Combining uncertainties and judging validity

Building up the total

1. Work out the percentage uncertainty of each measurement: balance, volumetric flask, pipette, titre.

2. A value that comes from two readings (a titre, a mass by difference, a temperature change) has double the single-reading uncertainty.

3. Add the percentage uncertainties. Scaling by an exact factor (x 10 for an aliquot, x 5 from an equation) does not add uncertainty.

4. Absolute uncertainty in the result = total % / 100 x result. Quote the result to a precision that matches it.

Which measurement matters most?

The measurement with the largest percentage uncertainty limits the result. Improving anything else makes little difference. Usually it is the smallest measured quantity: a small mass, a small titre or a small temperature change. Fix it by measuring more (a larger mass, a more dilute titrant to give a bigger titre, a larger temperature rise) or by using higher-resolution apparatus.

Judging validity

• Compare the percentage error (from the accepted value) with the total percentage uncertainty.
• If the error is within the uncertainty, the result agrees with the accepted value as well as the apparatus allows.
• If the error is far larger, there is a systematic problem: an assumption that does not hold, heat loss, a side reaction, or a step that changes the amount (such as air oxidising iron(II) in a sample before titration).
• A valid conclusion also needs controlled variables and a method that measures what it claims to.

Worked example

Iron in tablets: mass 1.45 g (±0.01 g by difference), volumetric flask 0.12%, pipette 0.24%, titre 22.15 cm³ (±0.10 cm³). Find the total % uncertainty.

1. Balance: 0.01 / 1.45 x 100 = 0.69%
2. Titre: 0.10 / 22.15 x 100 = 0.45%
3. Total = 0.69 + 0.12 + 0.24 + 0.45

Answer: 1.50%

Check yourself

1. Percentage uncertainties: balance 0.69%, volumetric flask 0.12%, pipette 0.24%, titre 0.45%. Calculate the total percentage uncertainty.
   Show answer

   1.5 %. 0.69 + 0.12 + 0.24 + 0.45 = 1.50%.

2. A tablet is found to contain 28.4% iron by mass, with a total uncertainty of 1.5%. Calculate the absolute uncertainty in the percentage of iron.
   Show answer

   0.43. 1.5 / 100 x 28.4 = 0.43, so 28.4 ± 0.4% iron.

3. Each reading on a thermometer has an uncertainty of ±0.5 °C. The temperature rises from 21.5 °C to 34.5 °C. Calculate the percentage uncertainty in the temperature change.
   Show answer

   7.7 %. ΔT = 13.0 °C, uncertainty 2 x 0.5 = 1.0 °C; 1.0 / 13.0 x 100 = 7.7%.

4. A titre is 11.20 cm³ (±0.05 cm³ per reading). Calculate its percentage uncertainty.
   Show answer

   0.89 %. 0.10 / 11.20 x 100 = 0.89%.

5. Uncertainties: balance 2.0%, pipette 0.24%, titre 0.40%, flask 0.10%. Which change would improve the result most?
   • Using a pipette of higher grade
   • Using a larger volumetric flask
   • Using a larger mass of sample
   • Using a more concentrated titrant
   Show answer

   Using a larger mass of sample. The balance gives by far the largest percentage, so a bigger mass helps most. A more concentrated titrant would make the titre smaller and worse.

6. A result has a percentage error of 0.9% and a total percentage uncertainty of 1.5%. What can you conclude?
   • The difference from the accepted value can be explained by measurement uncertainty
   • There must be a large systematic error
   • The method is invalid
   • The apparatus was faulty
   Show answer

   The difference from the accepted value can be explained by measurement uncertainty. The error lies within the uncertainty.

7. In a calculation, moles in a 25.0 cm³ portion are multiplied by 10 to give moles in 250.0 cm³. How does this affect the percentage uncertainty?
   • It multiplies it by 10
   • It divides it by 10
   • It does not change it, because 10 is an exact factor
   • It adds 10% to it
   Show answer

   It does not change it, because 10 is an exact factor. Only measured quantities carry uncertainty; the flask and pipette uncertainties are already counted.

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Sources

• Pearson Edexcel IAL Chemistry (2018) specification
• Pearson IAL Chemistry teacher practical guide
• Pearson examiners' report, WCH16 October 2024

Last updated 8 November 2026. Spotted a mistake? Tell us.