Relative formula mass and conservation of mass
By the end of this chapter you will be able to
- Use the periodic table to find Ar, and add the Ar values to find Mr
- Work out the percentage by mass of an element in a compound
- Balance a symbol equation by counting atoms on each side
- Find an empirical formula from the masses of the elements in a compound
- Use the masses in a balanced equation to predict the mass of a product or gas
You should already know
- Relative atomic mass from the periodic table (Chapter 1)
- Formulae and atoms in formulae (Chapter 1)
Where this leads
- The mole, reacting masses and limiting reactants (Chapter 8)
- Concentration of solutions (Chapter 9)
- Electrolysis and Faraday masses (Chapter 11)
GCSE Chemistry. Content follows the GCSE (9-1) subject content for England (Edexcel and AQA). Content references: Calculate relative formula mass (Mr) from relative atomic masses, Calculate the percentage by mass of an element in a compound, Explain conservation of mass, balance symbol equations and use state symbols, Calculate the empirical formula from masses or percentages, Use a balanced equation to find the mass of a product or a gas, and mass ratios.
Exercise P Do you remember?
Method. Multiply 2 by 16.
- Multiply. 2 x 16 = 32.32
- Write the answer. 32
Check. 32 / 2 = 16. ✓
Method. Multiply first, then add.
- Multiply. 2 x 16 = 32.32
- Add. 12 + 32 = 44.44
- Write the answer. 44
Check. 44 - 32 = 12. ✓
Method. Dividing by 100 and multiplying by 100 cancel.
- Simplify. The two steps give 40 / 100 x 100 = 40.40
- Write the answer. 40
Check. 40 / 100 = 0.4, and 0.4 x 100 = 40. ✓
Method. Read the subscript after O.
- Read. The subscript 2 is after O.2 O atoms
- Write the answer. 2
Check. CO2 has one carbon and two oxygen atoms. ✓
Method. Add the two values.
- Add. 23 + 35.5 = 58.5.58.5
- Write the answer. 58.5
Check. 58.5 - 35.5 = 23. ✓
Relative formula mass (Mr)
The relative atomic mass (Ar) of an element is on the periodic table. The relative formula mass (Mr) of a compound is the sum of the Ar values of all the atoms in the formula. Relative masses have no units. Multiply each Ar by the number of atoms of that element, then add the results.
| Element | Relative atomic mass (Ar) |
|---|---|
| H | 1 |
| C | 12 |
| N | 14 |
| O | 16 |
| Na | 23 |
| Mg | 24 |
| S | 32 |
| Cl | 35.5 |
| Ca | 40 |
| Fe | 56 |
| Cu | 64 |
| Compound | Working | Mr |
|---|---|---|
| H2O | 2 x 1 + 16 | 18 |
| CO2 | 12 + 2 x 16 | 44 |
| CaCO3 | 40 + 12 + 3 x 16 | 100 |
| H2SO4 | 2 x 1 + 32 + 4 x 16 | 98 |
| Na2CO3 | 2 x 23 + 12 + 3 x 16 | 106 |
Key ideas
- Mr = the sum of all the relative atomic masses in the formula.
- Multiply each Ar by the number of atoms first, then add.
- Relative masses have no units.
- Brackets are not used here; write each formula out in full.
Method. Multiply, then add.
- Hydrogen. There are 2 H atoms, so 2 x 1 = 2.2 x 1 = 2
- Oxygen. There is 1 O atom, so 1 x 16 = 16.16
- Add. Mr = 2 + 16.2 + 16 = 18
- Write the answer. 18
Check. Water has Mr 18. ✓
Method. Add the three elements, with the correct numbers of atoms.
- Calcium. 1 Ca atom: 1 x 40 = 40.40
- Carbon. 1 C atom: 1 x 12 = 12.12
- Oxygen. 3 O atoms: 3 x 16 = 48.48
- Add. 40 + 12 + 48.100
- Write the answer. 100
Check. Calcium carbonate has Mr 100. ✓
Method. Use the number of atoms of each element.
- Sodium. 2 Na atoms: 2 x 23 = 46.46
- Carbon. 1 C atom: 12.12
- Oxygen. 3 O atoms: 3 x 16 = 48.48
- Add. 46 + 12 + 48 = 106.106
- Write the answer. 106
Check. Sodium carbonate has Mr 106. ✓
Watch out
Watch out: multiply each Ar by the number of atoms before you add. A common mistake is to add 16 once for each O, when there are three O atoms in CaCO3.
