1. Quantitative Chemistry
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02/12/2018
Quantitative Chemistry
AQA 2016 Chemistry topic 3

2. 3.1 Conservation of Mass and Balanced Equations
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3.1 Conservation of Mass and Balanced Equations

3. Mass of products = mass of reactants
Chemical Reactions
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A chemical reaction is when atoms are basically rearranged into something different. For example, consider burning methane:
Methane oxygen
Carbon dioxide + water
Notice that no atoms were made or destroyed in this reaction, they were simply rearranged. Therefore we can write the Law of the Conservation of Mass:
Mass of products = mass of reactants

4. Sodium + water sodium hydroxide + hydrogen
Balancing equations
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Consider the following reaction:
Sodium + water sodium hydroxide + hydrogen Na O H O H Na + H +
This equation doesn’t balance – there are 2 hydrogen atoms on the left hand side (the “reactants” and 3 on the right hand side (the “products”)

5. Balancing equations We need to balance the equation:
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We need to balance the equation:
Sodium + water sodium hydroxide + hydrogen Na O H O H Na O H Na O H + H + Na
Now the equation is balanced, and we can write it as:
2Na(s) + 2H2O(l) NaOH(aq) + H2(g)

6. Some examples 2 2 3 2 3 Mg + O2 Zn + HCl Fe + Cl2 NaOH + HCl CH4 + O2
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Mg O2
Zn HCl
Fe Cl2
NaOH HCl
CH O2
Ca H2O
NaOH H2SO4
CH3OH O2
MgO
ZnCl H2
FeCl3
NaCl H2O
CO H2O
Ca(OH) H2
Na2SO H2O 2

7. PROTON NUMBER = number of protons (obviously)
Atomic mass
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RELATIVE ATOMIC MASS, Ar (“Mass number”) = number of protons + number of neutrons He 2 4
SYMBOL
PROTON NUMBER = number of protons (obviously)

8. Some simple compounds…
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Methane, CH4
Carbon dioxide, CO2
Water, H2O
Key
Hydrogen
Oxygen
Carbon
Sulphur
Sulphuric acid, H2SO4
Ethyne, C2H2

9. Relative formula mass, Mr
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The relative formula mass of a compound is the relative atomic masses of all the elements in the compound added together.
Relative atomic mass of O = 16
E.g. water H2O:
Relative atomic mass of H = 1
Therefore Mr for water = 16 + (2x1) = 18
Work out Mr for the following compounds:
HCl
NaOH
MgCl2
H2SO4
K2CO3
H=1, Cl=35 so Mr = 36
Na=23, O=16, H=1 so Mr = 40
Mg=24, Cl=35 so Mr = 24+(2x35) = 94
H=1, S=32, O=16 so Mr = (2x1)+32+(4x16) = 98
K=39, C=12, O=16 so Mr = (2x39)+12+(3x16) = 138

10. An example of Conservation of Mass
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Here’s a classic experiment where magnesium is burned in a crucible:
Mass of magnesium and crucible after burning = 78.56g
Mass of magnesium and crucible before burning = 78.25g
2Mg + O2 2MgO
Mass is always conserved in any reaction, so where did this extra mass come from?

11. Example Questions
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For each of the following reactions, state whether or not the mass of the total system should go up or down and explain your answer:
Iron + oxygen iron oxide
Copper carbonate copper oxide + carbon dioxide
For higher tier, write a balanced equation for each reaction, given that iron oxide is Fe2O3 and copper carbonate is CaCO3.

12. EXTENSION Write balanced symbol equations for above reactions
Example Questions
1) aluminium + oxygen → aluminium oxide
If you start with 27g of aluminium and 24g of oxygen, how much aluminium oxide will you make?
2) magnesium + oxygen → magnesium oxide
If you start with 24g of magnesium and make 40g of magnesium oxide, how much oxygen was used?
3) potassium oxide + water → potassium hydroxide
If you start with 9g of water and make 56g of potassium hydroxide, how much potassium oxide was used?
51g
16g
47g
EXTENSION Write balanced symbol equations for above reactions

13. 3.2 Moles (Higher only)
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14. Recap Questions
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Here are carbon and oxygen on the Periodic Table and a picture of carbon dioxide:
Carbon dioxide, CO2 C 6 12 O 8 16
What is the atomic mass of carbon?
What is the atomic mass of oxygen?
What is the molecular mass of carbon dioxide?

