Percentage Composition and Molar Gas Volume, Grade 10
A chemical formula is a prediction. These two Grade 10 practicals check whether nature agrees.
Percentage composition is arithmetic on the periodic table, and most learners can do it inside a lesson. What almost nobody does is measure it, then explain the gap between the calculated number and the measured one.
Chapter 18 of the Grade 10 book prescribes two experiments that do exactly that. One predicts a volume of gas and asks you to collect it. The other predicts a mass of solid and asks you to weigh it. Both are on this page, with worked numbers, the two things the textbook leaves out, and a free worksheet and memo.
Percentage composition, in one worked example
You need nothing but the formula and a periodic table. Take sodium carbonate, Na2CO3.
| Element | Mass in one mole |
|---|---|
| Na | 2 × 23,0 = 46,0 g |
| C | 1 × 12,0 = 12,0 g |
| O | 3 × 16,0 = 48,0 g |
| Total | 106,0 g·mol-1 |
Mass percentage of an element = mass of the element ÷ mass of the compound × 100
| Element | Working | Percentage |
|---|---|---|
| Na | 46,0 ÷ 106,0 × 100 | 43,4 % |
| C | 12,0 ÷ 106,0 × 100 | 11,3 % |
| O | 48,0 ÷ 106,0 × 100 | 45,3 % |
They add to 100 per cent, and that is the check. Every gram of the compound is a gram of one of its elements and nothing else. A learner whose percentages do not add to about 100 has an arithmetic error, every time, and finding it themselves is worth more than being told.
Where this fits in the curriculum
| Subject | Physical Sciences |
|---|---|
| Grade | 10 |
| Term | 4 |
| Topic | Topic 6, Chemical change. Quantitative aspects |
| Status | Both experiments are prescribed |
| Marks | 63 on our worksheet. None is prescribed |
These are the book's own experiments, not ours. What we have added is the two corrections below, a method for weighing magnesium on the balance a school actually owns, and the answer to a question the textbook asks and never answers.
Experiment 1: molar gas volume
The idea. One mole of any gas takes up the same volume, whatever gas it is. Predict how many moles of carbon dioxide a measured mass of bicarbonate of soda should give, then collect the gas and see.
2NaHCO3(s) + H2SO4(aq) → Na2SO4(aq) + 2CO2(g) + 2H2O(l)
Method
- Weigh 0,168 g of bicarbonate of soda onto filter paper and tip it all into a large test tube
- Half fill a bowl with water. Fill a second test tube with water, cover the mouth with a finger and invert it in the bowl
- Feed the end of the delivery tube up into the inverted tube
- Measure 10 ml of dilute sulfuric acid, 0,1 mol·dm-3
- Work quickly. Add the acid to the bicarbonate and push the stopper home in one movement
- Carbon dioxide bubbles across and pushes the water out of the collecting tube
- When the bubbling stops, stopper the collecting tube while it is still under water
- Measure the gas volume. Pour the water left in the tube into a measuring cylinder and record it. Then fill the tube completely and pour that in too. The difference is the volume of gas you collected
What the formula predicts
| Step | Working | Result |
|---|---|---|
| M(NaHCO3) | 23,0 + 1,0 + 12,0 + 48,0 | 84,0 g·mol-1 |
| 168 g gives | 2 × 44,0 | 88 g of CO2 |
| So 0,168 g gives | ÷ 1 000 | 0,088 g of CO2 |
| Moles | 0,088 ÷ 44,0 | 0,002 mol |
| Volume at STP | 0,002 × 22,4 dm3 | 44,8 cm3 |
Why 44,8 cm³ is the wrong number to compare against
This is the most useful thing on the page, and no school textbook we have seen mentions it.
22,4 dm3 per mole is the molar volume at STP, and STP is 0 °C. Your classroom is not at 0 °C. It is nearer 25 °C, where a gas has expanded and one mole occupies 24,45 dm3.
| Prediction | Volume of 0,002 mol of CO2 |
|---|---|
| At STP, 0 °C, as the book calculates | 44,8 cm3 |
| At 25 °C, where the experiment actually runs | 48,9 cm3 |
That is 9,2 per cent higher, and it is the figure a class should be comparing their measurement to.
In an exam, still use 22,4
This is a point about measuring, not about answering questions. The South African curriculum defines molar volume at STP and 22,4 dm3·mol-1 is the value to use in a test or an exam, every time.
24,45 dm3·mol-1 is what you need when you are explaining why a real measurement on a warm bench did not land on the calculated number. Different job. Our Grade 11 stoichiometry page says the same thing from the calculation side.