Exam tip
Exam tip. Write the working as a list of elements and totals before you add. It makes it easy to check.
Exercise 7A Relative formula mass
Method. Read the periodic table.
- Read. The relative atomic mass of oxygen is 16.16
- Write the answer. 16
Check. O is element 8 in the periodic table. ✓
Method. Read the periodic table.
- Read. The relative atomic mass of sodium is 23.23
- Write the answer. 23
Check. Sodium has atomic number 11. ✓
Method. One C and two O.
- Carbon. 1 x 12 = 12.12
- Oxygen. 2 x 16 = 32.32
- Add. 12 + 32 = 44.44
- Write the answer. 44
Check. Carbon dioxide has Mr 44. ✓
Method. One Mg and one O.
- Magnesium. 1 x 24 = 24.24
- Oxygen. 1 x 16 = 16.16
- Add. 24 + 16 = 40.40
- Write the answer. 40
Check. Magnesium oxide has Mr 40. ✓
Method. One N and three H.
- Nitrogen. 1 x 14 = 14.14
- Hydrogen. 3 x 1 = 3.3
- Add. 14 + 3 = 17.17
- Write the answer. 17
Check. Ammonia has Mr 17. ✓
Method. One C and four H.
- Carbon. 1 x 12 = 12.12
- Hydrogen. 4 x 1 = 4.4
- Add. 12 + 4 = 16.16
- Write the answer. 16
Check. Methane has Mr 16. ✓
Method. Two Al and three O.
- Aluminium. 2 x 27 = 54.54
- Oxygen. 3 x 16 = 48.48
- Add. 54 + 48 = 102.102
- Write the answer. 102
Check. Aluminium oxide has Mr 102. ✓
Method. One Mg and two Cl.
- Magnesium. 1 x 24 = 24.24
- Chlorine. 2 x 35.5 = 71.71
- Add. 24 + 71 = 95.95
- Write the answer. 95
Check. Magnesium chloride has Mr 95. ✓
Method. Two H, one S and four O.
- Hydrogen. 2 x 1 = 2.2
- Sulfur. 1 x 32 = 32.32
- Oxygen. 4 x 16 = 64.64
- Add. 2 + 32 + 64 = 98.98
- Write the answer. 98
Check. Sulfuric acid has Mr 98. ✓
Method. One Cu, one S and four O.
- Copper. 1 x 64 = 64.64
- Sulfur. 1 x 32 = 32.32
- Oxygen. 4 x 16 = 64.64
- Add. 64 + 32 + 64 = 160.160
- Write the answer. 160
Check. Copper sulfate has Mr 160. ✓
Method. Two Fe and three O.
- Iron. 2 x 56 = 112.112
- Oxygen. 3 x 16 = 48.48
- Add. 112 + 48 = 160.160
- Write the answer. 160
Check. Iron(III) oxide has Mr 160. ✓
Method. Multiply the number of O atoms by the Ar of oxygen.
- Oxygen. 4 x 16 = 64.64
- Write the answer. 64
Check. The other atoms make up 98 - 64 = 34. ✓
Method. Think about the formula.
- Think. A formula shows every atom in one molecule.every atom
- Conclude. So adding each atom’s relative mass gives the total mass of the molecule.total mass
- Write the answer. Accept any sentence that says the Mr is the total mass of all the atoms in the formula.
Check. Relative masses have no units. ✓
Method. Check the number of O atoms.
- Look. CO2 has two O atoms; pupil A used only one.two O atoms
- Conclude. So pupil B is correct, with Mr = 44.B
- Write the answer. B
Check. Pupil A forgot one oxygen atom. ✓
Method. Think about isotopes.
- Think. Chlorine has isotopes with different mass numbers.isotopes
- Conclude. The Ar is the weighted average of these, so it can be a decimal.average
- Write the answer. Accept any sentence that says the Ar is an average of the isotopes.