15. A “Mole” in numbers Definition:
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Definition:
A mole of a substance is the relative formula mass of that substance in grams,
For example, 12g of carbon would be 1 mole of carbon...
...and 44g of carbon dioxide (CO2) would be 1 mole etc...
Q. How many moles are the following?
23g of sodium
48g of magnesium
36g of carbon
28g of iron
1 mol
2 mol
3 mol
0.5 mol

16. Avogadro’s Constant: 1 mole = 6.02x1023 molecules
A “Mole”
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Definition:
A mole of a substance ALWAYS contains the same number of molecules/ions/particles/atoms:
Avogadro’s Constant: 1 mole = 6.02x1023 molecules
Q. How many moles are the following?
How many molecules are in 2 moles of carbon?
What about 2 moles of magnesium?
How many molecules are in 46g of sodium?
How many molecules are in 23g of iron?
1.2x1024
1.2x1024
1.2x1024
3.0x1023

17. Molar Calculations No. of moles = Mass (g) Molar mass (g/mol) N = m M
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No. of moles =
Mass (g)
Molar mass (g/mol)
N = m M
Some example questions:
Calculate the mass of 4 mol of lithium
Calculate the mass of 2 mol of sodium
Calculate the number of moles in 36g of carbon
Calculate the number of moles in 88g of carbon dioxide
Calculate the number of moles in 27g of water
28g
46g
3 mol
2 mol
1.5 mol

18. Calculating the mass of a product
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E.g. what mass of magnesium oxide is produced when 60g of magnesium is burned in air?
IGNORE the oxygen in step 2 – the question doesn’t ask for it
Step 1: READ the equation:
2Mg + O MgO
Step 2: WORK OUT the relative formula masses (Mr):
2Mg = 2 x 24 = MgO = 2 x (24+16) = 80
Step 3: LEARN and APPLY the following 3 points:
48g of Mg makes 80g of MgO
1g of Mg makes 80/48 = 1.66g of MgO
60g of Mg makes 1.66 x 60 = 100g of MgO

19. Calculating the mass of a product using moles
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Calculating the mass of a product using moles
Let’s try this question again but using moles:
Step 1: READ the equation:
2Mg + O MgO
“2 moles of magnesium + 1 mole of oxygen forms 2 moles of magnesium oxide”
Step 2: WORK OUT the relative formula masses (Mr) of MgO:
2MgO = 2 x (24+16) = 80
Step 3: Apply these steps:
60g of Mg is equal to 1.25 moles (60/48)
Therefore we will make 1.25 moles of magnesium oxide
Therefore we make 100g of MgO (1.25 moles)

20. Mr: 2Al2O3 = 2x((2x27)+(3x16)) = 204 4Al = 4x27 = 108
When water is electrolysed it breaks down into hydrogen and oxygen:
2H2O H2 + O2
What mass of hydrogen is produced by the electrolysis of 6g of water?
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Work out Mr: 2H2O = 2 x ((2x1)+16) = H2 = 2x2 = 4
36g of water produces 4g of hydrogen
So 1g of water produces 4/36 = 0.11g of hydrogen
6g of water will produce (4/36) x 6 = 0.66g of hydrogen
2) What mass of calcium oxide is produced when 10g of calcium burns?
2Ca + O CaO
Mr: 2Ca = 2x40 = CaO = 2 x (40+16) = 112
80g produces 112g so 10g produces (112/80) x 10 = 14g of CaO
3) What mass of aluminium is produced from 100g of aluminium oxide?
2Al2O Al + 3O2
Mr: 2Al2O3 = 2x((2x27)+(3x16)) = Al = 4x27 = 108
204g produces 108g so 100g produces (108/204) x 100 = 52.9g of Al2O3

21. So mass of product = (4/36) x 6g = 0.66g of hydrogen
Another method
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Try using this equation:
Mass of product IN GRAMMES
Mass of reactant IN GRAMMES
Mr of product
Mr of reactant
Q. When water is electrolysed it breaks down into hydrogen and oxygen:
2H2O H2 + O2
What mass of hydrogen is produced by the electrolysis of 6g of water?
Mass of product IN GRAMMES 4 6g 36
So mass of product = (4/36) x 6g = 0.66g of hydrogen

