The blue crystals in the jar are labelled copper(II) sulfate, and the label is not the whole story. Water is built into the crystal — a definite number of water molecules for every sulfate, the same number every time, which is why the crystals are blue rather than white and why they are heavier than the label’s formula says they should be.
Nobody is going to tell you what that number is. You have a balance and a burner, and between them they are enough.
What you are trying to find out
A formula is a ratio of counts, and you cannot count. What you can do is weigh, and the mole is the bridge between the two — which is exactly the kind of problem this unit exists to solve.
Drive the water out of a weighed sample of the blue solid and the mass that leaves is the water. Convert both masses to moles, take the ratio, and if the chemistry is what it claims to be the ratio should come out to a small whole number.
That “should” is doing a lot of work, and testing it is the investigation. A ratio of 4.98 is a success. A ratio of 4.6 is a question about your procedure with a specific answer, and the last section of this page is about finding it.
What you have to work with
- Hydrated copper(II) sulfate, the blue crystalline solid. If your station has hydrated magnesium sulfate instead, everything below applies unchanged and your whole number will be different.
- Crucible and lid, pipe-clay triangle, tripod, burner, or a hot plate rated for the job. Tongs. Heat-resistant mat.
- Balance, with its resolution written on it. A desiccator if the room has one.
- Mortar and pestle, for reducing large crystals.
Your design decisions, written down and checked before you light anything:
- The mass of your sample. Too small and the water lost disappears into the balance’s resolution; too large and you cannot drive the water out of the middle of the pile in one period. Justify your choice with an actual calculation: what mass of water would you expect to lose, and how many times the balance’s resolution is that?
- Whether you grind the crystals, and what that changes. There is a real trade-off here and both sides of it matter.
- How you will know all the water is gone. This is the whole procedure. Write down the rule you will apply, in numbers, before you start — and note that “it turned white” is a colour, not a criterion.
- How you will handle the crucible between heatings, given that it must be cool before it goes on the balance and that the anhydrous solid starts taking water back out of the room air as soon as it is cool.
The standard rule for the third of those is heating to constant mass: heat, cool, mass; heat again, cool, mass again; and stop when two successive masses agree to within the balance’s resolution. Decide how long each heating is and stick to it.
Ceramic, a burner, and a solid that can be pushed too far
- Hot crucibles look exactly like cold crucibles. There is no colour, no shimmer, no clue. Everything moves with tongs, and a crucible that has been off the flame for two minutes will still burn you. Assume hot.
- Never put a hot or warm crucible on the balance. It damages the pan, and the rising air off a hot object makes the reading drift — downward — so you would get a wrong number as well as a repair bill.
- Heat gently and evenly at first. A cold crucible taken straight into a hot flame can crack and throw fragments. Warm it in the outer part of the flame before going in.
- Do not heat to red heat, and do not lean over the crucible. Push copper(II) sulfate hard enough and you stop removing water and start decomposing the sulfate itself, which releases an irritating gas. Moderate heat, and your face out of the column of air above it.
- Waft any odour toward you. Never inhale over the crucible.
- Copper compounds are harmful if swallowed and toxic to aquatic life. Solid waste to the labelled container, never the sink. Wash your hands before you leave.
- Tie hair back and secure sleeves before the burner is lit, and know where the extinguisher and blanket are.
- Leftover crystals go to waste. Nothing goes back in the jar.
The prediction you write first
In your journal, before the balance is touched:
- The whole number you expect, and why you expect a whole number at all rather than any old ratio.
- The mass of water you predict will be lost from the sample size you chose. Show the calculation. If you cannot do it without the answer, predict a range and say what fixes it.
- How many significant figures your final ratio is entitled to, worked out from the balance’s resolution and your sample mass — not from how many digits the calculator shows.
- Which direction you expect to miss in, and the reason. Commit.