Check. This is the same idea as Chapter 1. ✓
Percentage by mass
The percentage by mass of an element in a compound is:
percentage = (Ar x number of atoms of the element) / Mr x 100
Use the Mr from section 7.1, and the number of atoms of the element in one formula.
| Compound | Element | Working | Percentage by mass |
|---|---|---|---|
| MgO | Mg | 24 / 40 x 100 | 60% |
| MgO | O | 16 / 40 x 100 | 40% |
| CaCO3 | O | 48 / 100 x 100 | 48% |
| Fe2O3 | Fe | 112 / 160 x 100 | 70% |
| CuO | Cu | 64 / 80 x 100 | 80% |
Key ideas
- Percentage by mass = (Ar x number of atoms) / Mr x 100.
- The Mr is the total mass of the compound; the Ar x number is the mass of the element in it.
- Give the answer to an appropriate number of significant figures, usually one or two decimal places.
- Check that the element percentages in a compound add up to 100 if you have them all.
Method. Use the formula.
- Mass of Mg. One Mg atom has mass 24.24
- Mr. The Mr of MgO is 24 + 16 = 40.40
- Percentage. 24 / 40 x 100 = 60.60
- Write the answer. 60
Check. The oxygen is the other 40%, and 60 + 40 = 100. ✓
Method. Find the mass of carbon, and the Mr.
- Mass of C. One C atom has mass 12.12
- Mr. The Mr of CaCO3 is 100.100
- Percentage. 12 / 100 x 100 = 12.12
- Write the answer. 12
Check. Carbon is 12% of calcium carbonate by mass. ✓
Method. Two Fe atoms contribute the iron mass.
- Mass of Fe. Two Fe atoms: 2 x 56 = 112.112
- Mr. The Mr of Fe2O3 is 160.160
- Percentage. 112 / 160 x 100 = 70.70
- Write the answer. 70
Check. The oxygen makes up the other 30%. ✓
Watch out
Watch out: use the number of atoms of the element (for example 2 Fe in Fe2O3), not 1. Forgetting the number of atoms is the most common error.
Exam tip
Exam tip. Write the Mr first, then the mass of the element, then divide and multiply by 100. Show each line.
Exercise 7B Percentage by mass
Method. One Cu and one O.
- Add. 64 + 16 = 80.80
- Write the answer. 80
Check. Copper oxide has Mr 80. ✓
Method. Oxygen is 16 out of 40.
- Divide. 16 / 40 x 100 = 40.40
- Write the answer. 40
Check. Magnesium is the other 60%. ✓
Method. One Ca, out of Mr 100.
- Divide. 40 / 100 x 100 = 40.40
- Write the answer. 40
Check. Calcium is 40% of calcium carbonate. ✓
Method. Three O atoms out of Mr 100.
- Mass of O. 3 x 16 = 48.48
- Divide. 48 / 100 x 100 = 48.48
- Write the answer. 48
Check. 40 + 12 + 48 = 100. ✓
Method. One Cu out of Mr 80.
- Divide. 64 / 80 x 100 = 80.80
- Write the answer. 80
Check. The oxygen is the other 20%. ✓
Method. Two Fe out of Mr 160.
- Mass of Fe. 2 x 56 = 112.112
- Divide. 112 / 160 x 100 = 70.70
- Write the answer. 70
Check. The rest is oxygen: 30%. ✓
Method. One C out of Mr 44.
- Mass of C. 12.12
- Divide. 12 / 44 x 100 = 27.27..., which is 27.3 to one decimal place.27.3
- Write the answer. 27.3
Check. The oxygen is about 72.7%. ✓
Method. Two H out of Mr 18.
- Mass of H. 2 x 1 = 2.2
- Divide. 2 / 18 x 100 = 11.11..., which is 11.1.11.1
- Write the answer. 11.1
Check. The oxygen is about 88.9%. ✓
Method. Multiply 60% by the Mr.
- Percentage. 60% of 40 = 0.6 x 40.0.6 x 40
- Answer. The mass of magnesium is 24.24
- Write the answer. 24
Check. Magnesium has Ar 24. ✓
Method. One N out of Mr 17.
- Mass of N. 1 x 14 = 14.14
- Divide. 14 / 17 x 100 = 82.35..., which is 82.4 to one decimal place.82.4
- Write the answer. 82.4
Check. Hydrogen is 17.6%. ✓
Method. Think about the Mr and the percentage.
- Think. The percentage depends on the Mr and on the mass of oxygen only.depends
- Conclude. A compound with a larger Mr from other elements can have a lower percentage of oxygen.lower percentage
- Write the answer. Accept any sentence that says the percentage depends on the other elements as well as oxygen.
Check. This is a comparison of percentages, not of masses. ✓
Method. Compare the two percentages.
