1. CH 11: The Mole
Section 1 Counting Matter

2. Counting Matter
What are some everyday ways
we count matter?
1. DOZEN = 12 things
2. 1 GROSS = 144 things
What about molecules? Or atoms?
3. BUSHEL of corn = 21.772 kg 1 MOLE = ???

3. The Mole
 It represents a
counted number of
things.
 IN Chemistry the term
MOLE represents the
number of particles in
a substance.
In Chemistry is NOT this furry little animal
or the spot on your face…

4. Just how many is a mole?
 One mole represents 6.02 x 1023 of things
(units, molecules, compounds, formula units).
This is called Avogadro’s number.
 One mole of most elements contains
6.02 x 1023 atoms.
 1 mole O2 = 6.02x1023 molecules of O2
 602 000 000 000 000 000 000 000

5. Just how big is a mole?
 Listen to The Mole Song!
 An Avogadro's number of standard soft drink
cans would cover the surface of the earth to a
depth of over 200 miles
 If you had Avogadro's number of un-popped
popcorn kernels, and spread them across the
United States of America, the country would be
covered in popcorn to a depth of over 9 miles.
 If we were able to count atoms at the rate of 10
million per second, it would take about 2 billion
years to count the atoms in one mole.

6. Solving the Problems Samples
Required: dimensional analysis/factor label
 How many molecules are in 3.00 moles of
N2?
6.02 x 1023 moleculesN 2
3 molesN 2 1.81 1024 molecules
1 mole N 2
 How many moles of Na are in 1.10 x 1023
atoms?
23 1 mole Na
1.10 10 atoms 0.182 moles Na
6.02 x 10 23 atoms Na

7. Practice moles to particles
 Determine the number of atoms in 2.50
mol Zn.
 Given 3.25 mol AgNO3, determine the
number of formula units.
 Calculate the number of molecules in 11.5
mol H2O.

8. Practice Particles to Moles
 How many moles contain each of the
following?
 5.75 x 1024 atoms Al
 3.75 x 1024 molecules CO2
 3.58 x 1023 formula units ZnCl2
 2.50 x 1020 atoms Fe

9. Mixed Avogadro’s number Practice
1. How many moles are in 2x1060 atoms of Cu?
2. If there are 1.25x1045 molecules of dihydrogen
monoxide in a glass, how many moles are there?
3. 5 mol of Iron III sulfate is equal to how many
compounds of Fe2(SO4)3
4. For every 3.5 mol of S there are how many
atoms of sulfur?
5. How many mol of O atoms are in 1.50 mol SO2?
6. How many mol of H are in 1 mol (NH4) 2CO3?
7. How many atoms of H are in 1 mol (NH4) 2CO3?

10. 11-2 Mass & the Mole
11-3 Moles of Compounds

11. Molar Mass
 Defn: is the mass (think grams) of one
mole of a substance
 Atomic masses (from periodic table)
represent molar mass.
 Units g/mol
 1 mole of Carbon has 6.02 x 1023 atoms of C
and they have a mass of 12.01 grams.
 To calculate the molar mass of a
compound, you add up the molar masses
of all the elements in that compound

12. Molar Mass Practice
 What is the mass of 1.00 mole of
Oxygen? Of Nitrogen? 1 mole O = 16.0 grams
1 mole N = 14.0 grams
 Find the molar mass for:
 SO3 SO3= 80 g/mole
 Na2SO4 1 Mole = 142.043g
Tutorial Site
Molar Mass Calculator for homework help

13. Molar Mass Practice
 When you see 1.00 mole = _?_
g, think “g means GO to the
PERIODIC TABLE” to find the molar
mass.
http://www.webelements.com/

14. Practice Problems
 Determine the molar mass of each of the
following ionic compounds:
 NaOH
 CaCl2
 KC2H3O2
 HCN
 CCl4
 H2O

15. Grams-Mole Conversions
 How many moles are in 56.8 g of HCl?
1 moleHCl
56.8 g HCl 1.58 molesHCl
36 g HCl
 How many grams are in .05 moles Na2SO4?
90 g Na 2SO 4
.05 mole Na 2SO 4 4.5 g Na 2SO 4
1 mole Na 2SO 4

16. Practice Mole to Grams
 Determine the mass in grams of each of
the following.
 3.57 mol Al
 42.6 mol Si
 3.45 mol Co
 2.45 mol Zn

17. Practice Gram to Mole
 How many atoms are in each of the
following samples?
 55.2 g Li
 0.230 g Pb
 11.5 g Hg
 45.6 g Si
 0.120 kg Ti

