1. Unit Conversions
© R. A. Hill

2. Unit Conversions Within the S.I. System
Need to know prefixes used in S.I. system

3. S.I. Prefixes:
pp 10 in text
Prefix
Multiple
Symbol
mega
kilo
hecto
deka
deci
centi
milli
micro
nano
pico

4. S.I. Prefixes:
Prefix
Multiple
Symbol
mega
106 M
kilo
hecto
deka
deci
centi
milli
micro
nano
pico

5. S.I. Prefixes:
Prefix
Multiple
Symbol
mega
106 M
kilo
103 k
hecto
deka
deci
centi
milli
micro
nano
pico

6. S.I. Prefixes:
Prefix
Multiple
Symbol
mega
106 M
kilo
103 k
hecto
102 h
deka
deci
centi
milli
micro
nano
pico

7. S.I. Prefixes:
Prefix
Multiple
Symbol
mega
106 M
kilo
103 k
hecto
102 h
deka 10 da
deci
centi
milli
micro
nano
pico

8. S.I. Prefixes:
Prefix
Multiple
Symbol
mega
106 M
kilo
103 k
hecto
102 h
deka 10 da
deci
10-1 d
centi
milli
micro
nano
pico

9. S.I. Prefixes:
Prefix
Multiple
Symbol
mega
106 M
kilo
103 k
hecto
102 h
deka 10 da
deci
10-1 d
centi
10-2 c
milli
micro
nano
pico

10. S.I. Prefixes:
Prefix
Multiple
Symbol
mega
106 M
kilo
103 k
hecto
102 h
deka 10 da
deci
10-1 d
centi
10-2 c
milli
10-3 m
micro
nano
pico

11. S.I. Prefixes:
Prefix
Multiple
Symbol
mega
106 M
kilo
103 k
hecto
102 h
deka 10 da
deci
10-1 d
centi
10-2 c
milli
10-3 m
micro
10-6 μ
nano
pico

12. S.I. Prefixes:
Prefix
Multiple
Symbol
mega
106 M
kilo
103 k
hecto
102 h
deka 10 da
deci
10-1 d
centi
10-2 c
milli
10-3 m
micro
10-6 μ
nano
10-9 n
pico

13. S.I. Prefixes:
Prefix
Multiple
Symbol
mega
106 M
kilo
103 k
hecto
102 h
deka 10 da
deci
10-1 d
centi
10-2 c
milli
10-3 m
micro
10-6 μ
nano
10-9 n
pico
10-12 p

14. S.I. Prefixes: Prefix Multiple Symbol mega 106 M kilo 103 k hecto 102
deka 10 da
deci
10-1 d
centi
10-2 c
milli
10-3 m
micro
10-6 μ
nano
10-9 n
pico
10-12 p
Ex:
1 Mm = ___m

15. S.I. Prefixes: Prefix Multiple Symbol mega 106 M kilo 103 k hecto 102
deka 10 da
deci
10-1 d
centi
10-2 c
milli
10-3 m
micro
10-6 μ
nano
10-9 n
pico
10-12 p
Ex:
1 Mm = 106 m

16. S.I. Prefixes: Prefix Multiple Symbol mega 106 M kilo 103 k hecto 102
deka 10 da
deci
10-1 d
centi
10-2 c
milli
10-3 m
micro
10-6 μ
nano
10-9 n
pico
10-12 p
Ex:
1 Mm = 106 m
1 ns = ____s

17. S.I. Prefixes: Prefix Multiple Symbol mega 106 M kilo 103 k hecto 102
deka 10 da
deci
10-1 d
centi
10-2 c
milli
10-3 m
micro
10-6 μ
nano
10-9 n
pico
10-12 p
Ex:
1 Mm = 106 m
1 ns = s

18. S.I. Prefixes: Prefix Multiple Symbol mega 106 M kilo 103 k hecto 102
deka 10 da
deci
10-1 d
centi
10-2 c
milli
10-3 m
micro
10-6 μ
nano
10-9 n
pico
10-12 p
Ex:
1 Mm = 106 m
1 ns = s
1 mmol = ___mol

19. S.I. Prefixes: Prefix Multiple Symbol mega 106 M kilo 103 k hecto 102
deka 10 da
deci
10-1 d
centi
10-2 c
milli
10-3 m
micro
10-6 μ
nano
10-9 n
pico
10-12 p
Ex:
1 Mm = 106 m
1 ns = s
1 mmol = mol

20. S.I. Prefixes:
Prefix
Multiple
Symbol
mega
106 M
kilo
103 k
hecto
102 h
deka 10 da
deci
10-1 d
centi
10-2 c
milli
10-3 m
micro
10-6 μ
nano
10-9 n
pico
10-12 p
Memorize these 6 prefixes.

