AQA GCSE Combined Science (8464), Higher tier · Chemistry › Quantitative chemistry › Chemical measurements, conservation of mass and the
Practise Chemical measurements. 12 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Every measurement has some uncertainty. You need to calculate the mean of repeat results, use the range to estimate the uncertainty of the mean, and use uncertainties to compare results. These skills come up in practical and data questions on both papers.
Grade by grade
What you need to be able to do, from the first marks up to the top grade.
3
Calculate a mean from repeat readingsAdd up the results, leaving out any anomalous ones, and divide by how many you added.
4
Find the range of a set of resultsRange = highest value − lowest value.
5
Identify an anomalous resultA result that clearly does not fit the pattern of the others; leave it out of the mean.
6
Calculate the uncertainty from the rangeUncertainty = ± half the range, e.g. a range of 0.4 g gives ± 0.2 g.
7
Write a mean with its uncertaintyGive the mean ± uncertainty with a unit, e.g. 24.3 ± 0.2 cm3.
8
Use uncertainties to compare sets of resultsA smaller uncertainty means more precise results; check whether a value lies within mean ± uncertainty.
Notes
Uncertainty in measurements
Whenever a measurement is made there is always some uncertainty about the result. Repeating it usually gives slightly different values.
Causes include the resolution of the instrument (the smallest change it can show, e.g. a balance that reads to 0.01 g) and random errors, such as judging exactly when a colour changes.
Repeating measurements and calculating a mean reduces the effect of random errors.
Mean, range and uncertainty
Mean = sum of the results ÷ number of results. Leave out any anomalous results.
Range = highest value − lowest value of the results you used.
Uncertainty = ± (range ÷ 2). The true value is likely to lie between mean − uncertainty and mean + uncertainty.
Worked example: gas volumes of 36.4, 37.0, 36.6 and 36.8 cm3. Mean = 146.8 ÷ 4 = 36.7 cm3. Range = 37.0 − 36.4 = 0.6 cm3. Uncertainty = ± 0.3 cm3. Result: 36.7 ± 0.3 cm3.
Give the mean to the same number of decimal places as the data.
Key words
Precise: results are close together, with little spread about the mean. A smaller uncertainty means more precise results.
Accurate: a result that is close to the true value.
Repeatable: the same person, using the same method and equipment, gets similar results.
Reproducible: a different person, or a different method or equipment, gets similar results.
Another value agrees with your result if it lies inside the range from mean − uncertainty to mean + uncertainty.
Cheatsheet
Mean = total of results ÷ number of results (leave out anomalies)
Range = highest − lowest
Uncertainty = ± range ÷ 2
Write results as mean ± uncertainty, with a unit
Precise = little spread about the mean
Accurate = close to the true value
Resolution = smallest change an instrument can measure
Repeatable = same person and method; reproducible = different person, method or equipment
How to answer each type of question
Calculate a mean, leaving out an anomaly
2 marks4
Spot any result that does not fit the others and leave it out.
Add the remaining results and divide by how many there are.
Round to the same number of decimal places as the data and give the unit.
Example. A student measured the temperature rise in a reaction four times: 6.2 °C, 6.6 °C, 9.1 °C, 6.4 °C Calculate the mean temperature rise. Do not include the anomalous result. [2 marks]
Show the model answer
(6.2 + 6.6 + 6.4) ÷ 3 (1) = 6.4 °C (1)
Calculate the uncertainty of the mean
2 marks6
Find the range: highest − lowest.
Halve it and write it with ± and the unit.
Example. A student measured the mass of copper oxide made in five repeats: 1.98 g, 2.04 g, 2.01 g, 1.96 g, 2.01 g The mean is 2.00 g. Calculate the uncertainty in the mean. [2 marks]
Show the model answer
range = 2.04 − 1.96 = 0.08 g (1) uncertainty = ± 0.04 g (1)
Suggest how to reduce the uncertainty
1 to 2 marks5
Name a specific change, such as a balance or measuring cylinder with a higher resolution.
Say why it helps: the reading is closer to the true value, or repeat results are closer together.
Example. A student used a balance that reads to the nearest 0.1 g to weigh about 0.5 g of magnesium ribbon. Suggest how the student could reduce the uncertainty in the mass. Give a reason. [2 marks]
Show the model answer
Use a balance with a higher resolution, e.g. one that reads to 0.01 g (1). The uncertainty in each reading is then much smaller compared with the mass being measured (1).
Compare results using their uncertainties
2 to 3 marks8
Compare the sizes of the uncertainties: smaller means more precise.
Work out each range (mean − uncertainty to mean + uncertainty).
Say whether the expected value lies inside each range, and which mean is closer to it (more accurate).