What to collect
| Measurement | Value | Unit |
|---|---|---|
| Resolution of the balance | g | |
| Mass of empty crucible and lid | g | |
| Mass of crucible, lid, and hydrated solid | g | |
| Mass of hydrated solid | g | |
| Mass after first heating and cooling | g | |
| Mass after second heating and cooling | g | |
| Mass after third heating and cooling | g | |
| Final mass of crucible, lid, and anhydrous solid | g | |
| Mass of anhydrous solid | g | |
| Mass of water driven off | g |
Record the colour at each stage alongside the masses. The colour change is corroborating evidence and it is not the criterion — a sample can look white on the surface while the middle is still blue, which is precisely what constant mass is designed to catch.
Then the calculation, which is the point of the day:
Molar masses to two decimal places, every intermediate value carried at full precision, and rounding only at the very end. If you round the moles to two figures partway through, you will not be able to tell a genuine 4.6 from a rounding artefact — see Significant Figures in Practice.
What to do if your ratio comes out 4.6
First: do not round it to 5 and move on, and do not round it to 4 and hope. A number that is not close to a whole number is telling you something, and it is usually one of these.
Water still in the sample. The commonest cause by a wide margin. If some water never left, the mass of the “anhydrous” solid is too high and the mass of water lost is too low, so the ratio comes out below the true value. A ratio of 4.6 against a true value of 5 means roughly 8% of the water stayed put — which is exactly what one short heating of a large lump produces. The fix is more heating cycles until the mass genuinely stops changing.
Water taken back up while cooling. Anhydrous copper(II) sulfate is a drying agent; it pulls moisture out of room air. A crucible left to cool on the bench for ten minutes has been quietly regaining mass the whole time, which again pushes the ratio down. Cool in a desiccator if you have one, mass promptly if you do not, and be consistent about the interval.
A sample that was already partly dried out. Crystals from the bottom of an old jar can have lost water in storage. Then there was less water to lose than the formula says, and again the ratio comes out low.
Notice that all three of the common causes push the same way. If your ratio came out above the whole number, none of these explains it and you should be looking at overheating, at a cracked crucible losing fragments, or at an arithmetic slip.
What to bring to the consolidation discussion
- Your full mass table, including every intermediate heating.
- Your ratio, with its uncertainty argued rather than asserted, and the whole number you are proposing.
- The formula you are claiming, written properly.
- The class spread. Collect everyone’s ratio and look at the shape of the scatter: are the values spread evenly around the whole number, or do they sit mostly on one side? A one-sided scatter is a systematic error the whole class shares, and finding it is more valuable than any individual result.
- One sentence on what you would change to halve your uncertainty.
What you should not claim
- Constant mass is not proof that only water left. It is proof that mass stopped changing under your heating conditions. If you overheated, something else left as well, and the balance cannot tell you what.
- A whole-number ratio does not prove the formula. It is consistent with the formula, which is a weaker and more honest statement. Two different hydrates can be distinguished by this method only if their ratios differ by more than your uncertainty.
- Your ratio is not more precise than your masses. If the balance reads to 0.01 g and you lost 1.08 g of water, that measurement carries three significant figures at best, and a ratio quoted as 4.9832 is claiming a precision no part of your apparatus ever had. Round at the end, and round honestly.
- “Human error” is not a source of error. Weighing the wrong crucible is a blunder — repeat the trial. A source of error is something built into the method that would still be there if you did everything perfectly, like the seconds between the desiccator and the balance pan.
- Every systematic error named above pushes the ratio down. That is a real and slightly uncomfortable finding: this method is biased, in a known direction, and knowing the direction is worth more than pretending it is unbiased. Say so in your conclusion.
Curriculum connection
D2.2
conduct an inquiry to calculate the percentage composition of a compound (e.g., a hydrate) [PR, AI]
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D2.4
determine the empirical formulae and molecular formulae of various chemical compounds, given molar masses and percentage composition or mass data [AI]
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A1.13
express the results of any calculations involving data accurately and precisely, to the appropriate number of decimal places or significant figures
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