The equation says one number. The balance says another. Everything in this unit has been building toward the moment those two numbers sit next to each other on a page with your name on it, and toward your being able to explain the gap in grams rather than in apologies.
This is your investigation. Your reaction, your scale, your limiting reagent chosen on purpose, and your account of where the missing mass went — or where the extra mass came from, which is the more interesting outcome.
The situation
Somebody, somewhere, needs to know how much of something a reaction will produce, and needs to be right. A pharmacist compounding a dose. A water operator dosing a coagulant. A food producer working out how much raising agent goes in. An operator at a plant deciding how much reagent to buy for next month. In every case the calculation is the one you have been doing all unit, and in every case being wrong has a cost that lands on somebody.
You are going to do it once, carefully, at bench scale — and then find out what it looks like when the same arithmetic is done at a scale where being out by two percent matters.
Part 1 — Design and run the reaction
Choose a reaction you can run with school reagents, where you can recover and mass a product. Options that work well:
| Reaction | What you recover | Why it is a good choice |
|---|---|---|
| Iron with copper(II) sulfate solution | Copper metal | Single displacement, visible, and the product is easy to wash |
| A precipitation of your choosing | The precipitate | You choose the limiting reagent explicitly |
| Heating sodium hydrogen carbonate | The solid residue | Mass loss is the measurement, which changes the error analysis |
| Neutralisation followed by evaporation | The dry salt | Slow, and the drying step is the whole difficulty |
You may propose something else. Bring it early.
What you have to decide, and defend in writing before you run anything:
- The balanced equation, with states.
- Which reactant you make limiting, and by how much you make the other exceed it, expressed as a percentage excess with a reason. This is a deliberate design choice, not something you discover afterwards.
- The scale. Choose amounts so the recovered mass is at least a couple of hundred times the balance’s resolution, and show the calculation that justifies it.
- The theoretical yield, in grams, to the correct number of significant figures, calculated before the lab.
- Your recovery and drying plan, with a stopping rule. The rule is constant mass — dry, cool, mass, repeat until two successive masses agree to within the balance’s resolution — and you should say how many cycles you have time for.
- How many trials. One of anything tells you nothing about spread.
- Your predicted percentage yield, with a direction. Commit, in writing, to whether you expect to land above or below 100% and why.
Your procedure is checked before you run it — every time
Submit the written procedure, the equipment list, the hazards, and what you would do if each hazard materialised. Some will come back for a redesign, and that is the system working rather than a judgement of you.
Non-negotiable, whatever you design:
- School reagents only, at the concentrations supplied. Nothing from home, nothing from another room, no concentrated acids.
- Combine only what your approved procedure lists. Substances that are harmless apart can produce a toxic gas together and there is no way to tell by looking, which is why this rule is absolute rather than a matter of judgement.
- Add acid to water, never water to acid. The heat released has somewhere to go when the water is already in the container; poured the other way it concentrates in a few drops that can boil and spit acid back at you.
- Sodium hydroxide does not warn you. It feels soapy rather than painful, and it burns deeper than a dilute acid of the same strength because you do not pull away. Rinse any suspected contact for 15 minutes and tell me, whether or not it hurts.
- Eye protection from the first move to the last of the cleanup. Hair back, sleeves secured, closed-toe shoes.
- Hot glassware, hot ceramic, and hot metal look exactly like cold ones. Tongs. Nothing warm goes on the balance — it damages the pan and the rising air drags the reading low.
- Never pipette by mouth. Bulb or pump, every liquid, every time.
- Waft, do not sniff. Nothing is tasted, including a product you are confident you have identified.
- Nothing that makes a gas is sealed in a rigid container, and nothing sealed is ever heated.
- Never return unused reagent to a stock bottle.
- Know where the eyewash, shower, extinguisher, blanket, and spill kit are before you start, and report every incident immediately, however small.
Full agreement: Safety in the Lab and Lab Safety and WHMIS.
Part 2 — Where the arithmetic has consequences
Research one setting where quantitative accuracy in a chemical calculation genuinely matters, and what happens when it is not observed. Directions that work:
- Water or wastewater treatment, where a dose that is too low fails and one that is too high creates a different problem.
- Agricultural application rates, and what leaves a field when the rate is wrong.
- An industrial process where an off-specification batch has to be disposed of rather than sold.
- A workplace exposure limit, and how a concentration is measured against it.
- Dosage in a health setting, where the calculation is the same one you have been doing.
What I want from this section is not a general statement that accuracy is important. I want the specific consequence: what goes wrong, where the material ends up, and who bears it.