Example. Two groups measured the volume of hydrogen produced by the same reaction. Group A: 47.2 ± 0.4 cm3 Group B: 48.0 ± 1.5 cm3 The expected volume is 48.2 cm3. Compare the two groups' results. [3 marks]
Show the model answer
Group A's results are more precise because their uncertainty is smaller (1). Group B's mean is closer to the expected value, so it is more accurate (1). 48.2 cm3 lies within Group B's range (46.5 to 49.5 cm3) but not within Group A's range (46.8 to 47.6 cm3) (1).
Shortcuts and memory tricks
Uncertainty is half the spread: find the range, then halve it.
Sense check: the mean must lie between the lowest and highest values you used.
Think of darts: a tight group is precise; a group around the bullseye is accurate. You can be precise without being accurate.
Draw a quick number line from mean − uncertainty to mean + uncertainty to see whether another value falls inside.
Where marks are lost
Including the anomalous result in the mean or the range.
Giving the whole range as the uncertainty instead of half of it.
Leaving out the ± sign or the unit.
Mixing up precise (close together) and accurate (close to the true value).
Giving the mean to more decimal places than the data, e.g. 36.733 cm3 from readings to 0.1 cm3.
Exam technique
Show the range as its own line of working: it is often worth a mark on its own.
When comparing results, quote numbers: the ranges, and whether a value lies inside them.
Use 'precise', 'accurate', 'repeatable' and 'reproducible' with their exact meanings, and avoid vague words such as 'reliable'.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
A student measured the temperature of a solution three times: 21.5 °C, 22.0 °C and 21.0 °C. Calculate the mean temperature.
21.5 °C
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy4 marks
Every measurement made with an instrument has some uncertainty.
(a) A balance shows the mass of a sample as 12.47 g. What is the resolution of the balance? Tick (✓) one box.[1]
0.01 g
0.1 g
1 g
12.47 g
(b) Give one reason why scientists repeat a measurement several times and calculate a mean.[1]
(c) A student measured the temperature of a solution three times: 21.5 °C, 22.0 °C and 21.0 °C. Calculate the mean temperature.[1]
(d) The uncertainty in the mean can be estimated as half the range of the readings. Calculate the uncertainty in the mean temperature.[1]
Show the answer and mark scheme
(a)Answer: 0.01 g
(b)
a single reading may be unusually high or low (anomalous) / repeating reduces the effect of random errors / repeating shows whether the results are repeatable
(c)Answer: 21.5 °C
21.5 (°C)
(d)Answer: ± 0.5 °C
range = 22.0 − 21.0 = 1.0 (°C), so the uncertainty is ± 0.5 (°C)
Question 2Medium5 marks
Whenever a measurement is made there is some uncertainty in the result.
(a) A student needs to measure 25.0 cm3 of sodium hydroxide solution as accurately as possible. Which piece of apparatus should the student use? Tick (✓) one box.[1]
Beaker
Conical flask
Measuring cylinder
Volumetric pipette
(b) The student measured a temperature using a thermometer with a resolution of 0.5 °C. What is meant by the resolution of a measuring instrument?[1]
(c) The student's balance was not set to zero. It read 0.12 g with nothing on it. The student used it to measure the masses of several samples. Name the type of error this causes and describe its effect on the measured masses.[2]
(d) Explain why finding the mass of a sample by difference (weighing a container before and after adding the sample) removes this error.[1]
Show the answer and mark scheme
(a)Answer: Volumetric pipette
(b)
the smallest change in the quantity that the instrument can measure / the size of the smallest scale division
(c)
systematic error / zero error
every mass reading is 0.12 g too high / all readings are wrong by the same amount
(d)
the extra 0.12 g is in both readings, so it cancels out when one reading is subtracted from the other
Question 3Hard5 marks
Two students, Priya and Sam, each measured the volume of gas produced when the same mass of calcium carbonate reacted with excess dilute hydrochloric acid. Priya used a measuring cylinder to collect the gas over water. Sam used a gas syringe. Each student repeated their method four times. Priya's mean was 62 ± 4 cm3. Sam's mean was 65.0 ± 0.5 cm3.
(a) Compare the precision of Priya's results with Sam's results. Use the data given.[2]
(b) Suggest one reason why a gas syringe gives more precise readings than collecting gas over water in a measuring cylinder.[1]
(c) The theoretical volume of gas expected, calculated from the mass of calcium carbonate used, was 65.8 cm3. State whether this value lies within the uncertainty of each student's mean.[2]
Show the answer and mark scheme
(a)
Sam's results are more precise (smaller uncertainty, ± 0.5 compared with ± 4)
Sam's repeat readings were closer together / less spread out than Priya's
(b)
allow: a gas syringe has a finer scale (better resolution) / less gas is lost or dissolves in the water when using a gas syringe / it is easier to read the scale accurately on a gas syringe
(c)
it lies within Priya's uncertainty (62 ± 4 covers 58 to 66 cm3)
it does not lie within Sam's uncertainty (65.0 ± 0.5 covers only 64.5 to 65.5 cm3)