1. Mass Relationships in Chemical Reactions
Chapter 3
Mass Relationships in Chemical Reactions

2. Atomic Mass What is atomic mass?
Mass of an atom in atomic mass units (AMU)
1 AMU is the mass of 1/12 of a carbon-12 atom
Also called atomic weight

3. Relative Atomic Mass
What does the relative atomic mass of an element represent?
Average mass of all known existing isotopes of that element
It is “unitless”
Proportioned based on abundance
Ex. Carbon has a mass of which is an average of all of the carbon isotopes

4. Isotope Proportions
A certain sample of element Z contains 60% of 69Z and 40% of 71Z.
What is the relative atomic mass of element Z in this sample?
𝑥=60% %(71)
𝑥= (71) 𝑥=
𝑥=69.8

5. Isotope Proportions
Chlorine exists as two isotopes, 35Cl and 37Cl. The relative atomic mass of chlorine is
Calculate the percentage abundance of each isotope.

6. Molar Mass and NA
What unit is used to measure the number of atoms/molecules?
Moles (mol) – the number of atoms in 12 grams of a carbon-12 sample
1 mole = 6.02 x 1023
Avogadro's number (NA)
We use it like we would a pair (2), dozen (12), or a gross (144) to simplify our math because it is freaking huge

7. How Big Is A Mole?
If you would distribute 1 mole of pennies among the current population of the Earth, how much would everyone get?
How long would it take to spend this amount if you would spend $1,000/day?
How many people could you make from 1 mole of cells?
How long is 1 mole of seconds?
If we took a mole of regular 8.5 x 11 inch sheets of paper and started laying them out side by side on the planet’s surface. What percentage of the Earth would be covered?

8. How Big Is A Mole? Answers
$900 million dollars
2,500,000 years
10 billion
950,000 x age of the universe (14 billion yrs)
100 %
…and it would be 17 million sheets thick

9. Molar Mass How is molar mass different from relative atomic mass?
It is the mass of one mole of a substance
Abbreviated MM
Same number as atomic mass, but with different units
Units: 𝑔 𝑚𝑜𝑙
IB Units: g mol-1

10. Molar Mass What is the molar mass (MM) of the following elements?
Lithium
Plutonium
Bromine
6.94 𝑔 𝑚𝑜𝑙
𝑔 𝑚𝑜𝑙
𝑔 𝑚𝑜𝑙

11. Molar Mass How do we determine the molar mass of a molecule?
What is the molar mass of water?
Add up the molar masses of each element within the molecule
H2O
MM = 2(H) + 1(O)
MM = 2(1.01) + 1(16.00 )
MM = 𝑔 𝑚𝑜𝑙

12. Molecular Vs. Molar
What is the difference between atomic, molecular and molar mass?
Different units for different purposes
Atomic/Molecular Mass  AMU’s
Molar Mass
 𝑔 𝑚𝑜𝑙
Can be used interchangeably

13. Molar Mass What is the molar mass of each of the following species:
KBr
FeCl3
Sodium Hydroxide
Lead (II) Oxide
𝑔 𝑚𝑜𝑙
𝑔 𝑚𝑜𝑙
𝑔 𝑚𝑜𝑙
𝑔 𝑚𝑜𝑙

14. Navigating
How can we navigate between mass (m), moles (n) and the number of atoms, molecules or particles?
We use molar mass (MM) and Avogadro's number (NA)

16. Double Circles

17. Double Triangles m N NA n n MM mass number moles moles molar mass
Avogadro's number n
moles n
moles MM
molar mass

18. Mass-Mole Conversions
How many moles in 28 grams of CO2 ?
What is the mass of 5 moles of Fe2O3 ?
Find the number of moles of argon in 452 g of argon.
Find the grams in 1.26 x 10-4 mol of HC2H3O2.
Find the mass in 2.6 mol of lithium bromide.
1 – 0.64 mol
2 – 800 g
3 – 11.3 mol
4 – g
5 – 230 g