- Compare. MgO is 60% magnesium; CaCO3 is 40% calcium.60% and 40%
- Decide. So MgO has the larger percentage of its metal.MgO
- Write the answer. MgO
Check. Both values were calculated above. ✓
Conservation of mass and balancing equations
In a chemical reaction, the total mass of the reactants equals the total mass of the products. This is the law of conservation of mass. Atoms are rearranged, not created or destroyed. A balanced symbol equation has the same number of each type of atom on both sides.
Use state symbols in brackets: (s) solid, (l) liquid, (g) gas, (aq) aqueous solution.
| Equation | Atoms on each side | Result |
|---|---|---|
| 2Mg + O2 -> 2MgO | 2 Mg, 2 O | balanced |
| CH4 + 2O2 -> CO2 + 2H2O | 1 C, 4 H, 4 O | balanced |
| N2 + 3H2 -> 2NH3 | 2 N, 6 H | balanced |
Key ideas
- Mass is conserved in a reaction; the total mass is the same before and after.
- Balance by changing the numbers in front of formulae (coefficients), never the small numbers in formulae.
- Count each element on both sides before you finish.
- State symbols: (s), (l), (g) and (aq).
Method. Count the atoms, then add numbers in front.
- Count. Left: 2 H and 2 O. Right: 2 H and 1 O.2 O on left, 1 O on right
- Balance O. Put 2 in front of H2O: now 2 O and 4 H on the right.2H2O
- Balance H. Put 2 in front of H2: now 4 H and 2 O on each side.2H2 + O2 -> 2H2O
- Write the answer. 2H2 + O2 -> 2H2O
Check. Four H and two O on each side. ✓
Method. Balance the oxygen first, then the magnesium.
- Count. Left: 1 Mg and 2 O. Right: 1 Mg and 1 O.2 O on left
- Balance. Put 2 in front of MgO: 2 Mg and 2 O on the right.2MgO
- Check. Put 2 in front of Mg: 2 Mg and 2 O on each side.2Mg + O2 -> 2MgO
- Write the answer. 2Mg + O2 -> 2MgO
Check. Two Mg and two O on each side. ✓
Method. Decide the state of the product.
- Look. The silver chloride formed is a solid that comes out of solution.solid
- Decide. The state symbol for a solid is (s).(s)
- Write the answer. (s)
Check. The other products are aqueous. ✓
Watch out
Watch out: never change the small subscript numbers in a formula to balance an equation. For example, H2O must stay H2O; only the number in front (2H2O) can change.
Exam tip
Exam tip. Balance the equation, then count each element on both sides once more before you write the answer.
Exercise 7C Conservation of mass and balancing equations
Method. Recall the law.
- Recall. The total mass of the products equals the total mass of the reactants.total mass same
- Write the answer. mass is not created or destroyed in a reaction
Check. Atoms are rearranged. ✓
Method. Balance the oxygen to 2 O first.
- Balance. Put 2 in front of MgO and 2 in front of Mg.2Mg + O2 -> 2MgO
- Write the answer. 2
Check. Two Mg atoms on each side. ✓
Method. Each chlorine atom needs one sodium.
- Balance. Cl2 has 2 Cl; put 2 in front of NaCl, then 2 in front of Na.2Na + Cl2 -> 2NaCl
- Write the answer. 2
Check. Two Na and two Cl on each side. ✓
Method. Balance C, then H, then O.
- C and H. One C and four H on each side is already balanced once H2O has 2 in front.2H2O
- O. Right side: 2 (from CO2) + 2 (from 2H2O) = 4 O, so 2O2 on the left.2O2
- Write the answer. 2
Check. CH4 + 2O2 -> CO2 + 2H2O is balanced. ✓
Method. Balance the N first, then the H.
- N. Two N on the left, so 2 NH3.2NH3
- H. Six H are needed on the right, so 3H2 on the left.3H2
- Write the answer. 3, 2
Check. N2 + 3H2 -> 2NH3 is balanced. ✓
Method. Count each element.
- Ca. 1 Ca on each side.1 Ca
- C. 1 C on each side.1 C
- O. 3 O on each side.3 O
- Write the answer. yes
Check. All the atoms are balanced. ✓
Method. Recall the state symbols.
