1 of 34

Moles and Molar Mass�Counting by Weighing

2 of 34

There are equal numbers of balls on each balance.
Would they have the same mass?

5.00

.03

kg

1 doz b

=

2 kg b

1 doz p

=

0.03 kg p

b =

p =

3 of 34

Counting by Weighing

We can count the number of objects there are in a sample by weighing the sample.

1 doz b = 2 kg b

1 doz b = 12 b

If a cardboard box contains 50 kilograms of baseballs (kg b), how many dozen baseballs (doz b) are in the box?

In other words, we can count by weighing.
In order to do this, we must know what a given quantity of a substance weighs.

4 of 34

5.00

.03

kg

1 doz b

=

2 kg b

b =

5 of 34

5.00

.03

kg

1 doz b

=

2 kg b

1 doz p

=

0.03 kg p

b =

p =

50 kg b

x

=

2 kg b

1 doz b

25

doz b

6 of 34

The Mole: Counting by Weighing

In chemistry, we can’t directly count the number of particles in a sample.
Just as in the previous example, we must weigh the sample and calculate the number of particles in it.
To do this, we must know what a mole of different substances weigh.
Just as a dozen baseballs weighs differently than a dozen tennis balls, a mole of one substance weighs differently than another substance.

1 mol C	=	12.0 g C

1 doz b	=	2.0 kg b

1 doz t	=	0.7 kg t

1 mol S	=	32.0 g S

7 of 34

Mass of a Particle

Before we discuss the mass of a mole, let’s recall the relative mass of a particle.
A particle’s relative mass is measured in the units amu (atomic mass unit).
To determine the relative mass of one particle, determine the number and mass of each type of atom in that particle.
Atomic masses are found below the symbol in most periodic tables.
What is the relative mass of the following particles?

amu

Particle	Mass

C

O₂

CO₂

Al₂(CO₃)₃

8 of 34

50

40

30

20

10

50 mL

Pyrex^®

Quantum

World

Macroscopic

World

48

1 mol

6.02 x 10²³

Beaker weighs

30 grams

amu

g

9 of 34

Mass of a Mole

The mass of a mole of a substance is called its molar mass.
The molar mass of a substance is equal to its particle mass (amu) expressed in grams.
This is not a coincidence – it takes 6.02 x 10²³ amu to equal 1 gram.
The reason we count using the mole is that it is easy to determine the mass of a mole because of the relationship above.
If we counted by another grouping, such as 1 x 10²⁴, determining the mass would not be so straight forward.

1 particle

1 mol

12.011 amu

6.940 amu

12.011 g

6.940 g

10 of 34

How to Determine Molar Mass

Use the periodic table to find the atomic mass of the element.
Write the number down and put the unit ‘grams/mole (g/mol)’ after it.

Atomic Number

Atomic Mass

Example: Find the molar mass of molybdenum (Mo).

Molar Mass of Mo =

Element	Molar Mass	Element	Molar Mass
H		I
N		U
Zn		Fe
Am		Mg

95.95

g/mol

Practice Problems: Determine the molar mass for each of the following elements.