18. Ex: Mass to Particle Conversion
 Gold is one of a group of metals called the coinage
metals (copper, silver and gold). How many atoms of
gold (Au) are in a pure gold nugget having a mass of
25.0 g?
Known: Unknown:
Mass = 25.0 g Au Number of atoms = ? Atoms Au
Molar mass Au = 196.97 g/mol Au
25.0 g Au x 1 mole Au x 6.02 x 1023 atoms Au = 7.65 x 1022 atoms Au
196.97 g Au 1 mol Au

19. Practice Problems
 How many atoms are in each of the
following samples?
 55.2 g Li
 0.230 g Pb
 11.5 g Hg
 45.6 g Si
 0.120 kg Ti

20. Ex: Particle to Mass Conversion
 A party balloon contains 5.50 x 1022 atoms of helium
(He) gas. What is the mass in grams of the helium?
Known: Unknown:
Number of atoms = 5.50 x 1022 atoms He Mass = ? G He
Molar mass He = 4.00 g/mol He
5.50 x 1022 atoms He x 1 mol He x 4.00 g He = 0.366 g He
6.02 x 1023 atoms He 1 mol He

21. Practice Problems
 What is the mass in grams of each of the
following?
 6.02 x 1024 atoms Bi
 1.00 x 1024 atoms Mn
 3.40 x 1022 atoms He
 1.50 x 1015 atoms N
 1.50 x 1015 atoms U

22. Molar Volume
 The volume of a gas is usually measured at
standard temperature and pressure (_STP_)
 Standard temp = ___0°_ C
 Standard pressure = ___1___ atmosphere
(atm)
 1 mole of any gas occupies __22.4__ L of
space at STP

23. Molar Volume Practice
 How many moles would 45.0 L of He gas
be?
 How many liters of O2 would 3.8 moles
occupy?

24. Putting it all together
 1.0 mole = _6.02 x 1023___atoms or molecules
1.0 mole = _?__ g(PT)
1.0 mole = _22.4 L (at STP)

25. Helpful Chart!
MOLES
Volume
Grams
in Liters
Atoms
or Molecules

26. Chemical Formulas and the
Mole
 Chemical formula for a compound indicates
the types of atoms and the number of each
contained in one unit.
 Ex. CCl2F2 - Freon
 Ratio of carbon to chlorine to fluorine is 1:2:2
 Ratios can be written: or
 In one mole of freon you would have 1 mole of carbon,
2 moles of chlorine and 2 moles of fluorine.

27. Ex: Mole Relationship from
Chemical Formulas
 Determine the moles of aluminum ions (Al3+)
in 1.25 moles of aluminum oxide
1.25 molAl2O3 x 2 mol Al3+ ions = 2.50 mol Al3+ ions
1 mole Al2O3

28. Practice Problems
 Determine the number of moles of chloride ions
in 2.53 mol ZnCl2.
 Calculate the number of moles of each element
in 1.25 mol glucose (C6H12O6).
 Determine the number of moles of sulfate ions
present in 3.00 mol iron (III) sulfate (Fe2(SO4)3).
 How many moles of oxygen atoms are present
in 5.00 mol diphosphorus pentoxide?
 Calculate the number of moles of hydrogen
atoms in 11.5 mol water.

29. Practice Problems Mixed
 How many chloride ions are in 2.50 mol of ZnCl2
 Calculate the number of atoms of each element
in 1.25 mol glucose (C6H12O6).
 Determine the number of moles of sulfate ions
present in 6.02x1023 compounds of iron (III)
sulfate (Fe2(SO4)3).
 How many atoms of oxygen are present in
3.01x1023 molecules of diphosphorus pentoxide?
 Calculate the number of molecules in 11.5 mol
water.

30. Practice Problems
 A sample of silver chromate has a mass of 25.8 g.
 How many Ag+ ions are present?
 How many CrO42- ions are present?
 What is the mass in grams of one unit of silver chromate?
 What mass of sodium chloride contains 4.59 x 1024
units?
 A sample of ethanol (C2H5OH) has a mass of 45.6 g.
 How many carbon atoms does the sample contain?
 How many hydrogen atoms are present?
 How many oxygen atoms are present?