22. Using Moles to balance equations
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Example question:
130g of zinc reacts with 146g of hydrochloric acid (HCl) to form 272g of zinc chloride (ZnCl2) and some hydrogen (H2). Answer the following:
How much hydrogen was produced?
How many moles of each substance were reacted/produced?
Write a balanced chemical equation for this reaction. 4g
1 of Zn, 2 of HCl, 1 of ZnCl2, 1 of H2
Zn + 2HCl ZnCl2 + H2

23. Recap questions Key Carbon dioxide, CO2 Oxygen, O2 Methane, CH4
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Carbon dioxide, CO2
Oxygen, O2
Methane, CH4
Water, H2O
Key
Hydrogen
Oxygen
Carbon
Sulphur
What are the molecular masses of these four compounds?
How many grams of each compound would you have if you had one mole of each one?
Which mole is the heaviest?

24. Limiting Reactants
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What if we don’t get the ratios right? Example question:
Consider the reaction you have when you burn methane:
CH4 + 2O CO2 + 2H2O
A student burns 32g of methane in 72g of oxygen. Which reactant is used up completely?
32g of methane is 2 moles. 72g of oxygen is 2.25 moles of O2. Therefore this reaction is limited by the 2 moles of methane – the “limiting reactant”.
2 moles (88g)
Q. How much CO2 would we expect to produce?

25. A note about volume…
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The two most commonly used units of volume in chemistry are the cm3 and the dm3:
1dm3 (= 1000cm3)
1cm3
Convert 1250cm3 into dm3
Convert 1cm3 into dm3
Convert 0.056dm3 into cm3
Convert 1.28dm3 into cm3

26. Concentration
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Concentration means “how much of a chemical there is in a fixed volume” and can be measured in g/dm3 or mol/dm3.
A solution of low concentration (“dilute”)
A solution of high concentration (“strong”)

27. Questions on Concentration
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To calculate the concentration of a substance you could use one of these formulae:
Conc. = Mass of substance (g)
Volume of solvent (dm3)
Conc. = Amount of solute (mol)
Calculate, with units, the concentration of the following:
A solution of 10g salt in 1dm3 of water
2mol of hydrochloric acid in 500cm3 of water
10kg of salt in 200dm3 of water
0.5mol of sodium hydroxide in 100cm3 of water

28. Converting concentrations
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To convert g/dm3 into mol/dm3 you can use the following formula:
Concentration = Concentration (g/dm3)
(mol/dm3) Molar mass
Convert the following:
0.5mol/dm3 of sodium hydroxide into g/dm3.
2mol/dm3 of HCl into g/dm3.
20g/dm3 of NaCl into mol/dm3.
500g/dm3 of CaCl2 into mol/dm3.

29. Changing a Concentration
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Wow that’s a strong acid! How can I make it less concentrated?
What would you do to change an acid of concentration 1 mol/dm3 to an acid of concentration 0.1 mol/dm3?
Can you think of some examples where dilution is needed in food?

30. 3.3 Yield and Atom Economy of Chemical Reactions (Chem only)
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3.3 Yield and Atom Economy of Chemical Reactions (Chem only)

31. Problems with calculating mass
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Calculating the amount of a product or reactant may not always give you a reliable answer...
The reaction may not have completely _______
The reaction may have been _______
Some of the product may have been ____
Some of the reactants may have produced other _______
The amount of product that is made is called the “____”. This number can be compared to the maximum theoretical amount as a percentage, called the “percentage yield”.
Words – lost, yield, finished, reversible, products

32. Percentage Yield Percentage yield = Actual yield Predicted yield
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Percentage yield =
Actual yield
Predicted yield
X 100%
Some example questions:
The predicted yield of an experiment to make salt was 10g. If 7g was made what is the percentage yield?
Dave is trying to make water. If he predicts to make 15g but only makes 2g what is the percentage yield?
Sarah performs an experiment and has a percentage yield of 33%. If she made 50g what was she predicted to make?
70%
13%
150g

33. Percentage Yield (harder)
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Theoretical yield = the amount of product that should be made as calculated from the masses of atoms
Actual yield = what was actually produced in a reaction
Percentage yield = actual yield (in g)
theoretical yield
Example question:
65g of zinc reacts with 73g of hydrochloric acid and produces 102g of zinc chloride. What is the percentage yield?
Zn + 2HCl ZnCl2 + H2
The theoretical yield is 136g (using Cl = 35.5) so the % yield is 75%

