1. The Arithmetic of
Chemistry
Stoichiometry and
Chemical Equations

2. 1. FORMULA: Potassium bromide
2. FORMULA: Iron (III) oxide
3. NAME: BaCl2
4. NAME: (NH4)2S
5. What IFA exist/s between ammonia and
acetone?

3. Micro World Macro World
atoms & molecules grams
Atomic mass is the mass of an atom in
atomic mass units (amu)
By definition:
1 atom 12C “weighs” 12 amu
On this scale
1H = 1.008 amu
16O = 16.00 amu
3.1

4. Natural lithium is:
7.42% 6Li (6.015 amu)
92.58% 7Li (7.016 amu)
Average atomic mass of lithium:
7.42 x 6.015 + 92.58 x 7.016
= 6.941 amu
100
3.1

5. Average atomic mass (6.941)

7. The mole (mol) is the amount of a substance that
contains as many elementary entities as there
are atoms in exactly 12.00 grams of 12C
1 mol = NA = 6.0221367 x 1023
Avogadro’s number (NA)
3.2

8. The Mole
Therefore:
1.00 mole of water = 6.02 x 1023 molecules
of H2O
1.00 mole of NaCl = 6.02 x 1023 Na+ ions
= 6.02 x 1023 Cl- ions

9. eggs
Molar mass is the mass of 1 mole of shoes in grams
marbles
atoms
1 mole 12C atoms = 6.022 x 1023 atoms = 12.00 g
1 12C atom = 12.00 amu
1 mole 12C atoms = 12.00 g 12C
1 mole lithium atoms = 6.941 g of Li
For any element
atomic mass (amu) = molar mass (grams)
3.2

10. Mole to Mass Relationships
Balanced chemical reaction gives molar ratios

11. Amadeo Avogadro Jean Baptiste Perrin
(1776-1856) ( 1870-1942)
Jean Perrin originated the term “Avogadro’s
Number” in 1909. Perrin won the Nobel
Physics Prize in 1926

12. One Mole of:
C S
Hg
Cu Fe
3.2

13. 1 12C atom 12.00 g 1.66 x 10-24 g
x 23 12C atoms
=
12.00 amu 6.022 x 10 1 amu
1 amu = 1.66 x 10-24 g or 1 g = 6.022 x 1023 amu
M = molar mass in g/mol
NA = Avogadro’s number
3.2

14. Do You Understand Molar Mass?
How many atoms are in 0.551 g of potassium (K) ?
1 mol K = 39.10 g K
1 mol K = 6.022 x 1023 atoms K
1 mol K 6.022 x 1023 atoms K
0.551 g K x x =
39.10 g K 1 mol K
8.49 x 1021 atoms K
3.2

15. Molecular mass (or molecular weight) is the sum of
the atomic masses (in amu) in a molecule.
1S 32.07 amu
2O + 2 x 16.00 amu
SO2 SO2 64.07 amu
For any molecule
molecular mass (amu) = molar mass (grams)
1 molecule SO2 = 64.07 amu
1 mole SO2 = 64.07 g SO2
3.3

16. Do You Understand Molecular Mass?
How many H atoms are in 72.5 g of C3H8O ?
1 mol C3H8O = (3 x 12) + (8 x 1) + 16 = 60 g C3H8O
1 mol C3H8O molecules = 8 mol H atoms
1 mol H = 6.022 x 1023 atoms H
1 mol C3H8O 8 mol H atoms 6.022 x 1023 H atoms
72.5 g C3H8O x x x =
60 g C3H8O 1 mol C3H8O 1 mol H atoms
5.82 x 1024 atoms H
3.3

17. Percent composition of an element in a compound =
n x molar mass of element
x 100%
molar mass of compound
n is the number of moles of the element in 1 mole
of the compound
2 x (12.01 g)
%C = x 100% = 52.14%
46.07 g
6 x (1.008 g)
%H = x 100% = 13.13%
46.07 g
1 x (16.00 g)
%O = x 100% = 34.73%
46.07 g
C2H6O 52.14% + 13.13% + 34.73% = 100.0%
3.5

18. A process in which one or more substances is changed into one
or more new substances is a chemical reaction
A chemical equation uses chemical symbols to show what
happens during a chemical reaction
3 ways of representing the reaction of H2 with O2 to form H2O
reactants products
3.7

19. How to “Read” Chemical Equations
2 Mg + O2 2 MgO
2 atoms Mg + 1 molecule O2 makes 2 formula units MgO
2 moles Mg + 1 mole O2 makes 2 moles MgO
48.6 grams Mg + 32.0 grams O2 makes 80.6 g MgO
IS NOT
2 grams Mg + 1 gram O2 makes 2 g MgO
3.7

20. Balancing Chemical Equations
 Must have the same
number of each
element on both
sides of the equation

21. Recall: The Laws of Chemical
Combination
 Law of Conservation of Matter
Matter is neither created nor destroyed in a chemical
reaction.
 Law of Definite Composition
Elements combine in fixed amounts in a compound.
 Law of Multiple Proportion
If two elements A and B combine to form more than
one compound, the masses of B that react with a given
mass of A are in ratio of small whole numbers.