19. Mole-Number Conversions
How many moles of magnesium is 3.01 x 1022 atoms of magnesium?
How many molecules are there in 4.00 moles of glucose, C6H12O6?
How many moles are 1.20 x 1025 atoms of phosphorous?
How many atoms are in moles of zinc?
How many oxygen atoms are in moles of N2O5?
1 – mol
2 – 2.41E24 molecules
3 – 19.9 mol
4 – 4.52E23 atoms
5 – 1.21E14 oxygen atoms

20. To the right, To the right
How many atoms are in 20.0 grams of gold?
Mass  20.0 g
Divide by molar mass to get to moles
0.102 moles
Multiply by Avogadro's number to get to atoms
6.14E22 Au atoms

21. To the left, To the left Number  1.00E24 atoms
What is the mass of 1.00E24 carbon atoms?
Number  1.00E24 atoms
Divide by Avogadro's number to get to moles
1.66 moles
Multiply by molar mass to get mass
19.9 grams

22. Combined
Find the mass in grams of 2.00 x 1022 molecules of diatomic fluorine.
Find the number of molecules in 60.0 g of dinitrogen monoxide.
How many molecules are in 5 mg of aspartame, C14H18N2O5?
1 – 1.26 g

23. Combined
Calculate the mass, in grams, of 6.69x1021 ethane (C2H6) molecules.
Urea [(NH2)2CO] is used for fertilizer and many other things. Calculate the number of N,C,O and H atoms in 1.68 x 104 grams of urea.
The density of water is 𝑔 𝑚𝐿 at 4°C. How many water molecules are present in 2.56 mL of water at this temperature?
4 – 0.334g
5 – 3.37E26 N atoms, 1.69E26 C atoms, 1.69E26 O atoms, 6.74E26 H atoms
6 – 8.56E22 molecules

24. PRELAB 1
Gum

25. PRELAB 1 Sugar in Chewing Gum
How can we test for the mass of sugar in chewing gum?

26. PRELAB 1 Sugar in Chewing Gum
In your notebook, please calculate the following with proper uncertainties, sig figs and units.
Experimental mass of sugar in the gum with the correct uncertainties
Percent mass of sugar in your piece of gum
Percent error = 𝐸𝑥𝑝 − 𝑇𝑟𝑢𝑒 𝑇𝑟𝑢𝑒 ×100

28. PRELAB 1 Sugar in Chewing Gum
Compare and contrast your measured percentage of sugar, and the actual percentage from the nutrition label for the brand of gum that you used.
What are some possible reasons for any differences in these values, and how you might increase the accuracy of your data collection?

29. PRELAB 1 Sugar in Chewing Gum
What mathematical relationship/formula did you use to determine percent by mass? Why?
If you were given one molecule of sucrose, C6H12O6, what information do you think you would need to figure out the percent mass of carbon? Why?

30. Percent Composition What is percent composition?
What two pieces of info do we need?
Relative measure of the mass of each different element present in the compound
𝑃𝑎𝑟𝑡 𝑊ℎ𝑜𝑙𝑒 x 100
Mass of the element and the compound

31. Percent Composition How do we calculate it?
Calculate the mass of the compound
Calculate the mass of each element
𝑚 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑚 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑 × 100

32. Percent Composition What is the percent mass of hydrogen in water?
2 hydrogens
2(1.01) = 2.02 g/mol
Water is H2O
18.02 g/mol
2.02/18.02 x100 =
11.2% (tenths place)

33. Percent Composition
Calculate the percent composition of oxygen in sodium sulfate.
Na2SO4  g/mol
4 oxygens
4(16.00) = g/mol
(64.00/142.04) x 100 =
45.1%

34. Percent Composition
Tartrazine, or yellow dye # 5, is commonly found in many foods. Its molecular formula is C16H9N4Na3O9S2 . What is the percent composition of Carbon and Sulfur? The molar mass of Tartrazine is g/mol.

