Chemical measurements — AQA GCSE Combined Science
Test yourself on Chemical measurements with AQA GCSE practice questions.
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Chemical measurements explained
Every measurement carries uncertainty because instruments have finite resolution and readings vary.
Read the full explanation
When you read a burette, the true volume lies within a small range around your recorded value. Uncertainty is not the same as a mistake: it is the unavoidable doubt about the true value. You estimate it from the scale division: for analogue instruments like a burette read to 0.1 cm³, it is often ± half the smallest division (±0.05 cm³), whereas for digital instruments like a balance reading to 0.01 g, it is ± the smallest division (±0.01 g). Repeating a measurement and taking a mean reduces the effect of random variation, but a systematic offset, such as a zero error, shifts all results and is not removed by averaging.
represent the distribution of results and make estimations of uncertainty
When a measurement is repeated, the results scatter about a central value. Representing that distribution means tabulating every reading, then plotting a suitable graph such as a dot plot, tally chart or histogram so the spread is visible. The mean is calculated by adding the readings and dividing by how many there are. Uncertainty is then estimated from the spread: a simple estimate is half the range, found by subtracting the smallest reading from the largest and halving the difference. For example, titre volumes 24.10 cm³, 24.30 cm³ and 24.20 cm³ have a range of 0.20 cm³, so the estimated uncertainty is ±0.10 cm³ and the result is quoted as 24.20 ± 0.10 cm³. A wide distribution signals imprecise technique; a narrow one suggests reliable measurements.
use the range of a set of measurements about the mean as a measure of uncertainty.
The range describes how far apart the smallest and largest readings are, and it gives a quick measure of how uncertain a mean value is. To use it, first calculate the mean of the repeated measurements, then subtract the smallest reading from the largest to find the range. The uncertainty is estimated as half the range, written with a ± sign after the mean. For instance, if four titres are 23.80 cm³, 24.00 cm³, 23.90 cm³ and 24.10 cm³, the mean is 23.95 cm³ and the range is 0.30 cm³, so the uncertainty is ±0.15 cm³. A small range relative to the mean indicates precise, repeatable measurements; a large range warns that the mean is less trustworthy and that technique or apparatus may need checking.
Your focus
- Estimate the uncertainty of a reading from the smallest scale division of the instrument used, distinguishing between analogue and digital scales.
- Explain why repeating a measurement and taking a mean reduces random variation but not systematic error.
- Report a measurement with an appropriate uncertainty and a justified number of significant figures.
Show all 9 objectives
- Record repeated measurements and calculate their mean accurately.
- Determine the range and use half the range to estimate uncertainty.
- Construct and interpret a dot plot, tally chart or histogram showing the distribution of results.
- Calculate the range of a set of repeated measurements.
- Use half the range to estimate and quote the uncertainty of a mean value.
- Explain how the size of the range affects confidence in a measured result.
Chemical measurements exam tips
Marking Points
- Uncertainty arises because every instrument has a smallest scale division, so a reading is only known to lie within a range around the recorded value.
- The uncertainty of a single reading is commonly estimated as half the smallest scale division for analogue scales (e.g. ±0.05 cm³ for a 0.1 cm³ burette), or the smallest division for digital scales (e.g. ±0.01 g for a 0.01 g balance).
- Repeating a measurement and calculating a mean reduces the effect of random variation on the reported value.
- Systematic errors, such as a zero error or a mis-set balance, shift all readings in one direction and are not reduced by averaging.
- Uncertainty should be stated with the measurement, for example 24.60 cm³ ± 0.05 cm³, so the precision of the result is clear.
- The size of the uncertainty affects how many significant figures are justified in a final calculated answer.
- Records each repeat measurement accurately, including correct units and a consistent number of decimal places.
- Calculates the mean by summing the readings and dividing by the number of readings.
- Finds the range by subtracting the smallest reading from the largest reading.
- Estimates uncertainty as half the range and quotes the final result with a ± value and unit.
- Represents the distribution using an appropriate method, such as a dot plot, tally chart or histogram, with a sensible scale and labelled axes.
- Comments on what the spread of results indicates about the precision or reliability of the measurements.
- Identifies the largest and smallest values in a set of repeated measurements.
- Calculates the range by subtracting the smallest value from the largest value.
- Calculates the mean of the measurements before quoting the uncertainty.
- Estimates uncertainty as half the range and expresses the result as mean ± uncertainty with correct units.
- Interprets a small range as indicating greater precision and a large range as indicating greater uncertainty.
- Applies the method to data from a practical context, such as titration volumes or temperature changes.
Examiner Tips
- 💡State the uncertainty with the correct unit and sign, for example ±0.05 cm³, rather than writing only a number.
- 💡When asked to improve reliability, link repeating and averaging to reducing random variation, and mention checking for zero error to address systematic error.
- 💡In calculations, carry the uncertainty through to the final answer and round the result to a sensible number of significant figures.
- 💡Show the mean calculation and the range calculation separately so the examiner can award method credit even if the final value slips.
- 💡Keep units throughout and give the uncertainty the same unit and decimal precision as the mean.
- 💡When asked to represent a distribution, label both axes and choose a scale that uses most of the grid without distorting the spread.
- 💡Write the range calculation explicitly, for example 24.10 − 23.80 = 0.30 cm³, before halving it.
- 💡State the final answer in the form mean ± uncertainty with the unit given once, such as 23.95 ± 0.15 cm³.
- 💡If asked to comment, link the size of the range to precision or reliability rather than simply restating the number.
Common Mistakes
- Treating uncertainty as a mistake: the error is calling it an error to be eliminated; the correction is to describe it as the unavoidable doubt about the true value and to estimate its size from the instrument scale.
- Believing that repeating a measurement removes all uncertainty: the error is claiming repeats give the exact value; the correction is that repeats reduce random variation but a systematic offset remains.
- Quoting a mean to more decimal places than the instrument justifies: the error is writing 24.60333 cm³ from a burette read to 0.1 cm³; the correction is to round the mean to the precision of the readings, such as 24.60 cm³.
- Dividing by the wrong number when finding the mean, for example dividing by the number of readings minus one; correction: divide by the total number of readings taken.
- Quoting the range itself as the uncertainty; correction: the simple estimate of uncertainty is half the range.
- Drawing a histogram with unequal class widths and ignoring frequency density; correction: use frequency density on the y-axis when class widths differ, or choose equal class widths.
- Reporting the range as the uncertainty rather than half the range; correction: halve the range to estimate uncertainty about the mean.
- Forgetting to calculate the mean first and attaching the uncertainty to a single reading; correction: the uncertainty describes the mean of the set.
- Mixing units or decimal places between the mean and the uncertainty; correction: keep both in the same unit and to the same precision.