34. Total masses of products
Atom Economy
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Percentage atom economy =
Relative formula mass of useful product
Total masses of products
Calculate the atom economies of the following:
Converting ethanol into ethene (ethene is the useful bit):
C2H5OH C2H4 + H20
Making zinc chloride from zinc and hydrochloric acid:
Zn + 2HCl ZnCl2 + H2
61%
99%

35. 3.4 Using Concentrations in mol/dm3 (Chemistry only)
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3.4 Using Concentrations in mol/dm3 (Chemistry only)

36. Revision about Moles Consider two liquids:
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Consider two liquids:
20cm3 of 0.1mol/dm3 of hydrochloric acid
20cm3 of 0.1mol/dm3 of sodium hydroxide
These two beakers contain the same number of moles
Now consider two gases:
20cm3 of helium at room temperature and pressure
20cm3 of argon at room temperature and pressure
These two gases contain the same number of moles

37. Titration
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1) Fill a burette with sodium hydroxide solution of known concentration
2) Accurately measure out 25cm3 of acid and place it in the conical flask
3) Add phenolphthalein indicator to the flask
4) Slowly add the alkali until the mixture in the flask turns pink (down to the next drop!)
5) Repeat until you get similar results

38. Titration Equations
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Q. 0.05dm3 of HCl neutralises 0.1dm3 of NaOH of concentration 0.5mol/dm3. What is the concentration of the acid?
The key steps:
1) Look at the equation to compare the numbers of moles:
HCl + NaOH NaCl + H2O
Notice that 1 mole of HCl neutralises 1 mole of NaOH
2) Use this equation:
No. of moles = concentration x volume
So, the number of moles of NaOH is (0.5 x 0.1) = 0.05mol
According to the equation, this will neutralise 0.05mol of HCl
Therefore we have (0.05mol/0.05dm3) = 1mol/dm3 HCl

39. Titration Equations
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0.2dm3 of HCl neutralises 0.1dm3 of NaOH of concentration 0.5mol/dm3. What is the concentration of the acid?
H2SO4 of concentration 0.4mol/dm3 neutralises 0.1dm3 of NaOH of concentration 0.2mol/dm3. How much acid was used?
HCl + NaOH NaCl + H2O
0.25mol/dm3
H2SO4 + 2NaOH Na2SO4 + 2H2O
0.025mol/dm3

40. 3.5 Amounts of substances in relation to volumes
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3.5 Amounts of substances in relation to volumes

41. Calculating Volumes of Gases
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An important fact: 1 mole of a gas at room temperature (20OC) and pressure (1 atm) occupies a volume of 24dm3.
What is the volume of 2 moles of oxygen?
What is the volume of 0.25 moles of carbon dioxide?
How many moles would be in 8dm3 of nitrogen?
How much volume would 80g of argon occupy?
A balloon contains 12dm3 of carbon dioxide. What is the mass of this much CO2?
48dm3
6dm3
1/3 mol
48dm3
22g

42. Calculating the volume of a product
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REMEMBER THIS - At normal temperature and pressure the Relative Formula Mass (Mr) of a gas will occupy a volume of 24 litres
e.g. 2g of H2 has a volume of 24 litres
32g of O2 has a volume of 24 litres
44g of CO2 has a volume of 24 litres etc
Q. When water is electrolysed it breaks down into hydrogen and oxygen:
2H2O H2 + O2
What VOLUME of hydrogen is produced by the electrolysis of 6g of water?
From previous work “Calculating the mass of a product” we find that the MASS of hydrogen produced was 0.66g
2g of hydrogen (H2) will occupy 24 litres (from the red box above),
So 0.66g will occupy 0.66/2 x 24 = 8 litres

43. Example questions 24dm3 120dm3 1dm3
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What volume of hydrogen is produced when 18g of water is electrolysed?
2H2O H2 + O2
Marble chips are made of calcium carbonate (CaCO3). What volume of carbon dioxide will be released when 500g of CaCO3 is reacted with dilute hydrochloric acid?
CaCO3 + 2HCl CaCl2 + H2O + CO2
Magnesium will react with hydrochloric acid. What volume of hydrogen would be produced if you reacted 1g of magnesium with excess acid?
Mg + 2HCl MgCl2 + H2
24dm3
120dm3
1dm3