An experiment is only worth doing if you change one thing, measure one thing, and hold everything else still. This page covers how to set that up, which instrument to reach for, and how to say honestly how good your numbers are — which is where most of the marks hide.
📘 What you need to know
The independent variable is the one you deliberately change. The dependent variable is the one you measure. Everything else is a controlled variable.
Every measuring instrument has an uncertainty, and you are expected to quote it.
For a scale you read by eye, use half the smallest division. For a digital display, use the smallest digit it shows.
A burette reading needs two readings, so the uncertainty on a titre is doubled.
Percentage uncertainty = absolute uncertainty ÷ measured value × 100. When quantities are multiplied or divided, you add the percentages.
Random errors scatter your repeats. Systematic errors shift every result the same way. Repeating helps with the first, not the second.
Precise means the repeats agree with each other. Accurate means they agree with the true value. They are not the same thing.
The three kinds of variable
Think of it like a fair race. If you want to know whether one runner is faster, you make them run the same distance, on the same track, on the same day. Change two things at once and you learn nothing, because you cannot tell which change caused the result.
Variable
What it is
In a rates experiment
Usually goes
Independent
The one thing you deliberately change
Concentration of HCl
x-axis
Dependent
The thing you measure as a result
Time for the cross to disappear
y-axis
Controlled
Everything you deliberately keep the same
Temperature, volume, mass of Mg, same person judging
Written in the method
A quick check that saves you every time: say your aim out loud as “I am changing ___ to see what happens to ___.” The first blank is independent, the second is dependent. Anything else that could also affect the second blank has to be controlled.
Controlled variables need a method, not a promise. “Keep the temperature constant” is a wish. “Stand all solutions in a 25 °C water bath for 10 minutes before mixing” is a control. Say how.
Choosing the right instrument
Reaching for the nearest piece of glassware is how good experiments quietly go wrong. Match the instrument to how accurately that particular measurement needs to be made.
Instrument
Typical uncertainty
Use it for
Do not use it for
Burette (0.10 cm3 divisions)
±0.05 cm3 per reading
Titrating — adding a volume drop by drop
Measuring out a rough wash
Volumetric pipette, 25.00 cm3
±0.03 cm3
Transferring one fixed, exact volume
Any volume other than the one marked
Volumetric flask, 250.0 cm3
±0.3 cm3
Making up a standard solution
Storing or heating anything
Measuring cylinder, 50 cm3
±0.5 cm3
Rough volumes where 1% error is fine
Anything that feeds a final calculation
Balance reading to 3 d.p.
±0.001 g per reading
Weighing a solid accurately
Weighing something wet or steaming
Thermometer, 0.1 °C divisions
±0.05 °C per reading
Temperature change in calorimetry
Stirring the mixture with it
Stopwatch
±0.5 s in practice
Timing anything longer than about 20 s
Very fast reactions — your reaction time dominates
Notice the stopwatch. It displays to 0.01 s, but you are the slow part — your thumb takes a couple of tenths of a second to react. Quoting ±0.01 s for a stopwatch reading looks careless to an examiner.
Every measurement has an uncertainty
No instrument gives you a perfect number. Saying so is not admitting failure — it is part of the answer. There are two ways to write it.
The absolute uncertainty is the ± value in the same unit as the measurement: 23.45 ± 0.10 cm3. The percentage uncertainty turns that into something you can compare between very different measurements — you cannot compare 0.10 cm3 with 0.05 g, but you can compare 0.43% with 0.16%.
🧩 Getting the uncertainty right
Analogue scale you read by eye (burette, thermometer, measuring cylinder): take half the smallest division.
Digital display (balance, pH meter): take the smallest digit shown. A balance showing 1.246 g gives ±0.001 g.
Two readings? Double it. A titre is (final − initial), so 0.05 + 0.05 = ±0.10 cm3. Mass by difference works the same way.
Multiplying or dividing? Add the percentage uncertainties.
Adding or subtracting? Add the absolute uncertainties.
WORKED EXAMPLE
Percentage uncertainty in a titre
A student records an initial burette reading of 1.20 cm3 and a final reading of 24.65 cm3. The burette has 0.10 cm3 divisions. Find the titre and its percentage uncertainty.