- Recall. Gases use the symbol (g).(g)
- Write the answer. (g)
Check. Liquids use (l) and aqueous solutions use (aq). ✓
Method. Recall the state symbols.
- Recall. Liquids use the symbol (l).(l)
- Write the answer. (l)
Check. Water as a gas is (g). ✓
Method. Recall the state symbols.
- Recall. A substance dissolved in water is aqueous, (aq).(aq)
- Write the answer. (aq)
Check. Solid sodium chloride is (s). ✓
Method. Count the atoms on each side.
- Fe. One Fe on each side.1 Fe
- Cu, S, O. One Cu, one S and four O on each side.1 Cu, 1 S, 4 O
- Write the answer. yes
Check. Iron displaces copper from copper sulfate. ✓
Method. Think about the atoms.
- Atoms. The atoms are only rearranged in the reaction.rearranged
- Conclude. No atoms leave the flask, so the total mass is conserved.mass conserved
- Write the answer. Accept any sentence that says no atoms are lost or gained, so the total mass is conserved.
Check. A gas escaping from an open container seems to lose mass. ✓
Method. Think about the products.
- Products. Carbon dioxide and water vapour escape into the air.escape
- Conclude. If they are not collected, their mass is not measured, so the balance seems to change.not measured
- Write the answer. Accept any sentence that says the products escape as gases, so the mass of the products in the flask is not measured.
Check. In a closed system the mass is conserved. ✓
Empirical formula
The empirical formula is the simplest whole-number ratio of the atoms in a compound. To find it: divide the mass of each element by its Ar to get the ratio of moles of atoms, then divide each number by the smallest, and multiply to get whole numbers if needed.
Key ideas
- Empirical formula = simplest whole-number ratio of atoms.
- Step 1: divide the mass of each element by its Ar.
- Step 2: divide each result by the smallest result.
- Step 3: write the numbers as subscripts, if they are whole numbers.
Method. Divide each mass by the Ar, then find the simplest ratio.
- Magnesium. 2.4 / 24 = 0.1.0.1
- Oxygen. 1.6 / 16 = 0.1.0.1
- Ratio. The ratio is 0.1 : 0.1, which is 1 : 1.1 : 1
- Write the answer. MgO
Check. Magnesium oxide is MgO. ✓
Method. Use the Ar of each element.
- Iron. 5.6 / 56 = 0.1.0.1
- Oxygen. 2.4 / 16 = 0.15.0.15
- Ratio. Divide both by 0.05: 0.1 / 0.05 = 2 and 0.15 / 0.05 = 3, so 2 : 3.2 : 3
- Write the answer. Fe2O3
Check. Iron(III) oxide is Fe2O3. ✓
Method. Treat the percentages as masses in 100 g, then divide by the Ar.
- Carbon. 40 / 12 = 3.33.3.33
- Hydrogen. 6.7 / 1 = 6.7.6.7
- Oxygen. 53.3 / 16 = 3.33.3.33
- Ratio. Divide by 3.33: C = 1, H = 2, O = 1.C : H : O = 1 : 2 : 1
- Write the answer. CH2O
Check. The formula of a sugar-type compound (empirical). ✓
Watch out
Watch out: the empirical formula is the simplest ratio, not the real formula of a molecule. Glucose is C6H12O6, but its empirical formula is CH2O.
Exam tip
Exam tip. Set out a table: element, mass, Ar, divide, ratio. Keep at least two decimal places until the last step.
Exercise 7D Empirical formula
Method. Recall the definition.
- Recall. The empirical formula shows the simplest ratio of the atoms in a compound.simplest ratio
- Write the answer. the simplest whole-number ratio of atoms
Check. The real molecular formula may be larger. ✓
Method. Write the symbols with their ratio.
- Write. One Mg and one O: MgO.MgO
- Write the answer. MgO
Check. The ratio 1 : 1 gives no subscripts. ✓
Method. Divide the mass by the Ar.
- Divide. 2.4 / 24 = 0.1.0.1
- Write the answer. 0.1
Check. 0.1 x 24 = 2.4. ✓
Method. Divide the mass by the Ar.
- Divide. 1.6 / 16 = 0.1.0.1
- Write the answer. 0.1
Check. 0.1 x 16 = 1.6. ✓
Method. Divide both by the smaller number.
- Divide. 0.1 / 0.1 = 1 and 0.1 / 0.1 = 1.1 : 1
- Write the answer. 1 : 1
Check. The formula is MgO. ✓
Method. Divide the mass by the Ar.