35. Working in Reverse
If we start with %’s, what can that possibly lead us to?
Working the formula in reverse and using mole ratios, we can get the empirical and possibly the molecular formula

36. Determination of the Empirical Formula
How do we determine it?
Assume that you have 100% of the element and set equal to mass
Divide each element by its molar mass
Divide each by the smallest amount of moles
If numbers aren’t close to whole, multiply all of them by a coefficient

37. Butane’s Empirical Formula
Butane is made up of only carbon and hydrogen. If hydrogen makes up 17.34% of butane’s mass and carbon the remaining 82.66%, what is the empirical formula of butane?
C2H5
What is the molecular formula for butane if its molecular mass is g/mol?
Multiply each subscript by 2
C4H10

38. Determine the Empirical Formula
Determine the empirical formula of a compound having the following percent composition by mass…
K: 24.75%
Mn: 34.77%
O: %
Empirical Formula: KMnO4
What is the molecular formula if its molecular mass is g/mol?
ANSWER: KMnO4 (potassium permanganate)

39. Chemical Reactions and Equations
What is the difference between a chemical reaction and equation?
A chemical reaction is the process of making a new substance(s)
Ex. Iron oxidizing
A chemical equation is a symbolic representation of the reaction
4Fe + 3O2 → 2Fe2O3

40. Chemical Reactions and Equations
How do we read a chemical equation?
4Fe(s) + 3O2(g) → 2Fe2O3(s)
Reactants (left)
Products (right)
→ Goes in one direction
↔ Reversible reaction
Coefficients represent the mole ratios
Notations (s, l, g, aq) represent phases/states
Conservation of mass
Balanced

41. Chemical Reactions and Equations
What is a balanced equation?
The number of atoms on the left has to equal the number on the right
Use coefficients to balance them
Unbalanced:
CH4 + O2 → CO2 + H2O
Balanced:

42. Chemical Reactions and Equations
How do we balance the equations?
KClO3 → KCl + O2
2KClO3 → 2KCl + 3O2
Al + O2 → Al2O3
4Al + 3O2 → 2Al2O3
C2H6 + O2 → CO2 + H2O
2C2H6 + 7O2 → 4CO2 + 6H2O
223
432
2746

43. Chemical Reactions and Equations
Balance the following chemical equations:
K2CO3 + HCl  KCl + H2O + CO2
K2CO3 + 2HCl  2KCl + H2O + CO2
CaCO3 + HNO3  Ca(NO3)2 + H2O + CO2
CaCO3 + 2HNO3  Ca(NO3)2 + H2O + CO2
Pb(NO3)2 + NaI  PbI2 + NaNO3
Pb(NO3)2 + 2NaI  PbI2 + 2NaNO3
Al2(SO4)3 + NaOH  Al(OH)3 + Na2SO4
Al2(SO4)3 + 6NaOH  2Al(OH)3 + 3Na2SO4
12211
12111
1212
1623

44. Amounts of Reactants and Products
What is stoichiometry?
The study of any numerical observation within a chemical reaction
Using the mole method to determine how much reactant is needed (or product created) based on the number of moles

45. Amounts of Reactants and Products
What can be said about the reaction:
H2 + O2 → H2O
Reactants: Hydrogen and Oxygen
Products: Water
Unbalanced
Balanced: 2H2 + O2→2H2O
Proportion: 2 moles of hydrogen and 1 mole of oxygen create 2 moles of water

46. Amounts of Reactants and Products
How many moles of water should be formed with 8 moles of oxygen?
What happens when our measurements are not in moles?
1:2 Ratio
8 moles of oxygen is equivalent to 16 moles of water
Convert them into moles before starting using molar mass

47. Amounts of Reactants and Products

48. Amounts of Reactants and Products
I have the formula: Mg + HCl → MgCl2 + H2
What is the mass of MgCl2 that is formed when 20.0 g of HCl reacts with Mg?
Balance it
Mg + 2HCl → MgCl2 + H2
Convert into moles
(20.0 g)/(36.45 g/mol) = mol HCl
Use the mole ratio method
2:1 ratio → mol MgCl2
Convert back into mass
0.275 mol MgCl2 → 26.2 g