11 of 34

The Periodic Table

1

2

13

14

15

16

17

18

3

4

5

6

7

8

9

10

11

12

1A

2A

3A

4A

5A

6A

7A

8A

11

Na

Sodium

22.990

2

8

1

H

Hydrogen

1.008

1

2

He

Helium

4.003

2

3

Li

Lithium

6.940

2

1

5

B

Boron

10.810

2

3

4

Be

Beryllium

9.012

2

6

C

Carbon

12.011

2

4

7

N

Nitrogen

14.007

2

5

8

O

Oxygen

15.999

2

6

9

F

Fluorine

18.998

2

7

10

Ne

Neon

20.180

2

8

18

Ar

Argon

39.948

2

8

17

Cl

Chlorine

35.45

2

8

7

16

S

Sulfur

32.06

2

8

6

15

P

Phosphorus

30.974

2

8

5

14

Si

Silicon

28.085

2

8

4

13

Al

Aluminum

26.982

2

8

3

12

Mg

Magnesium

24.305

2

8

2

19

K

Potassium

39.098

2

8

1

20

Ca

Calcium

40.078

2

8

2

21

Sc

Scandium

44.956

2

8

9

2

22

Ti

Titanium

47.867

2

8

10

2

23

V

Vanadium

50.942

2

8

11

2

24

Cr

Chromium

51.996

2

8

13

1

25

Mn

Manganese

54.938

2

8

13

2

26

Fe

Iron

55.845

2

8

14

2

27

Co

Cobalt

58.933

2

8

15

2

28

Ni

Nickel

58.693

2

8

16

2

29

Cu

Copper

63.546

2

8

18

1

30

Zn

Zinc

65.38

2

8

18

2

31

Ga

Gallium

69.723

2

8

18

3

32

Ge

Germanium

72.630

2

8

18

4

33

As

Arsenic

74.922

2

8

18

5

34

Se

Selenium

78.971

2

8

18

6

35

Br

Bromine

79.904

2

8

18

7

36

Kr

Krypton

83.798

2

8

18

8

37

Rb

Rubidium

85.468

2

8

18

8

1

38

Sr

Strontium

87.62

2

8

18

8

2

39

Y

Yttrium

88.906

2

8

18

9

2

40

Zr

Zirconium

91.224

2

8

18

10

2

41

Nb

Niobium

92.906

2

8

18

12

1

42

Mo

Molybdenum

95.95

2

8

18

13

1

43

Tc

Technetium

(98)

2

8

18

13

2

44

Ru

Ruthenium

101.07

2

8

18

15

1

45

Rh

Rhodium

102.91

2

8

18

16

1

46

Pd

Palladium

106.42

2

8

18

47

Ag

Silver

107.87

2

8

18

1

48

Cd

Cadmium

112.41

2

8

18

2

49

I

In

Indium

114.82

2

8

18

3

50

Sn

Tin

118.71

2

8

18

4

51

Sb

Antimony

121.76

2

8

18

5

52

Te

Tellurium

127.60

2

8

18

6

53

I

Iodine

126.90

2

8

18

7

54

Xe

Xenon

131.29

2

8

18

8

55

Cs

Cesium

132.91

2

8

18

8

1

56

Ba

Barium

137.33

2

8

18

8

2

72

Hf

Hafnium

178.49

2

8

18

32

10

2

73

Ta

Tantalum

180.95

2

8

18

32

11

2

74

W

Tungsten

183.84

2

8

18

32

12

2

75

Re

Rhenium

186.21

2

8

18

32

13

2

76

Os

Osmium

190.23

2

8

18

32

14

2

77

Ir

Iridium

192.22

2

8

18

32

15

2

78

Pt

Platinum

195.08

2

8

18

32

17

1

79

Au

Gold

196.97

2

8

18

32

18

1

80

Hg

Mercury

200.59

2

8

18

32

18

2

81

Tl

Thallium

204.38

2

8

18

32

18

3

82

Pb

Lead

207.2

2

8

18

32

18

4

83

Bi

Bismuth

208.98

2

8

18

32

18

5

84

Po

Polonium

(209)

2

8

18

32

18

6

85

At

Astatine

(210)

2

8

18

32

18

7

86

Rn

Radon

(222)

2

8

18

32

18

8

87

Fr

Francium

(223)

2

8

18

32

18

8

1

88

Ra

Radium

(226)

2

8

18

32

18

8

2

104

Rf

Rutherfordium

(267)

2

8

18

32

10

2

105

Db

Dubnium

(268)

2

8

18

32

11

2

106

Sg

Seaborgium

(269)

2

8

18

32

12

2

107

Bh

Bohrium

(270)

2

8

18

32

13

2

108

Hs

Hassium

(277)

2

8

18

32

14

2

109

Mt

Meitnerium

(278)

2

8

18

32

15

2

111

Rg

Roentgenium

(282)

2

8

18

32

17

2

110

Ds

Darmstadtium

(281)

2

8

18

32

17

1

112

Cn

Copernicium

(285)

2

8

18

32

18

2

113

Nh

Nihonium

(286)

2

8

18

32

18

3

114

Fl

Flerovium

(289)

2

8

18

32

18

4

115

Mc

Moscovium

(290)

2

8

18

32

18

5

116

Lv

Livermorium

(293)