- Divide. 5.6 / 56 = 0.1.0.1
- Write the answer. 0.1
Check. 0.1 x 56 = 5.6. ✓
Method. Work out the oxygen ratio.
- Divide. 2.4 / 16 = 0.15.0.15
- Ratio. 0.15 / 0.05 = 3.3
- Write the answer. 3
Check. With iron, 0.1 / 0.05 = 2. ✓
Method. Divide both by the smaller number, 0.05.
- Divide. 0.1 / 0.05 = 2 and 0.15 / 0.05 = 3.2 : 3
- Formula. So the formula is Fe2O3.Fe2O3
- Write the answer. Fe2O3
Check. Iron(III) oxide. ✓
Method. Treat the percentages as masses in 100 g.
- Iron. 70 / 56 = 1.25.1.25
- Oxygen. 30 / 16 = 1.875.1.875
- Ratio. Divide by 1.25: Fe = 1, O = 1.5; doubling gives 2 : 3.2 : 3
- Write the answer. Fe2O3
Check. The formula is Fe2O3. ✓
Method. Use the three masses.
- Divide. C: 40/12 = 3.33; H: 6.7; O: 53.3/16 = 3.33.3.33 : 6.7 : 3.33
- Ratio. Divide by 3.33 to get 1 : 2 : 1.1 : 2 : 1
- Write the answer. CH2O
Check. The empirical formula is CH2O. ✓
Method. Compare the two formulae.
- Look. C6H12O6 is 6 times CH2O.6 x CH2O
- Conclude. The molecular formula is a whole-number multiple of the empirical formula.multiple
- Write the answer. Accept any sentence that says the molecular formula is a multiple of the empirical formula.
Check. Glucose is an example. ✓
Using balanced equations to find masses
A balanced equation gives a mass ratio. For example, in 2H2 + O2 -> 2H2O, the masses are 2 x 2 = 4 g of hydrogen, 32 g of oxygen, and 36 g of water. To find the mass of a product from a given mass of a reactant, take the mass ratio from the equation and scale it to the mass you have.
Key ideas
- Mass ratios come from the balanced equation, using Mr values.
- In a reaction, the total mass of products equals the total mass of reactants.
- A gas that escapes from an open container has a mass that you must calculate, not measure.
- Check your answer: products must add up to the reactant mass when all products are counted.
Method. Use the masses from the balanced equation.
- Ratio. The equation makes 2 x 18 = 36 g of water from 4 g of hydrogen, with 32 g of oxygen.36 g
- Scale. The hydrogen mass is 4 g, which is exactly the mass in the equation.no scaling needed
- Write the answer. 36
Check. Oxygen 32 g + hydrogen 4 g = 36 g. ✓
Method. Use the mass of CO2 per 100 g of CaCO3.
- Equation. 100 g of CaCO3 gives 44 g of CO2.44 g per 100 g
- Scale. 25 g is a quarter of 100 g, so 44 / 4 = 11 g.11 g
- Write the answer. 11
Check. The mass of CaO is 25 - 11 = 14 g, which is 56 / 4. ✓
Method. Use the mass ratio of Mg to MgO from the equation.
- Ratio. The equation has 48 g of Mg giving 80 g of MgO.48 : 80
- Scale. So 4.8 g gives 4.8 x 80 / 48 = 8.0 g of MgO.8.0 g
- Write the answer. 8
Check. Check: 8.0 g MgO - 4.8 g Mg = 3.2 g of oxygen, which is 32 x 4.8 / 48 = 3.2. ✓
Watch out
Watch out: a mass ratio uses the masses from the balanced equation (2 x Mr for 2 molecules), not the Mr of one molecule alone.
Exam tip
Exam tip. First write the balanced equation, then the mass of each substance in the equation, then scale to the mass given.
Exercise 7E Using balanced equations to find masses
Method. Add the masses of the reactants.
- Hydrogen. 2 x 2 = 4 g.4 g
- Oxygen. O2 has mass 32 g.32 g
- Total. 4 + 32 = 36 g.36
- Write the answer. 36
Check. 36 g of water is made. ✓
Method. Use the Mr of CO2.
- Mr. The Mr of CO2 is 44.44
- Mass. The mass of CO2 made is 44 g.44 g
- Write the answer. 44
Check. 100 = 56 + 44. ✓
Method. Use the Mr of CaO.