21. S.F. in Nonmeasured Numbers
If a number is not measured then it does not have an estimated digit in it.
 treat it as if it has ∞ S.F.
Ex: #s in definitions objects = 1 dozen objects
1 mm = 10−3 m
counting number of objects i.e. 15 people

22. S.D. in Conversion Factors
Conversion factors involving the def. of prefixes have ∞ S.F.
Ex: In 1 km = m, both the 1 and the 103 have ∞ S.F.
When both #s in a relationship have ∞ S.F. it is called an
exact relationship.
Conversion factors not involving the def. of a prefix or def. have a limited # of S.F.
Ex: In 2.2 lbs = 1 kg, the 2.2 has 2 S.F. & the 1 has ∞ S.F.

23. Unit Conversions Within the S.I. System
243 mm = ? m

24. Unit Conversions Within the S.I. System
0.01 km = ? cm

25. Unit Conversions Between Different Systems of Measurement
3.21 cal = ? J

26. Unit Conversions Between Different Systems of Measurement
8.9 lbs = ? g

27. Unit Conversions Between Different Systems of Measurement
0.20 km = ? in

28. Squared and Cubed Conversion Factors
562 in2 = ? ft2
Wait…
1 ft = 12 in
but does
1 ft2 = 12 in2 ? 1
ft2
562 in2 = 12
in2

29. Well, this is 1 ft2…
1 ft
1 ft

30. And this is 1 ft2…
12 in
12 in

31. which is 144 in2 !
12 in
12 in

32. 562 in2 = ? ft2 2 1 ft
562 in2 =
3.9027… ft = ft2 12 in
Squaring the entire conversion factor gives the relationship between squared units!
Lets try this again…

33. Cubing the entire conversion factor gives the relationship between cubed units!
So for ft3 and in3 …
0.74 ft3 = ? in3 3 12 in
0.74 ft3 =
12 in 1 ft
= in3
= in3
12 in
12 in

34. Unit Conversions Between Different Systems of Measurement
3.25 g/ml = ? lbs/ft3

35. Unit Conversions with Equivalent Measurements
density (def)
– the mass per volume for a substance.
What is the mass of 1.25 l of Hg (density = 13.6 g/ml)?

37. atomic weights (def)

38. atomic weights (def) – the average mass of an atom of an element relative to an atom of carbon-12 being assigned a mass of exactly 12 a.m.u.

39. atomic weights (def) – the average mass of an atom of an element relative to an atom of carbon-12 being assigned a mass of exactly 12 a.m.u.

40. atomic weights (def) – the average mass of an atom of an element relative to an atom of carbon-12 being assigned a mass of exactly 12 a.m.u.
a.m.u. = atomic mass unit

41. atomic weights (def) – the average mass of an atom of an element relative to an atom of carbon-12 being assigned a mass of exactly 12 a.m.u.
a.m.u. = atomic mass unit
These can be found on the periodic chart.
Ex: hydrogen

42. atomic weights (def) – the average mass of an atom of an element relative to an atom of carbon-12 being assigned a mass of exactly 12 a.m.u.
a.m.u. = atomic mass unit
These can be found on the periodic chart.
Ex: hydrogen

43. formula weight

44. formula weight (def) – the sum of all the atomic weights of every atom present in the formula for a substance.

45. formula weight (def) – the sum of all the atomic weights of every atom present in the formula for a substance.
Ex: H2O

46. formula weight (def) – the sum of all the atomic weights of every atom present in the formula for a substance.
Ex: H2O
2 H
1 O

47. formula weight (def) – the sum of all the atomic weights of every atom present in the formula for a substance.
Ex: H2O
2 H (1.008)
1 O

48. formula weight (def) – the sum of all the atomic weights of every atom present in the formula for a substance.
Ex: H2O
2 H (1.008)
1 O

49. formula weight (def) – the sum of all the atomic weights of every atom present in the formula for a substance.
Ex: H2O
2 H (1.008)
1 O (16.0)

50. formula weight (def) – the sum of all the atomic weights of every atom present in the formula for a substance.
Ex: H2O
2 H (1.008)
1 O (16.0)

51. formula weight (def) – the sum of all the atomic weights of every atom present in the formula for a substance.
Ex: H2O
2 H (1.008) =
1 O (16.0) =
18.016

52. formula weight (def) – the sum of all the atomic weights of every atom present in the formula for a substance.
Ex: H2O
2 H (1.008) =
1 O (16.0) =
= = f.w.

53. mole (def)

54. mole (def) – a quantity of substance that contains as many particles as there are atoms present in exactly 12 g of carbon-12.

55. mole (def) – a quantity of substance that contains as many particles as there are atoms present in exactly 12 g of carbon-12.
This # has been experimentally determined to be:

56. mole (def) – a quantity of substance that contains as many particles as there are atoms present in exactly 12 g of carbon-12.
This # has been experimentally determined to be:
6.022 x 1023

57. mole (def) – a quantity of substance that contains as many particles as there are atoms present in exactly 12 g of carbon-12.
This # has been experimentally determined to be:
6.022 x 1023
Avogadro’s Number

58. mole (def) – a quantity of substance that contains as many particles as there are atoms present in exactly 12 g of carbon-12.
This # has been experimentally determined to be:
6.022 x 1023
Avogadro’s Number
In problems, the word “particles” is
replaced with the term “atom”,
“molecule” or whatever is appropriate.

