good that estimate is.
Random uncertainty
- These errors vary unpredictably between readings, so repeating the measurement and averaging reduces their effect.
Systematic error
- The same error affects every reading in one direction,
- such as a thermometer that reads 1 °C too high,
- and repetition does not remove it.
Absolute uncertainty
- The size of the possible error in the units of the measurement, written as ± a number.
Percentage uncertainty
- Absolute uncertainty divided by the measured value, multiplied by 100, which allows fair comparison between measurements.
Part 2 of 6Propagating Uncertainty
Propagating Uncertainty
Adding or subtracting
- Add the absolute uncertainties, as in a titre found from two burette readings.
Multiplying or dividing
- Add the percentage uncertainties of the values being multiplied or divided.
Powers
- Multiply the percentage uncertainty by the power to which the value is raised.
Final answer
- Round the uncertainty to one significant figure and quote the result to the same decimal place.
Part 3 of 6Working Through an Uncertainty Calculation
1
List each measured value with its absolute uncertainty and convert each to a percentage uncertainty.
2
Decide whether each step in the calculation is an addition, a multiplication or a power.
3
Combine the uncertainties by the rule that matches each step.
4
Convert the total percentage uncertainty back to an absolute value by multiplying by the final result.
5
Compare the total uncertainty with the difference from the accepted value to judge whether the error is explained.
Part 4 of 6Using Uncertainty in Evaluation
Dominant source
- The measurement with the largest percentage uncertainty has the biggest effect, and improving it gives the largest gain.
Percentage error
- Calculate the difference from the literature value divided by the literature value, multiplied by 100.
Explained or not
- If the percentage error is smaller than the total uncertainty, random uncertainty may explain the difference;
- otherwise a systematic error is likely.
Range
- The spread of repeat results gives an estimate of the random uncertainty, which can be shown with error bars.
Part 5 of 6Worked Example
Question
- In a calorimetry experiment 50.0 g of water (±0.1 g) rises in temperature by 8.0 °C, from two thermometer readings each ±0.5 °C.
- Calculate q = mcΔT with its uncertainty, taking c = 4.18 J g⁻¹ K⁻¹ as exact.
- q = 50.0 × 4.18 × 8.0 = 1672 J = 1.7 kJ.
- Percentage uncertainty in mass = 0.1 ÷ 50.0 × 100 = 0.2 %.
- ΔT uncertainty = 0.5 + 0.5 = ±1.0 °C, which is 1.0 ÷ 8.0 × 100 = 12.5 %.
- Total = 0.2 + 12.5 = 12.7 %, and 12.7 % of 1672 J is about 212 J, rounded to 0.2 kJ.
Answer q = 1.7 ± 0.2 kJ
Part 6 of 6Exam Checklist & Tips
7.3.3 – Key Points for the Exam
- Random error A scatter in readings that varies unpredictably from one measurement to the next.
- Systematic error A consistent offset in the readings caused by the method or the instrument.
- Absolute uncertainty The possible error in a value, in the same unit as the value.
- Percentage uncertainty The absolute uncertainty as a percentage of the measured value.
- Error propagation Combining the uncertainties of individual measurements to find the uncertainty in a calculated result.
Common Mistakes
- Adding percentage uncertainties for a subtraction, when absolute uncertainties should be added.
- Quoting uncertainties to many significant figures, when one figure is normally enough.
- Treating a systematic error as if averaging more readings would remove it.
- Ignoring the uncertainty of the temperature change, which is often the largest one in calorimetry.
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