2

8

18

32

18

6

117

Ts

Tennessine

(294)

2

8

18

32

18

7

118

Og

Oganesson

(294)

2

8

18

32

18

8

57

La

Lanthanum

138.91

2

8

18

9

2

58

Ce

Cerium

140.12

2

8

18

19

9

2

59

Pr

Praseodymium

140.91

2

8

18

21

8

2

60

Nd

Neodymium

144.24

2

8

18

22

8

2

61

Pm

Promethium

(145)

2

8

18

23

8

2

62

Sm

Samarium

150.36

2

8

18

24

8

2

63

Eu

Europium

151.96

2

8

18

25

8

2

64

Gd

Gadolinium

157.25

2

8

18

25

9

2

65

Tb

Terbium

158.93

2

8

18

27

8

2

66

Dy

Dysprosium

162.50

2

8

18

28

8

2

67

Ho

Holmium

164.93

2

8

18

29

8

2

68

Er

Erbium

167.26

2

8

18

30

8

2

69

Tm

Thulium

168.93

2

8

18

31

8

2

70

Yb

Ytterbium

173.05

2

8

18

32

8

2

71

Lu

Lutetium

174.97

2

8

18

32

9

2

89

Ac

Actinium

(227)

2

8

18

32

18

9

2

90

Th

Thorium

232.04

2

8

18

32

18

10

2

91

Pa

Protactinium

231.04

2

8

18

32

20

9

2

92

U

Uranium

238.03

2

8

18

32

21

9

2

93

Np

Neptunium

(237)

2

8

18

32

22

9

2

94

Pu

Plutonium

(244)

2

8

18

32

24

8

2

95

Am

Americium

(243)

2

8

18

32

25

8

2

96

Cm

Curium

(247)

2

8

18

32

25

9

2

97

Bk

Berkelium

(247)

2

8

18

32

27

8

2

98

Cf

Californium

(251)

2

8

18

32

28

8

2

99

Es

Einsteinium

(252)

2

8

18

32

29

8

2

100

F

Fm

Fermium

(257)

2

8

18

32

30

8

2

101

Md

Mendeleevium

(258)

2

8

18

32

31

8

2

102

No

Nobelium

(259)

2

8

18

32

8

2

103

Lr

Lawrencium

(266)

2

8

18

32

8

3

60

Nd

144.24

92

U

238.04

65

Tb

158.93

97

Bk

(247)

70

Yb

173.05

102

No

(259)

57

La

138.91

89

Ac

(227)

58

Ce

140.12

90

Th

232.04

59

Pr

140.91

91

Pa

231.04

61

Pm

(145)

93

Np

(237)

62

Sm

150.36

94

Pu

(244)

63

Eu

151.96

95

Am

(243)

64

Gd

157.25

96

Cm

(247)

66

Dy

162.50

98

Cf

(251)

67

Ho

164.93

99

Es

(252)

68

Er

167.26

100

Fm

(257)

69

Tm

168.93

101

Md

(258)

71

Lu

174.97

103

Lr

(266)

6

7

21

Sc

44.956

39

Y

88.906

1

H

1.008

11

Na

22.990

19

K

39.098

37

Rb

85.468

55

Cs

132.91

87

Fr

(223)

4

Be

9.012

12

Mg

24.305

20

Ca

40.078

38

Sr

87.62

56

Ba

137.33

88

Ra

(226)

25

Mn

54.938

43

Tc

(98)

75

Re

186.21

107

Bh

(270)

30

Zn

65.38

48

Cd

112.41

80

Hg

200.59

112

Cn

(285)

9

F

18.998

17

Cl

35.450

35

Br

79.904

53

I

126.90

85

At

(210)

117

Ts

(294)

22

Ti

47.867

40

Zr

91.224

72

Hf

178.49

104

Rf

(267)

23

V

50.942

41

Nb

92.906

73

Ta

180.95

105

Db

(268)

24

Cr

51.996

42

Mo

95.95

74

W

183.84

106

Sg

(269)

26

Fe

55.845

44

Ru

101.07

76

Os

190.23

108

Hs

(277)

27

Co

58.933

45

Rh

102.91

77

Ir

192.22

109

Mt

(278)