22. Recall: Writing the Formula
of Compounds
 Formulas for molecules:
H2O, CO2, CH4, C6H12O6
 Formulas for ions (charged particles):
OH- , NO3- , PO43- ,
H+, NH4+
 Formulas for ionic compounds
NaOH, NH4NO3, FeCl3

23. Balancing Chemical Equations
1. Write the correct formula(s) for the reactants on
the left side and the correct formula(s) for the
product(s) on the right side of the equation.
Ethane reacts with oxygen to form carbon dioxide and water
C2H6 + O2 CO2 + H2O
2. Change the numbers in front of the formulas
(coefficients) to make the number of atoms of
each element the same on both sides of the
equation. Do not change the subscripts.
2C2H6 NOT C4H12
3.7

24. Balancing Chemical Equations
3. Start by balancing those elements that appear in
only one reactant and one product.
C2H6 + O2 CO2 + H2O start with C or H but not O
2 carbon 1 carbon
multiply CO2 by 2
on left on right
C2H6 + O2 2CO2 + H2O
6 hydrogen 2 hydrogen
multiply H2O by 3
on left on right
C2H6 + O2 2CO2 + 3H2O
3.7

25. Balancing Chemical Equations
4. Balance those elements that appear in two or
more reactants or products.
C2H6 + O2 2CO2 + 3H2O multiply O2 by 7
2
2 oxygen 4 oxygen + 3 oxygen = 7 oxygen
on left (2x2) (3x1) on right
C2H6 + 7 O2 remove fraction
2CO2 + 3H2O
2 multiply both sides by 2
2C2H6 + 7O2 4CO2 + 6H2O
3.7

26. Balancing Chemical Equations
5. Check to make sure that you have the same
number of each type of atom on both sides of the
equation.
2C2H6 + 7O2 4CO2 + 6H2O
12C (2 xx2)
14 H (2 6)
4 O (7 2) 1412 H (6 2 + 6)
O (4 C x 2)
4x
Reactants Products
4C 4C
12 H 12 H
14 O 14 O
3.7

27. Mass Changes in Chemical Reactions
1. Write balanced chemical equation
2. Convert quantities of known substances into moles
3. Use coefficients in balanced equation to calculate the
number of moles of the sought quantity
4. Convert moles of sought quantity into desired units 3.8

28. Methanol burns in air according to the equation
2CH3OH + 3O2 2CO2 + 4H2O
If 209 g of methanol are used up in the combustion,
what mass of water is produced?
grams CH3OH moles CH3OH moles H2O grams H2O
molar mass coefficients molar mass
CH3OH chemical equation H2O
1 mol CH3OH 4 mol H2O 18.0 g H2O
209 g CH3OH x x x =
32.0 g CH3OH 2 mol CH3OH 1 mol H2O
235 g H2O
3.8

29. Limiting Reagents
6 green used up
red left over
3.9

30. Assembling a Handout

31. Assembling a Handout

32. Assembling a Handout
What is the limiting page?

33. Assembling a Handout
What is the limiting page?

34. Assembling a Handout
What is the limiting page?

35. Do You Understand Limiting Reagents?
In one process, 124 g of Al are reacted with 601 g of Fe2O3
2Al + Fe2O3 Al2O3 + 2Fe
Calculate the mass of Al2O3 formed.
g Al mol Al mol Fe2O3 needed g Fe2O3 needed
OR
g Fe2O3 mol Fe2O3 mol Al needed g Al needed
1 mol Al 1 mol Fe2O3 160. g Fe2O3
124 g Al x x x = 367 g Fe2O3
27.0 g Al 2 mol Al 1 mol Fe2O3
Start with 124 g Al need 367 g Fe2O3
Have more Fe2O3 (601 g) so Al is limiting reagent
3.9

36. Use limiting reagent (Al) to calculate amount of product that
can be formed.
g Al mol Al mol Al2O3 g Al2O3
2Al + Fe2O3 Al2O3 + 2Fe
1 mol Al 1 mol Al2O3 102. g Al2O3
124 g Al x x x = 234 g Al2O3
27.0 g Al 2 mol Al 1 mol Al2O3
3.9

37. Theoretical Yield is the amount of product that would
result if all the limiting reagent reacted.
Actual Yield is the amount of product actually obtained
from a reaction.
Actual Yield
% Yield = x 100
Theoretical Yield
3.10

38. Test yourself: Limiting reagent
 In the Haber process, ammonia (NH3) is
produced from hydrogen gas and nitrogen
gas. If I have 40.0g hydrogen gas and 30.0g
nitrogen gas, what will be the mass of
ammonia I produce? What amount (in
moles) of reactants will be used up?

