1.7.3Physical Chemistry
Error and Uncertainty — Edexcel AS Chemistry Revision Notes & Topical Questions
5 min read 6 parts Lesson 31 of 42
Section 1 of 6Types of Error
Random error
- Unpredictable differences between repeated readings, such as judging the colour change at a titration end point.
Systematic error
- A consistent shift in all readings in one direction, for example a balance that is not zeroed.
Reducing random error
- Repeat measurements and calculate a mean, and use concordant results.
Reducing systematic error
- Calibrate instruments, use better apparatus or change the method.
Section 2 of 6Uncertainty in Measurements
Uncertainty in Measurements
Reading uncertainty
- The smallest division on the scale limits how precisely a value can be read.
Two readings
- A burette volume needs two readings, so the uncertainty of the difference is double that of one reading.
Tolerance
- Glassware such as a pipette is marked with a manufacturer tolerance, for example ±0.06 cm³ for a 25 cm³ pipette.
Balance
- Mass found by difference uses two weighings, so uncertainty doubles again.
| Apparatus | Typical uncertainty |
|---|---|
| Burette (one reading) | ±0.05 cm³ |
| Burette (titre) | ±0.10 cm³ |
| 25 cm³ pipette | ±0.06 cm³ |
| Top-pan balance (2 d.p.) | ±0.005 g per reading |
Section 3 of 6Percentage Uncertainty
1
Identify the absolute uncertainty of each measurement from the apparatus.
2
Calculate percentage uncertainty = (absolute uncertainty ÷ measured value) × 100.
3
Add the percentage uncertainties for all measurements used in a calculation to get the combined uncertainty.
4
Express the final result with an uncertainty, such as ± 0.65%.
5
Compare it with the percentage difference between the experiment and the accepted value to judge significance.
Section 4 of 6Improving Precision
Larger measurement
- A bigger titre or a larger mass lowers the percentage uncertainty because the same absolute error is a smaller fraction.
Better apparatus
- A burette with finer divisions reduces reading uncertainty.
Repeat and mean
- Averaging results reduces the effect of random error but not of systematic error.
Identify the largest
- The measurement with the largest percentage uncertainty dominates the total and is the best one to improve.
Section 5 of 6Worked Example
Question
- A titre of 24.30 cm³ is measured with a burette (±0.05 cm³ per reading) and 25.0 cm³ is delivered by a pipette (±0.06 cm³).
- Find the combined percentage uncertainty.
- Titre uncertainty uses two readings2 × 0.05 = ±0.10 cm³.
- Percentage uncertainty of titre = 0.10 ÷ 24.30 × 100 = 0.41%.
- Percentage uncertainty of pipette = 0.06 ÷ 25.0 × 100 = 0.24%.
- Add the percentages0.41 + 0.24 = 0.65%.
Answer Combined uncertainty ≈ ±0.65%
Section 6 of 6Exam Checklist & Tips
1.7.3 – Key Points for the Exam
- Accuracy How close a result is to the true value.
- Precision How close repeated measurements are to each other.
- Absolute uncertainty The size of the possible error in a measurement, in the same units.
- Percentage uncertainty Absolute uncertainty as a percentage of the measured value.
Common Mistakes
- Using one reading uncertainty for a burette titre that needs two readings.
- Mixing up accuracy and precision.
- Adding absolute uncertainties of measurements with different units instead of percentage uncertainties.
- Claiming repeats remove systematic errors.
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