31. 11-4 Empirical &
Molecular Formulas

32. Percent Composition
 the percentage by mass of each element
in a compound
 The percent comp. is found by using the
following formula:
mass of 1 element
% Mass 100
molarmass of compound

33. Percent Composition Example
Ex. Compound XY is 55g element X and 45g
element Y
55 g of element X x 100 = 55 % element X
100 g of compound
45 g of element Y x 100 = 45 % element Y
100 g of compound

34. Percent Composition from
Chemical Formula
 First find the molar mass of each element and
the molar mass of the compound
 Ex: what is the % composition of H in 1 mole of
H2O?
 Multiplythe molar mass of the element by its
subscript in the formula.
 1.01 g/mol H x 2 mol = 2.02 g H
% by mass H = 2.02 g x 100 = 11.2% H
18.02 g H2O

35. Percent Composition from
Chemical Formula
Example continued –
 Molar mass of O for each mole of H2O?
 16.00 g/mol O x 1mol O = 16.00 g O
16.00 g x 100 = 88.8 % O
18.02 g

36. % Composition Practice
 What is the percent of C & H in C2H6?
 What is the percent of each element in
Na2SO3?

37. Empirical Formulas
 This is the LOWEST whole number ratio of
the elements in a compound. For
example, the empirical formula for
 Molecular Formula C6H6
 Empirical Formula CH
 What is the empirical formula for each?
 C2H6
 C6H12O6

38. 11-3: Calculating Empirical
Formula
 Steps for caluculating Empirical Formula give mass or
percent composition:
1. If given a percent sign (%), remove the sign &
change to GRAMS.
 You are assuming you have 100 g of the compound.
2. Convert grams ---> moles.
3. Select lowest number of moles
4. Divide each number of moles by this number.
5. If the number divides out evenly, these are the
subscripts of the elements in the compound.
6. If any of the numbers have a .5, MULTIPLY them
ALL by TWO & then place these numbers as the
subscripts.

39. Example Using Percent
Composition
 The percent composition of an oxide of
sulfur is 40.05% S and 59.95% O.
Assuming you have a 100g sample, it
contains 40.05g S and 59.95g O.
 Convert to moles using molar mass:
40.05g S x 1 mol = 1.249 mol S
32.07g
59.95g O x 1 mol = 3.747 mol O
16.00g

40. Example Using Percent
Composition
The mole ratio of S atoms to O atoms in the oxide
is 1.249 : 3.747.
Recognize that S has the smallest possible
number of moles at ~1. Make the mole value of
S equal to 1 by dividing both mole values by
1.249.
1.249 mol S = 1 mol S
1.249
3.747 mol O = 3 mol O
1.249
The simplest whole number mole ratio of S atoms to O atoms is 1 : 3.
The empirical formula for the oxide of sulfur is SO3.

41. Sample Problems
 What is the empirical formula for a
compound which is 75 % C and 25 % H?
 What is the empirical formula for a compound
which has
 48.64 % C,
 8.16 % H
 43.20 % O

42. Sample Problems #2
 What is the empirical formula of
 40.68 %C
 5.08 % H
 54.24 % O

43. Practice Problems
 A blue solid is found to contain 36.894% N and 63.16% O. What is
the empirical formula for this solid?
 Determine the empirical formula for a compound that contains
35.98% Al and 64.02% S.
 Propane is a hydrocarbon, a compound composed only of carbon
and hydrogen. It is 81.82% C and 18.18% H. What is the empirical
formula?
 The chemical analysis of aspirin indicates that the molecule is
60.00% C, 4.44% H and 35.56% O. Determine the empirical
formula.
 What is the empirical formula for a compound that contains 10.89%
Mg, 31.77% Cl, and 57.34% O?

44. Molecular Formula
 Specifies the actual number of atoms of
each element in one molecule or formula
unit of the substance
 n=ratio between experimentally determined
mass of compound and the molar mass of the
empirical formula.

45. Calculating Molecular Formula
 Molar mass of acetylene – 26.04 g/mol
Mass of empirical formula (CH) – 13.02 g/mol
 n – Obtained by dividing the molar mass by the mass of the
empirical formula indicates that the molar mass of acetylene
is two times the mass of the empirical formula.
Experimentally determined molar mass of acetylene = 26.04 g/mol = 2.000
mass of empirical formula CH 13.02 g/mol
 Molecular Formula = (CH)2
 Acetylene = C2H2

46. Determining a Molecular
Formula
 Succinic acid is a substance produced by lichens.
Chemical analysis indicates it is composed of 40.68% C,
5.08% H, and 54.24% O and has a molar mass of 118.1
g/mol. Determine the empirical and molecular formulas
for succinic acid.
Known: Unknown:
Percent by mass = 40.68% C empirical formula = ?
Percent by mass = 5.08% H molecular formula = ?
Percent by mass = 54.24% O

47. Practice Problems
 Analysis of a chemical used in photographic developing
fluid indicates a chemical composition of 65.45% C,
5.45% H, and 29.09% O. The molar mass is found to be
110.0 g/mol. Determine the molecular formula.
 A compound was found to contain 49.98 g C, and 10.47
g H. The molar mass of the compound is 58.12 g/mol.
Determine the molecular formula.
 A colorless liquid composed of 46.68% N and 53.32% O
has a molar mass of 60.01 g/mol. What is the molecular
formula?