- Mr. The Mr of CaO is 40 + 16 = 56.56
- Mass. So 56 g of CaO is made.56 g
- Write the answer. 56
Check. 56 + 44 = 100. ✓
Method. Subtract the product from the reactants.
- Subtract. 10 - 9.5 = 0.5.0.5
- Write the answer. 0.5
Check. Conservation of mass: the missing 0.5 g escaped as a gas. ✓
Method. Use the ratio of Mg to MgO.
- Ratio. 48 g of Mg makes 80 g of MgO.48 : 80
- Scale. For 20 g of MgO: 48 x 20 / 80 = 12 g.12 g
- Write the answer. 12
Check. 12 g of Mg with 8 g of O2 makes 20 g of MgO. ✓
Method. Use the ratio of Mg to O2.
- Ratio. 48 g of Mg reacts with 32 g of O2.48 : 32
- Scale. For 12 g: 32 x 12 / 48 = 8 g.8 g
- Write the answer. 8
Check. Mass conservation: 12 + 8 = 20 g of MgO. ✓
Method. Use conservation of mass: the products have the same mass as the reactants.
- Reactants. 16 g of methane reacts with 2 x 32 = 64 g of O2.16 + 64
- Products. The total mass of products is 80 g, the same as the reactants.80
- Write the answer. 80
Check. Conservation of mass gives 80 g. ✓
Method. Think about the escape of the gas.
- Escape. The gas escapes into the air, so it is not collected.escapes
- Calculate. Its mass can be found from the mass ratio or from the mass lost.calculated
- Write the answer. Accept any sentence that says the gas escapes, so it is found from the mass ratio or by subtraction.
Check. Conservation of mass makes this possible. ✓
Method. Use conservation of mass.
- Law. The total mass of the products equals the total mass of the reactants.equal
- Conclude. So a single product cannot be heavier than all the reactants together.not heavier
- Write the answer. Accept any sentence that says the total mass is conserved, so the products cannot be heavier than the reactants.
Check. Only the total is conserved, not each product separately. ✓
Chapter summary
| Skill | Method |
|---|---|
| Mr | The sum of the Ar values of all the atoms in the formula; no units. |
| Percentage by mass | (Ar x number of atoms) / Mr x 100. |
| Conservation of mass | The total mass of the products equals the total mass of the reactants. |
| Balancing equations | Change only the numbers in front; the same atoms on both sides. |
| State symbols | (s), (l), (g), (aq). |
| Empirical formula | Divide mass by Ar, divide by the smallest, write the simplest whole-number ratio. |
| Mass ratios | Use the masses in the balanced equation, then scale to the mass given. |
Can you…?
- I can calculate Mr from Ar values
- I can work out the percentage by mass of an element in a compound
- I can explain conservation of mass and balance symbol equations
- I can write state symbols correctly
- I can find an empirical formula from masses or percentages
- I can use a balanced equation to find the mass of a product or a gas
Key terms
- relative atomic mass (Ar)
- the average mass of an atom of an element, compared with carbon-12
- relative formula mass (Mr)
- the sum of the relative atomic masses of all the atoms in a formula
- conservation of mass
- the total mass of the products equals the total mass of the reactants
- balanced symbol equation
- an equation with the same number of each atom on both sides
- state symbol
- a symbol showing the physical state: (s), (l), (g) or (aq)
- empirical formula
- the simplest whole-number ratio of the atoms in a compound
Exercise 7Z Check-up
Method. One Ca and two Cl.
- Ca. 40.40
- Cl. 2 x 35.5 = 71.71
- Add. 40 + 71 = 111.111
- Write the answer. 111
Check. Calcium chloride has Mr 111. ✓
Method. Oxygen is 16 out of Mr 40.
- Divide. 16 / 40 x 100 = 40.40
- Write the answer. 40
Check. Magnesium is 60%. ✓
Method. Copper is 64 out of Mr 80.
- Divide. 64 / 80 x 100 = 80.80
- Write the answer. 80
Check. Oxygen is 20%. ✓
Method. Balance the Cl first.
- Balance. Two Cl on the right, so 2HCl on the left.2HCl
- Write the answer. 2
Check. Mg + 2HCl -> MgCl2 + H2 is balanced. ✓
Method. Recall the symbol for a solution.