And there is a second error, going the other way
Carbon dioxide dissolves in water, and this experiment collects it over water. Some of the gas produced never reaches the tube at all.
| Effect | Pushes the measured volume |
|---|---|
| Warm room rather than 0 °C | Up |
| CO2 dissolving in the collecting water | Down |
The two partly cancel, which is why the experiment appears to work despite both of them. A class that lands close to 44,8 cm3 is getting there for two wrong reasons that happen to nearly balance, and saying so out loud is a better chemistry lesson than the measurement itself.
The textbook asks the learner to "explain briefly why your measured volume is equal, or not equal, to the calculated volume" and then never answers it. That is the answer.
Experiment 2: percentage composition, measured
The idea. React a known amount of magnesium with vinegar, evaporate the water, weigh what is left, and compare it with what the formula of magnesium acetate says you should have.
Mg(s) + 2CH3COOH(aq) → Mg(CH3COO)2(aq) + H2(g)
Magnesium ribbon, never powder. The book puts this in a warning box and it is right. Powder reacts far too vigorously for a school bench.
The balance problem, and how to get round it
The method asks for 0,243 g of magnesium, which is 0,01 mol. It does not say what balance that needs, and on the balance most South African schools own, this measurement cannot be made.
| Balance readability | Uncertainty on 0,243 g |
|---|---|
| 0,001 g, analytical | 0,4 % |
| 0,01 g | 4,1 % |
| 0,1 g, what most schools have | ±41 % |
| 1 g, kitchen scale | ±412 % |
Weighing 0,243 g on a 0,1 g balance is not a measurement. It is a guess with a decimal point, and everything calculated from it inherits the same 41 per cent.
So do not weigh the magnesium. Weigh a metre of it and cut by length.
- Weigh a full 100 cm of ribbon on the balance you already have
- Divide by 100 to get grams per centimetre
- Cut the length that gives you 0,243 g
| Approach | Uncertainty |
|---|---|
| Weighing 0,243 g directly | ±41 % |
| Weighing 100 cm and cutting by length | ±10 % |
| Weighing 200 cm and cutting by length | ±5 % |
The balance error is spread over the whole length instead of landing on one small piece. It is the same trick as timing ten swings of a pendulum instead of one, and it turns an impossible measurement into a workable one on equipment already in the building.
Weigh your own ribbon. Thickness varies between suppliers, so a grams-per-metre figure printed on a page would be wrong for somebody.
Method
- Weigh the empty beaker and write the mass down
- Add the cut magnesium ribbon
- Stand the beaker on a heating stand on a tripod and drop in a few boiling stones
- Measure 32 ml of vinegar and add it slowly
- Wait until all the magnesium has gone. The bubbling stops and no metal is left
- Heat on a low flame until the liquid has nearly all evaporated, then turn the burner off
- Let the last of it evaporate at room temperature
- Reweigh the beaker and subtract the empty mass
What the formula predicts
| Step | Result |
|---|---|
| 0,243 g of Mg | 0,01 mol |
| M(Mg(CH3COO)2) | 142,3 g·mol-1 |
| Mass of product expected | 1,42 g |
And its percentage composition, straight off the periodic table:
| Element | Working | Percentage |
|---|---|---|
| Mg | 24,3 ÷ 142,3 × 100 | 17,1 % |
| C | 48,0 ÷ 142,3 × 100 | 33,7 % |
| H | 6,0 ÷ 142,3 × 100 | 4,2 % |
| O | 64,0 ÷ 142,3 × 100 | 45,0 % |
Worth pointing out to a class: hydrogen is 4,2 per cent of the mass but six of the fifteen atoms. Percentage composition is about mass, not about how many atoms there are. Learners who blur the two struggle with empirical formula next year.
The two things that ruin the second practical
Overheating. Magnesium acetate decomposes if it gets too hot and the mass comes out low. Low flame, and stop while there is still a little liquid in the beaker.
It is hygroscopic. Left on an open bench it pulls water back out of the air and the mass creeps up. A desiccator solves it. Without one, weigh it as soon as it is dry rather than the next afternoon.
Those two are why a class result comes out below or above 1,42 g, and knowing which happened is the point of the write-up.