49. Amounts of Reactants and Products
What mass of silver nitrate as a solution in water would need to be added to 5.0 g of sodium chloride to ensure a complete precipitation of the chloride?
AgNO3(aq)+ NaCl (aq)  AgCl(s) + NaNO3(aq)
15 g

50. Amounts of Reactants and Products
What mass of barium sulfate would be produced from 10.0 g of barium chloride in the following reaction?
BaCl2 + H2SO4  BaSO4 + HCl
Balanced: BaCl2 + H2SO4  BaSO4 + 2HCl
11.2 g

51. Amounts of Reactants and Products
What volume of ammonia gas would be needed to produce 40. g of ammonium nitrate in the following reaction.
NH3 (g) + HNO3 (aq)  NH4NO3 (aq)

52. Amounts of Reactants and Products
In a fermentation reaction, glucose is converted to alcohol and carbon dioxide according to the following equation. What mass of alcohol and carbon dioxide would be produced from 10. g of glucose?
C6H12O6  C2H5OH + CO2
Balanced: C6H12O6  2C2H5OH + 2CO2

53. Reaction Yield
What is the difference between theoretical and actual yield?
What is its purpose?
Theoretical is the predicted amount of product via stoichiometry
Actual is how much product you obtained experimentally
To determine the efficiency of the procedure and/or experiment

54. Reaction Yield
What is the % yield of CO2 if you started with g of O2 obtained g of CO2?
CO + O2  CO2
Balanced:
2CO + O2 → 2CO2

55. Limiting Reagent What is a limiting reagent?
The reactant that is depleted first during a reaction is limiting
Prevents a reaction from achieving 100% yield
Any reactants remaining after the reaction completes are called excess reagents
i.e. anything in excess cannot be a limiting reagent

56. Limiting Reagent
124 g of aluminum react with 601 g of iron (III) oxide. Calculate the mass of Al2O3 formed.
Al + Fe2O3 → Al2O3 + Fe
2Al + Fe2O3 → Al2O3 + 2Fe
Balance!
Determine the number of moles of each reactant.
Divide by the molar coefficient to determine the limiting reagent
Use that number of moles to determine the amount produced using proper stoichiometry

57. Limiting Reagent Table
Reaction
2Al
Fe2O3
Al2O3
2Fe
Molar Mass (g/mol)
Initial Mass (g)
Initial Moles (mol)
Limiting Reagent (mol)
Final Moles (mol)
Final Mass (g)

58. Limiting Reagent Table
Reaction
2Al
Fe2O3
Al2O3
2Fe
Molar Mass (g/mol)
26.98
159.70
101.96
55.85
Initial Mass (g)
124
601
Initial Moles (mol)
Limiting Reagent (mol)
Final Moles (mol)
Final Mass (g)

59. Limiting Reagent Table
Reaction
2Al
Fe2O3
Al2O3
2Fe
Molar Mass (g/mol)
26.98
159.70
101.96
55.85
Initial Mass (g)
124
601
Initial Moles (mol)
4.60
3.76
Limiting Reagent (mol)
Final Moles (mol)
Final Mass (g)

60. Limiting Reagent Table
Reaction
2Al
Fe2O3
Al2O3
2Fe
Molar Mass (g/mol)
26.98
159.70
101.96
55.85
Initial Mass (g)
124
601
Initial Moles (mol)
4.60
3.76
Limiting Reagent (mol)
2.30
Final Moles (mol)
Final Mass (g)

61. Limiting Reagent Table
Reaction
2Al
Fe2O3
Al2O3
2Fe
Molar Mass (g/mol)
26.98
159.70
101.96
55.85
Initial Mass (g)
124
601
Initial Moles (mol)
4.60
3.76
Limiting Reagent (mol)
2.30
Final Moles (mol)
Final Mass (g)
367
235
257
Note: The mass of reactants equals the approximate mass of the products

62. Limiting Reagent
How much chlorine is produced in the following reaction when g of manganese (IV) oxide reacts with 48.2 g of hydrochloric acid?
MnO2 + 4HCl → MnCl2 + Cl2 + 2H2O
Reaction
MnO2
4HCl
MnCl2
Cl2
2H2O
Molar Mass (g/mol)
Initial Mass (g)
Initial Moles (mol)
Limiting Reagent (mol)
Final Moles (mol)
Final Mass (g)