Step 1: The titre24.65 − 1.20 = 23.45 cm³Step 2: Uncertainty on each reading
Half of 0.10 → ±0.05 cm³Step 3: Two readings, so add them0.05 + 0.05 = ±0.10 cm³Step 4: Turn it into a percentage(0.10 ÷ 23.45) × 100 = 0.4264…23.45 ± 0.10 cm³, which is 0.43%forgetting to double is the single most common slip here
WORKED EXAMPLE
Carrying the uncertainty into the answer
25.00 ± 0.03 cm3 of 0.100 mol dm–3 NaOH is titrated against HCl. The titre is 23.45 ± 0.10 cm3. The reaction is 1:1. Find the concentration of the HCl and its uncertainty.
Step 1: Moles of NaOHn = 0.100 × 25.00 ÷ 1000 = 2.50 × 10⁻³ molStep 2: 1:1, so the same moles of HClc = 2.50 × 10⁻³ ÷ (23.45 ÷ 1000) = 0.10661 mol dm⁻³Step 3: Add the percentage uncertainties
Pipette: (0.03 ÷ 25.00) × 100 = 0.12%
Burette: (0.10 ÷ 23.45) × 100 = 0.43%
Total = 0.55%Step 4: Back to an absolute value0.10661 × 0.0055 = 0.00060.1066 ± 0.0006 mol dm⁻³the burette is nearly four times worse than the pipette — that is your weakest step
Use the percentages to write your evaluation. Once you can see that the burette contributes 0.43% and the pipette only 0.12%, you know exactly which piece of apparatus to talk about improving. That is a much stronger evaluation than “there may have been human error”.
Reading the scale properly
The uncertainty printed on a burette assumes you read it correctly. Read it from the wrong angle and you introduce an error bigger than the instrument’s own — which makes the ±0.05 cm3 a bit of a joke.
This error is called parallax. Notice it is bigger than the burette’s own ±0.05 cm3 — so it wipes out the whole reason for using a burette.
Random and systematic errors
Two different problems, two different fixes. Telling them apart is worth real marks in an evaluation.
A random error is the wobble. Sometimes a bit high, sometimes a bit low, no pattern. Judging the exact moment a colour changes, or a slightly different eye position each time. Because it goes both ways, repeating and averaging genuinely helps.
A systematic error is a bias. Every single reading is wrong in the same direction by roughly the same amount — a balance that was not zeroed, a thermometer reading 0.5 °C high, heat leaking out of a calorimeter. Repeating does nothing, because you just get the same wrong answer more times. You have to find the cause and fix it, or calibrate it out.
The second target is the dangerous one. Beautifully consistent results that are all wrong — and repeating them will never reveal the problem.
WORKED EXAMPLE
Which kind of error is it?
A student measures the enthalpy change of a neutralisation four times in a polystyrene cup and gets −51.2, −51.4, −51.1 and −51.3 kJ mol–1. The accepted value is −57.3 kJ mol–1. Comment on their results.
Step 1: Look at how much the repeats vary
Spread is only 0.3 kJ mol⁻¹ → very preciseStep 2: Compare with the true valueAll about 6 kJ mol⁻¹ too small, and all in the same direction.Step 3: Same direction every time means a bias
Heat is escaping to the cup, the air and the thermometer, so the temperature rise measured is always too small.
Precise but not accurate — a systematic errordoing a fifth repeat would not help at all — insulate the cup and put a lid on it instead
💡 Exam tip
Write the uncertainty with the same number of decimal places as the measurement: 23.45 ± 0.10 cm3, not 23.45 ± 0.1.
Quote uncertainties to one significant figure and round the answer to match it.
If a question asks which measurement to improve, work out the percentage uncertainties and point at the biggest one. Do not guess.
“Human error” is not an answer. Name the actual step — judging the endpoint, parallax on the burette, heat lost from the cup.
Use concordant titres (within 0.10 cm3 of each other) for your mean and say that is what you did.
Repeats fix random errors. Only better technique or calibration fixes systematic ones. Say which you mean.
⚠ Common mix-up
Using “precise” to mean “correct”. Five identical wrong answers are precise and useless.
Forgetting to double the burette uncertainty. A titre comes from two readings, so it is ±0.10 cm3, not ±0.05.
Adding absolute uncertainties when you multiply. Multiply or divide → add percentages. Add or subtract → add absolutes.
Quoting a stopwatch as ±0.01 s. The display is that good; your reflexes are not.
Calling an anomaly a systematic error. One odd result is random. A bias that shifts every result is systematic.
Listing controlled variables without saying how you control them. Name the method, not the intention.
Writing more decimal places than the instrument gives. A measuring cylinder cannot produce 25.00 cm3.
Up next: Applying Practical Techniques — the actual methods behind these measurements: titration, filtration, distillation, calorimetry and chromatography.
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