- Recall. A dissolved substance is aqueous, (aq).(aq)
- Write the answer. (aq)
Check. Copper metal is (s). ✓
Method. Divide each mass by its Ar.
- Oxygen. 1.6 / 16 = 0.1.0.1
- Magnesium. 2.4 / 24 = 0.1.0.1
- Write the answer. 0.1, 0.1
Check. The ratio is 1 : 1, so MgO. ✓
Method. Half of 100 g gives half of 44 g.
- Scale. 50 g is half of 100 g, so 44 / 2 = 22 g.22 g
- Write the answer. 22
Check. The mass of CaO made is 28 g. ✓
Method. Recall the law.
- Recall. Atoms are not created or destroyed in a reaction.not created
- Conclude. So the total mass of reactants equals the total mass of products.equal
- Write the answer. Accept any sentence that says the total mass of the products equals the total mass of the reactants.
Check. Atoms are rearranged. ✓
Method. Two Na, one C and three O.
- Na. 2 x 23 = 46.46
- C. 12.12
- O. 3 x 16 = 48.48
- Add. 46 + 12 + 48 = 106.106
- Write the answer. 106
Check. Sodium carbonate has Mr 106. ✓
Total 25 marks. Allow about 25 minutes.
Exercise 7X Exam-style questions
Method. Two Al and three O.
- Al. 2 x 27 = 54.54
- O. 3 x 16 = 48.48
- Add. 54 + 48 = 102.102
- Write the answer. 102
Check. Aluminium oxide has Mr 102. ✓
Method. Mass of Al divided by Mr.
- Al. 2 x 27 = 54.54
- Mr. Mr = 102.102
- Percentage. 54 / 102 x 100 = 52.94..., which is 52.9.52.9
- Write the answer. 52.9
Check. The oxygen is 47.1%. ✓
Method. Balance the Fe in Fe2O3 first.
- Fe. The right side has 2 Fe2O3, so 4 Fe atoms are needed on the left.4 Fe
- O. The right side has 6 O, so 3 O2 are needed on the left.3 O2
- Check. 4Fe + 3O2 -> 2Fe2O3: 4 Fe and 6 O on each side.4
- Write the answer. 4
Check. 4Fe + 3O2 -> 2Fe2O3 is balanced. ✓
Method. Recall the symbol for a gas.
- Recall. Water vapour is a gas, so the symbol is (g).(g)
- Write the answer. (g)
Check. Liquid water is (l). ✓
Method. Divide the mass by the Ar, then find the ratio.
- Fe. 5.6 / 56 = 0.1.0.1
- O. 2.4 / 16 = 0.15.0.15
- Ratio. Divide by 0.05: Fe = 2, O = 3, so Fe2O3.Fe2O3
- Write the answer. Fe2O3
Check. The formula is iron(III) oxide. ✓
Method. Use the mass ratio from the equation.
- Ratio. 48 g of Mg makes 80 g of MgO.48 : 80
- Scale. For 6.0 g: 80 x 6.0 / 48 = 10 g.10 g
- Write the answer. 10
Check. Oxygen used: 4 g. ✓
Method. Think about where the gas goes.
- Escape. The gas escapes into the air and is not in the container.escapes
- Conserve. Its mass is still part of the total, so the mass is conserved overall.conserved
- Write the answer. Accept any answer that says the gas escapes and is not weighed, though the total mass of all the products is conserved.
Check. Conservation applies to the whole system. ✓
Method. Divide each percentage by the Ar.
- Mg. 60 / 24 = 2.5.2.5
- O. 40 / 16 = 2.5.2.5
- Ratio. The ratio is 1 : 1, so the formula is MgO.MgO
- Write the answer. MgO
Check. Magnesium oxide. ✓
Method. Scale from 100 g.
- Ratio. 100 g of CaCO3 gives 44 g of CO2.44 g
- Scale. 10 g is one tenth, so 44 / 10 = 4.4 g.4.4 g
- Write the answer. 4.4
Check. The CaO made is 5.6 g. ✓
Method. Count the atoms on each side.
- Left. CH4 + 2O2 has 1 C, 4 H and 4 O.1 C, 4 H, 4 O
- Right. CO2 + 2H2O has 1 C, 4 H and 4 O.1 C, 4 H, 4 O
- Write the answer. Accept any answer that counts 1 C, 4 H and 4 O on each side.
Check. Each element is the same on both sides. ✓