48. 11-4 The Formula
for a Hydrate

49. Naming Hydrates
Hydrate: a compound that has a specific number of water
molecules bound to its atoms.
In the formula for a hydrate, the number of water molecules
associated with each formula unit of the compound is
written following a dot.
ex. Na2CO3·10H2O
called sodium carbonate decahydrate
deca- means 10 and hydrate means water
Therefore there are 10 water molecules are
associated with one formula unit of the compound.

50. Formulas for Hydrates and
Examples
Prefix Molecules H2O Formula Name
Mono- 1 (NH4)2C2O4·H2O Ammonium oxalate monohydrate
Di- 2 CaCl2·2H2O Calcium chloride dihydrate
Tri- 3 NaC2H3O2·3H2O Sodium acetate trihydrate
Tetra- 4 FePO4·4H2O Iron(III) phosphate tetrahydrate
Penta- 5 CuSO4·5H2O Copper(II) sulfate pentahydrate
Hexa- 6 CoCl2·6H2O Cobalt(II) chloride hexahydrate
Hepta- 7 MgSO4·7H2O Magnesium sulfate heptahydrate
Octa- 8 Ba(OH)2·8H2O Barium hydroxide octahydrate
Deca- 10 Na2CO3·10H2O Sodium carbonate decahydrate

51. Analyzing a Hydrate
 Must drive off the water by heating the
compound
 Substance remaining after heating is
anhydrous (without water)
 Example: hydrated cobalt(II) chloride is a
pink solid that turns a deep blue when the
water of hydration is driven off and anhydrous
cobalt(II) chloride is produced

52. Formula for a Hydrate
 To determine the formula for a
hydrate, you must determine the number
of moles of water associated with one
mole of the hydrate.

53. Example Problem – Determining the
Formula for a Hydrate
 A mass of 2.5 g of blue, hydrated copper
sulfate (CuSO4·xH2O) is placed in a
crucible and heated. After heating, 1.59 g
white anhydrous copper sulfate (CuSO4)
remains. What is the formula for the
hydrate? Name the hydrate.

54. Example Problem – (cont.)
Known:
Mass of hydrated compound = 2.50 g CuSO4·xH2O
Mass of anhydrous compound = 1.59 g CuSO4
Molar mass = 18.02 g/mol H2O
Molar mass = 159.6 g/mol CuSO4
Unknown:
Formula for hydrate = ?
Name of hydrate = ?

55. Example Problem – (cont.)
Subtract the mass of the anhydrous copper sulfate from the mass of the
hydrated copper sulfate to determine the mass of water lost:
mass of hydrates copper sulfate 2.50 g
mass of anhydrous copper sulfate - 1.59 g
mass of water lost 0.91 g
Calculate the number of moles of H2O and anhydrous CuSO4
1.59 g CuSO4 x 1 mol CuSO4 = 0.00996 mol CuSO4
159.6 g CuSO4
0.91 g H2O x 1 mol H2O = 0.050 mol H2O
18.02 g H2O

56. Example Problem – (cont.)
Determine the value of x.
x = moles H2O = 0.050 mol H2O = 5.0 mol H2O = 5
moles CuSO4 0.00996 mol CuSO4 1.0 mol CuSO4 1
The ratio of H2O to CuSO4 is 5 : 1, so the formula for the hydrate is
CuSO4·5H2O, copper(II) sulfate pentahydrate.

57. Practice Problems
 A hydrate is found to have the following percent
composition: 48.18% MgSO4 and 51.2% H2O. What is
the formula and name for this hydrate?
 If 11.75 g of the common hydrate cobalt(II) chloride is
heated, 9.25 g of anhydrous cobalt chloride remains.
What is the formula and name for this hydrate?

58. Uses of Hydrates
 Drying agents: CaCl2, CaSO4
 Storage of solar energy: Na2SO4·10H2O