59. molar mass

60. molar mass (def) – the mass of 1 mole of a subs.

61. molar mass (def) – the mass of 1 mole of a subs.
This is numerically equal to the formula weight of the
subs. but has units of g/mol.

62. molar mass (def) – the mass of 1 mole of a subs.
This is numerically equal to the formula weight of the
subs. but has units of g/mol.
Ex: C

63. molar mass (def) – the mass of 1 mole of a subs.
This is numerically equal to the formula weight of the
subs. but has units of g/mol.
Ex: C

64. molar mass (def) – the mass of 1 mole of a subs.
This is numerically equal to the formula weight of the
subs. but has units of g/mol.
Ex: C g/mol

65. molar mass (def) – the mass of 1 mole of a subs.
This is numerically equal to the formula weight of the
subs. but has units of g/mol.
Ex: C g/mol
H2O

66. molar mass (def) – the mass of 1 mole of a subs.
This is numerically equal to the formula weight of the
subs. but has units of g/mol.
Ex: C g/mol
H2O

67. molar mass (def) – the mass of 1 mole of a subs.
This is numerically equal to the formula weight of the
subs. but has units of g/mol.
Ex: C g/mol
H2O g/mol

68. molar volume

69. molar volume (def) – the volume of 1 mole of a subs.

70. molar volume (def) – the volume of 1 mole of a subs.
The molar volume of any gas at S.T.P. is

71. molar volume (def) – the volume of 1 mole of a subs.
The molar volume of any gas at S.T.P. is
S.T.P. = standard temperature & pressure =

72. molar volume (def) – the volume of 1 mole of a subs.
The molar volume of any gas at S.T.P. is
S.T.P. = standard temperature & pressure = OoC & 1 atm

73. molar volume (def) – the volume of 1 mole of a subs.
The molar volume of any gas at S.T.P. is 22.4 l/mol.
S.T.P. = standard temperature & pressure = OoC & 1 atm

74. particles mol g L Avogadro’s molar mass number molar volume
6.022 x 1023
particles
mol 1
mol g x x 1
particles
mol g
Avogadro’s
number
molar mass 1
mol
particles g
mol x x 1
6.022 x 1023
molar
volume
22.4 L
mol
mol L 1 x x
22.4 1 L
Gas at S.T.P.

75. particles mol g L Avogadro’s molar mass number molar volume
6.022 x 1023
particles
mol 1
mol g x x 1
particles
mol g
Avogadro’s
number
molar mass 1
mol
particles g
mol x x 1
6.022 x 1023
molar
volume
22.4 L
mol
mol L 1 x x
22.4 1 L
Gas at S.T.P.

76. 0.25 mol H2O contains how many H atoms?

77. What is the mass of 24.7 mmol of Fe2(SO4)3?

78. 0.458 mol of CH4 gas occupies how many ml at S.T.P.?

79. A 1 carat diamond (pure C) has a mass of 0. 200 g
A 1 carat diamond (pure C) has a mass of g. How many C atoms are present in a 1 carat diamond?

80. Octane (C8H18) has a density of 0. 80 g/ml
Octane (C8H18) has a density of 0.80 g/ml. What is the volume in ml of 1.00 x 1024 molecules of C8H18?

81. soln
solution
(def) – a homogeneous mixture.
solute
(def) – the substance present in a solution in the
lesser amount.
solvent
(def) – the substance present in a solution in the
greater amount.

82. molarity
(def) – the number of mole of solute per liter of
solution.
The units of mol/l soln are abbreviated as “M”
& read as “molar”.

83. Ex:
volumetric flask
Add H2O until V of soln = 1 liter
1 liter mark
3 mol of NaCl
1 l NaCl soln
3 mol NaCl
3 M NaCl soln
Note: (1) less than 1 liter of solvent is added
& the amount will differ with each solute
(2) in making solns, volumes are not always additive
ex: 50 ml H2O ml C3H7OH = 96 ml soln
…V of H2O + V of C3H7OH > V of soln
V of NH4Cl + V of H2O < V of soln

84. How would 1.000 l of 2.00 M CaCl2 be prepared?

85. 1.52 g of NaOH is diluted with H2O until a solution with a total volume of ml is obtained. What is the molarity of the NaOH solution?

86. Solution Dilution
Stock Solns
Concentration
H2SO4
18 M
HNO3
16 M
HCl
12 M
HC2H3O2
17 M
NH4OH
15 M

87.  V • M = n add more solvent solvent solute n1 = n2 mol L x = mol L
V1 • M1 = V2 • M2

88. How would 100.0 ml of 1 M HNO3 be prepared?