39. Some General Types of Simple
Chemical Reactions
1. Combination/Addition Reactions
2. Decomposition Reactions
3. Single replacement/displacement/substitution
4. Double replacement/displacement
5. Neutralization
6. Combustion

40. 1. Combination Reactions
 Two or more substances (elements or
compounds) react to produce one compound
 Also known as “synthesis” or “addition”
 A + Z  AZ
 Metal oxygen metal oxide
 Nonmetal oxygen nonmetal oxide
 Metal nonmetal salt
 Water metal oxide base
 Metal oxide nonmetal oxide salt

41. Test Yourself: Combination
1. Magnesium metal and oxygen react to form
a metal oxide. Balance the equation.
2. Sulfur trioxide and sulfur dioxide can be
formed (in separate reactions) from sulfur
and oxygen gas.
3. Carbon and oxygen combine to form two
different species, depending on the amount
of oxygen.
4. Water and sulfur trioxide form sulfuric acid.

42. Stoichiometry: Combination
 Working at 273.15K and 1atm (STP), I have 10.0g
of carbon and 56L of oxygen. Under these
conditions, I know 1mol of any gas has a volume of
22.4L (Molar volume at STP). What is the limiting
reagent? If carbon monoxide made sure to be
formed, what will be its volume?
 If the reaction takes place in a giant balloon, what
will be the final volume of the balloon (considering
the conditions are kept constant).

43. 2. Decomposition
 ONE substance reacts to form two or more
substances (elements or compounds).
 AZ  A + Z
 Compound compound/element oxygen
 Metal carbonate metal oxide carbon dioxide
 Hydrated salt salt water
 Compound compound/element water

44. Test yourself: decomposition
1. Mercury (II) oxide decomposes into mercury
and oxygen.
2. Potassium nitrate decomposes into
potassium nitrite and oxygen.
3. Hydrogen peroxide decomposes into
hydrogen and oxygen.
4. Water electrolysis creates hydrogen and
oxygen.

45. Stoichiometry: Decomposition
 Sodium azide produces nitrogen gas and
sodium metal. At standard temperature and
pressure, what will be the volume of nitrogen
gas produced from 60.0g sodium azide?

46. 3. Single Replacement
 Also known as single displacement or substitution.
 A metal (A) replaces a metal ion (B=metal) in its salt
or a hydrogen ion (B=H) in an acid
 A + BZ  AZ +B
 Ex. Fe(s) + CuSO4(aq)  FeSO4(aq) + Cu(s)
 Ex. Sn(s) + HCl(aq)  SnCl2(aq) + H2(g)
 A nonmetal (X) replacing another nonmetal (Z) in its
salt (B=metal) or acid (B=H)
 Cl2(g) + NaBr (aq)  _____________________________
 Bromine + Potassium Iodide ______________________

47. 4. Double Replacement
 Also known as “Double displacement”,
“Metathesis”, or “Double decomposition.”
 Two compounds are involved with the cation of
one compound EXCHANGING with the cation of
another compound.
 AX + BZ  AZ + BX
 These reactions proceed if one of the ff. is
satisfied:
1. An insoluble/slightly soluble product is formed
(PRECIPITATE formation)
2. A weakly ionized species is produced. The most common
species of this type is water.
3. A gas is produced as a product.

48. Test yourself: metathesis
1. Insoluble silver chloride is produced in the
double displacement of silver nitrate and
hydrochloric acid.
2. Nickel (II) nitrate reacts with sodium
hydroxide in a metathesis reaction.
3. Double decomposition occurs with the
addition of table salt to an aqueous solution
of silver nitrate.

49. 5. Neutralization
 Reaction of an acid and a base that usually
produces a salt and water.
 HX + MOH  MX + HOH
 Hydrochloric acid and sodium hydroxide.
 Hydrochloric acid and magnesium hydroxide.
 Sulfuric acid and Barium hydroxide
 To be discussed in a separate lesson

50. 6. Combustion
 Reactions involving oxygen (metal +oxygen),
(nonmetal + oxygen), (organic compounds + oxygen)
are sometimes called combustion reactions.
 Energy is given off in combustion reactions.
 For organic compounds, water and carbon dioxide
are usual byproducts.
 Ex. Metabolism of food, fuel combustion:
 Sucrose (C22H12O11) combusts
 Combustion of propane
 Combustion of hydrogen