28

Ni

58.693

46

Pd

106.42

78

Pt

195.08

110

Ds

(281)

29

Cu

63.546

47

Ag

107.87

79

Au

196.97

111

Rg

(282)

5

B

10.810

13

Al

26.982

31

Ga

69.723

49

In

114.82

81

Tl

204.38

113

Nh

(286)

6

C

12.011

14

Si

28.085

32

Ge

72.630

50

Sn

118.71

82

Pb

207.20

114

Fl

(289)

7

N

14.007

15

P

30.974

33

As

74.922

51

Sb

121.76

83

Bi

208.98

115

Mc

(290)

8

O

15.999

16

S

32.060

34

Se

78.971

52

Te

127.60

84

Po

(209)

116

Lv

(293)

2

He

4.003

10

Ne

20.180

18

Ar

39.948

36

Kr

83.798

54

Xe

131.29

86

Rn

(222)

118

Og

(294)

3

Li

6.940

1

2

3

4

5

6

7

12 of 34

Concept Check

What sample below contains the most number of atoms?

100.3 grams of mercury (g Hg)
32.1 grams of sulfur (g S)
30.1 grams of calcium (g Ca)
13.9 grams of lithium (g Li)

20

Ca

Calcium

40.078

16

S

Sulfur

32.06

3

Li

Lithium

6.940

80

Hg

Mercury

200.59

13 of 34

Molar Mass of a Molecule

Step 1: Use the chemical formula to determine the number of each type of atom present in the molecule.
Step 2: Multiply the atomic mass (from the periodic table) of each element by the number of its atoms present in the molecule (subscript).

You can round the atomic mass to the nearest tenth.

Step 3: Add it all together and put the units ‘grams/mole (g/mol)’ after the number.
Example: Find the molar mass of sodium carbonate, Na₂CO₃.

2

x

23.0

=

46.0

1

x

12.0

=

12.0

Na

C

O

3

x

16.0

=

48.0

Molar Mass

=

106.0 g/mol

add

14 of 34

Molar Mass of a Molecule

Example 2: Find the molar mass of calcium nitrate, Ca(NO₃)_2.

1

40.1

2

14.0

28.0

Ca

N

O

6

x

16.0

=

96.0

Molar Mass

=

164.1 g/mol

add

7

N

Nitrogen

14.007

2

5

8

O

Oxygen

15.999

2

6

20

Ca

Calcium

40.078

2

8

2

15 of 34

Molar Mass of a Molecule

Practice Problems: Calculate the molar mass for each of the following molecules.

Molecule	Molar Mass

Cl₂

H₂O

CBr₂F₂

Mg(OH)₂

16 of 34

Mass and Particle Number

g

Molar mass allows us to convert between mass and particle number.

Pb_MM= 207.2 g/mol

33 g H₂O

65.2 g Pb

1 mol Pb

207.2 g Pb

x

=

0.3 mol Pb

17 of 34

Mass and Particle Number

g

Molar mass allows us to convert between mass and particle number.

H₂O_MM= 18.0 g/mol

33 g H₂O

33.0 g H₂O

1 mol H₂O

18.0 g H₂O

x

=

1.8 mol H₂O

18 of 34

Mass and Particle Number

g

Molar mass allows us to convert between mass and particle number.

NaCl_MM= 58.4 g/mol

33 g H₂O

10.4 g NaCl

1 mol NaCl

58.4 g NaCl

x

=

0.2 mol NaCl

19 of 34

Mass and Moles

There are two primary ways to express the amount of a sample in chemistry:

Mass - the amount of matter, normally expressed in grams (g).
Particle Number – the number of particles, normally expressed in moles (mol).

Molar mass (M) allows us to covert between the two expressions.

Mass

grams (g)

Particle Number

moles (mol)

Molar Mass

44.0 g/mol

macroscopic

submicroscopic

Use only with torches designed for

Propane gas. Read and follow important

safety warnings on the side label.

NET WEIGHT 14.1 oz./ 400 g

	DANGER
	EXTREMELY FLAMMABLE FIRE/EXPLOSION HAZARD CONTENTS UNDER PRESSURE CARBON MONOXIDE HAZARD

Use only with torches designed for

Propane gas. Read and follow important

safety warnings on the side label.