63. Limiting Reagent
How much chlorine is produced in the following reaction when g of manganese (IV) oxide reacts with 48.2 g of hydrochloric acid?
MnO2 + 4HCl → MnCl2 + Cl2 + 2H2O
Reaction
MnO2
4HCl
MnCl2
Cl2
2H2O
Molar Mass (g/mol)
86.93
36.46
125.83
70.90
18.02
Initial Mass (g)
47.25
48.2
Initial Moles (mol)
Limiting Reagent (mol)
Final Moles (mol)
Final Mass (g)

64. Limiting Reagent
How much chlorine is produced in the following reaction when g of manganese (IV) oxide reacts with 48.2 g of hydrochloric acid?
MnO2 + 4HCl → MnCl2 + Cl2 + 2H2O
Reaction
MnO2
4HCl
MnCl2
Cl2
2H2O
Molar Mass (g/mol)
86.93
36.46
125.83
70.90
18.02
Initial Mass (g)
47.25
48.2
Initial Moles (mol)
0.5435
1.32
Limiting Reagent (mol)
Final Moles (mol)
Final Mass (g)

65. Limiting Reagent
How much chlorine is produced in the following reaction when g of manganese (IV) oxide reacts with 48.2 g of hydrochloric acid?
MnO2 + 4HCl → MnCl2 + Cl2 + 2H2O
Reaction
MnO2
4HCl
MnCl2
Cl2
2H2O
Molar Mass (g/mol)
86.93
36.46
125.83
70.90
18.02
Initial Mass (g)
47.25
48.2
Initial Moles (mol)
0.5435
1.32
Limiting Reagent (mol)
0.330
Final Moles (mol)
Final Mass (g)

66. Limiting Reagent
How much chlorine is produced in the following reaction when g of manganese (IV) oxide reacts with 48.2 g of hydrochloric acid?
MnO2 + 4HCl → MnCl2 + Cl2 + 2H2O
Reaction
MnO2
4HCl
MnCl2
Cl2
2H2O
Molar Mass (g/mol)
86.93
36.46
125.83
70.90
18.02
Initial Mass (g)
47.25
48.2
Initial Moles (mol)
0.5435
1.32
Limiting Reagent (mol)
0.330
Final Moles (mol)
0.660
Final Mass (g)

67. Limiting Reagent
How much chlorine is produced in the following reaction when g of manganese (IV) oxide reacts with 48.2 g of hydrochloric acid?
MnO2 + 4HCl → MnCl2 + Cl2 + 2H2O
Reaction
MnO2
4HCl
MnCl2
Cl2
2H2O
Molar Mass (g/mol)
86.93
36.46
125.83
70.90
18.02
Initial Mass (g)
47.25
48.2
Initial Moles (mol)
0.5435
1.32
Limiting Reagent (mol)
0.330
Final Moles (mol)
0.660
Final Mass (g)
28.7
48.1
41.5
23.4
11.9

68. Excess Reagent
If you started with g, how much manganese (IV) oxide is left in excess after the reaction is completed?
47.25 – 28.7 = 18.6 g of MgO2 excess
Reaction
MnO2
4HCl
MnCl2
Cl2
2H2O
Molar Mass (g/mol)
86.93
36.46
125.83
70.90
18.02
Initial Mass (g)
47.25
48.2
Initial Moles (mol)
0.5435
1.32
Limiting Reagent (mol)
0.330
Final Moles (mol)
0.660
Final Mass (g)
28.7
48.1
41.5
23.4
11.9

69. Limiting Reagent
0.709 g
LR – ozone
mol excess

70. Limiting Reagent
Practice Problem – pg. 93
NH3
1124 g
319 g

71. Limiting Reagent
Practice Problem – pg. 95
8.93 x 10^6
89%

72. Limiting Reagent
Practice Problem – pg. 96
863 g
93%

73. Reaction Yield
7.05 g
93%