Sources, cited in the format in Writing About Chemistry. Two at minimum, of the right kinds: a government or regulatory agency, a professional body, a company’s published technical documentation, a peer-reviewed article. Every figure traceable to something a reader can open. If you cannot find a reliable figure, write that you could not — see What Counts as Evidence.
What to hand in
1. A full lab report, in the sections set out in Writing a Lab Report, including:
- Your design decisions and their justifications, dated before the lab.
- Your predicted percentage yield with its direction, dated before the lab.
- A complete data table, every quantity with a unit and the resolution of the instrument that produced it.
- The theoretical yield calculation, shown, with molar masses to two decimal places.
- The mass account: theoretical, actual, difference with a sign, percentage yield.
- A ranked analysis of the gap. Each mechanism, the direction it pushes the yield, and an estimate in grams of how much of the gap it could account for. Ranked by size, and totalled — and if your named mechanisms do not add up to the gap you observed, say so. An unexplained residue is a real result.
2. A one-page section on Part 2, connecting your bench arithmetic to the setting you researched.
A yield over 100% is information, not an error to hide
If your recovered mass exceeds the theoretical yield, report it, and treat it as the most interesting result on your page. It is not possible for the reaction to have made more product than the limiting reagent allows, so the extra mass is something else, and naming what is a genuine piece of analysis.
The usual candidates, all of which add mass: water that had not finished leaving the product; soluble salts left behind because the product was not washed enough; filter paper or a container that gained moisture from the air between the two weighings.
A report that says “103.8%, most probably incomplete drying, since we dried for one period and never achieved constant mass” is worth far more than one that quietly reports 98%. Rounding an inconvenient number toward the expected one is the only thing here that would be a serious problem.
Before you hand in, check every one of these:
- The equation is balanced and carries states
- The limiting reagent is identified with a calculation, not asserted
- Every quantity has a unit
- Every measurement has its instrument’s resolution recorded
- Molar masses to two decimal places, rounding done once at the end
- The prediction is dated before the data
- Every error mechanism has a direction attached
- The percentage yield is quoted to a defensible number of figures
- Every researched figure is traceable to a source you can open
How it will be judged
| What I am looking for | Level 3 sounds like | Level 4 sounds like |
|---|---|---|
| Design | A workable procedure with the variables named | Scale, excess, and stopping rule each chosen with a stated reason |
| Limiting reagent | Correctly identified | Chosen deliberately, and the excess justified as a number |
| Prediction | States an expected yield | States it with a direction and a mechanism, before the data |
| Data | Complete, with units | Every measurement carries its resolution, and enough trials to show spread |
| Calculation | Correct, with sensible figures | Correct, with the significant figures argued rather than assumed |
| Analysis of the gap | Names sources of error | Ranks them, gives each a direction and a size in grams, and totals them |
| A yield over 100% | Reported | Reported, explained mechanically, and used to improve the procedure |
| Part 2 | A real setting, correctly described | The specific consequence named, and who bears it |
| Sources | Two appropriate sources, cited | Matched to the claims they support, with their limits noted |
What sinks an otherwise good investigation
- “Sources of error: human error.” A limitation is something about the method that would still be there if you ran it perfectly. Massing the wrong crucible is a blunder — repeat the trial.
- A list of errors with no directions. Half of them push the yield up and half push it down, and a list that does not say which is not an analysis. It is a list.
- A prediction written afterwards. It shows, every time.
- Drying “until it looked dry”. That is a colour, not a criterion. Constant mass is the criterion, and if you ran out of time to reach it, say so and say which direction that pushes your result.
- A percentage yield quoted to four figures from a balance reading to 0.01 g. Work out what your resolution allows before you write the number.
- Part 2 written as an essay about the importance of accuracy. Name the setting, name the failure, name who pays for it.
Where the technique came from: Percentage Yield of a Precipitate. The arithmetic: Limiting Reagent and Yield and Limiting Reagent Practice.
Curriculum connection
D1.1
analyse processes in the home, the workplace, and the environmental sector that involve the use of chemical quantities and calculations (e.g., mixing household cleaning solutions, calculating chemotherapy doses, monitoring pollen counts) [AI, C]
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D1.2
assess, on the basis of research, the importance of quantitative accuracy in industrial chemical processes and the potential impact on the environment if quantitative accuracy is not observed [IP, PR, AI, C]
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D2.7
conduct an inquiry to determine the actual yield, theoretical yield, and percentage yield of the products of a chemical reaction (e.g., a chemical reaction between steel wool and copper(II) sulfate solution), assess the effectiveness of the procedure, and suggest sources of experimental error [PR, AI]
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