If it does not work
| Problem | Cause | Fix |
|---|---|---|
| Almost no gas collects | The stopper is not sealing. The commonest failure by a long way | Press it firmly and check before adding the acid |
| Gas escapes at the start | The stopper went in too slowly | Have it in your hand ready. Acid in, stopper home, one movement |
| The collecting tube fills with air | It was not full of water when inverted | Fill it completely and cover the mouth until it is under water |
| Measured volume well under 44,8 cm3 | A leak, or a lot of CO2 dissolved | Discuss which, rather than repeating blindly |
| Product mass well below 1,42 g | Overheated. The acetate decomposed | Low flame, and finish the drying at room temperature |
| Product mass above 1,42 g | It absorbed water from the air, or vinegar is still in it | Desiccator, or reweigh sooner |
| The magnesium does not all react | Not enough vinegar, or tarnished ribbon | 32 ml is a 7 per cent excess. Rub the ribbon clean first |
| The reaction is violent | Powder was used instead of ribbon | Ribbon. Always |
| Bumping and spitting while heating | No boiling stones | Two or three of them |
Safety
- Safety glasses for both practicals. The book specifies them for each one
- Magnesium ribbon, never powder
- Dilute sulfuric acid at 0,1 mol·dm-3 is an irritant rather than a corrosive, but it still goes in eyes
- The second practical uses an open flame. Hair tied back, no loose sleeves, nothing flammable on the bench
- Hydrogen comes off in the second practical. Small amounts, into an open beaker. Never in a sealed vessel, and keep the burner away until the reaction has stopped
- The beaker stays hot long after the flame is out. Tongs, not fingers
- Boiling stones are not optional. Hot vinegar spitting out of a beaker is the realistic injury here
Disposal: everything goes down the sink with plenty of water. Magnesium acetate, sodium sulfate and dilute vinegar are all benign.
How the 63 marks are made up
| Section | Marks |
|---|---|
| Percentage composition from a formula | 10 |
| Molar gas volume, the prediction | 11 |
| Molar gas volume, the measurement and the two errors | 12 |
| Weighing the magnesium | 9 |
| Percentage composition, the measurement | 10 |
| What the product is made of | 6 |
| Conclusion | 5 |
No mark allocation is prescribed for either experiment. The worksheet and this split are ours.
The most valuable question on the sheet asks the learner to name the two errors in the gas experiment and say which way each one pushes the result. Very few can do it, and the whole practical lives in that answer.
The mark most often dropped is the conversion from dm3 to cm3. An answer of 0,0448 with no conversion is two marks out of three.
If you have time
Run the gas experiment twice, once with cold water in the trough and once with warm. More CO2 dissolves in the cold water, so the measured volume drops. That turns an argument on a page into a number on the bench.
Weigh 200 cm of ribbon instead of 100. The uncertainty halves again, and a class can see for itself that the fix scales.
Ask what happens to the percentage composition if you use twice as much magnesium. Nothing at all. The masses double and the percentages do not move, which is the difference between a quantity and a proportion, and it is the idea Grade 11 stoichiometry is built on.
Free worksheet and marking memo
Both free, no sign up, straight to the PDF.
- Learner worksheet, 63 marks, with the Na2CO3 calculation, both practicals, the recalculation at 25 °C, the balance uncertainty question and the ribbon-length table
- Marking memorandum, with worked answers, what to accept when a learner's product mass came out high rather than low, and the discussion to run on the two cancelling errors
Related practicals
- Stoichiometry: the mole, empirical formula and the calculations that follow. Where these calculations go next year, with limiting reagent and concentration
- Investigating physical and chemical changes. The other Grade 10 practical that collects a gas over water
- Percentage yield and limiting reagent, Grade 11. What happens when the measured mass and the predicted mass are the whole point
- Solubility and dissolving, Grade 10. Same topic block, earlier in the year
- Precipitation reactions and testing for ions, Grade 10. Chemical change, on the qualitative side
- Conservation of matter. Why the masses have to balance in the first place
Buy this experiment
We are putting together a Quantitative Chemistry Kit for Grade 10 with the test tubes, stoppers, delivery tube, beakers, measuring cylinder, watch glass and magnesium ribbon in one box, plus a printed teacher guide and the marking memo. Coming shortly.
Two of the four chemicals are supermarket items and we are not going to pretend otherwise. Bicarbonate of soda and vinegar come from the shop down the road. What you need from us is the glassware, the ribbon and the dilute acid.
The balance is the part worth thinking about. This practical works on a 0,1 g school balance if you weigh a metre of ribbon and cut by length. It does not work if you try to weigh 0,243 g directly, on any balance a normal school owns. The method above is the fix, and it costs nothing.
Everything else is standard: borosilicate test tubes at R4 each, low-form beakers, a glass measuring cylinder and a test tube rack.
The one thing to order early is the bent delivery tube. It is what makes the gas experiment possible, it is the most breakable item on the bench, and it is shared with the physical and chemical change practical. Buy the pack, not the single.