NET WEIGHT 14.1 oz./ 400 g

!

20 of 34

The Many Looks of Molar Mass

1

12

1

1 mol

g

44

1

H

Hydrogen

1.008

1

6

C

Carbon

12.011

2

4

21 of 34

The Many Looks of Molar Mass

1

12

1

1 mol

g

44

22 of 34

The Many Looks of Molar Mass

1

12

1

g

44

C₃H₈

1 mol

C₃H₈

23 of 34

The Many Looks of Molar Mass

1

12

1

g

44

C₃H₈

1 mol

C₃H₈

24 of 34

The Many Looks of Molar Mass

1

12

1

g

44

C₃H₈

1 mol

C₃H₈

=

25 of 34

The Many Looks of Molar Mass

Molar mass (M) can be expressed in many ways.
Example: what is the molar mass of propane (C₃H₈)?

Molar Mass

44.0 g C₃H₈

1 mol C₃H₈

Element	Count	Mass	Total

C

H

3

12.0

1.0

36.0

8.0

Total

x

=

add

8

44.0

=

44.0 g C₃H₈

1 mol C₃H₈

44.0 g C₃H₈

1 mol C₃H₈

44.0 g/mol

44.0 gmol^-1

1 mol C₃H₈ = 44.0 g C₃H₈

These conversion factors will be most useful for conversion problems.

26 of 34

Molar Mass Conversion Practice

How many moles (mol C₃H₈)are in 400.0 grams of propane (g C₃H₈)?

44.0 g C₃H₈

1 mol C₃H₈

44.0 g C₃H₈

1 mol C₃H₈

400.0 g C₃H₈

x

44.0 g C₃H₈

1 mol C₃H₈

=

What is the mass (g C₃H₈) of 11.8 moles of propane (mol C₃H₈)?

11.8 mol C₃H₈

x

44.0 g C₃H₈

1 mol C₃H₈

=

27 of 34

5.00

?

g

Sodium Fluoride (NaF) 41.99 g/mol

!

Causes serious eye irritation

Get me 4.5 moles of sodium fluoride, post haste!

28 of 34

Mole → Mass Conversions

How many grams of sodium fluoride (g NaF) are in 4.5 moles of sodium fluoride (mol NaF)?

1 mol NaF	=		g NaF
Conversion Factor 1		Conversion Factor 2

Sodium fluoride crystal

29 of 34

5.00

.03

g

Sodium Fluoride (NaF) 41.99 g/mol

!

Causes serious eye irritation

4.5 mol NaF

x

=

42.0 g NaF

1 mol NaF

189.0 g NaF

30 of 34

5.00

189.00

g

Sodium Fluoride (NaF) 41.99 g/mol

!

Causes serious eye irritation

4.5 mol NaF

x

=

42.0 g NaF

1 mol NaF

189.0 g NaF

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Mass → Mole Conversions

How many moles of ammonia (mol NH₃) are equal to 1200 grams of ammonia (g NH₃)?

1 mol NH₃	=		g NH₃
Conversion Factor 1		Conversion Factor 2

Ammonia Molecule

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Substance	Formula	Molar Mass	Molar Mass Equality
Carbon	C
Water	H₂O
Baking Soda	NaHCO₃

45

g

How many moles of carbon are there?

12 g C = 1 mol C

12 g/mol

Additional Problems

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50

40

30

20

10

50 mL

Pyrex^®

Substance	Formula	Molar Mass	Molar Mass Equality
Carbon	C
Water	H₂O
Baking Soda	NaHCO₃

g

How many moles of water are there?

45

12 g C = 1 mol C

18 g H₂O = 1 mol H₂O

12 g/mol

18 g/mol

Mass of Beaker = 30 grams

Additional Problems

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Substance	Formula	Molar Mass	Molar Mass Equality
Carbon	C
Water	H₂O
Baking Soda	NaHCO₃

g

How many moles of baking soda are there?

45

12 g/mol

18 g/mol

84 g/mol

12 g C = 1 mol C

18 g H₂O = 1 mol H₂O

84 g NaHCO₃= 1 mol NaHCO₃

Additional Problems