Ch # 3
Unit system and dimensional
analysis.
Measurement of Mass
The standard unit of mass in the SI
system is the kilogram. 1 kilogram is equal to
the mass of a platinum-iridium cylinder kept in
a vault at Sevres, France.
1 kg = 2.205 pounds
Metric Units of mass
Unit
Abbreviation Gram Equivalent
Exponential
Equivalent
kilogram
gram
kg
g
1,000 g
1g
103 g
100 g
decigram
dg
0.1 g
10-1 g
centigram
cg
0.01 g
10-2 g
milligram
mg
0.001 g
10-3 g
microgram
g
0.000001 g
10-6 g
Mass and Weight
• Matter: Anything that has mass and
occupies space.
• Mass : The quantity or amount of
matter that an object possesses.
– Fixed
– Independent of the object’s location
• Weight: A measure of the earth’s
gravitational attraction for an object.
– Not fixed
– Depends on the object’s location.
• Mass : The quantity or amount of
matter that an object possesses.
– Fixed
– Independent of the object’s location.
• Weight: A measure of the earth’s
gravitational attraction for an object.
– Not fixed
– Depends on the object’s location.
Measurement of Volume
• Volume is the amount of space
occupied by matter.
• In the SI system the standard unit of
volume is the cubic meter (m3).
• The liter (L) and milliliter (mL) are the
standard units of volume used in most
chemical laboratories.
Density
Density is the ratio
of the mass of a
substance to the
volume occupied by
that substance.
mass
d=
volume
Mass
is usually
The density
of gases is
expressed
expressed in
in grams
grams per
and
liter.volume in mL
or cm3.
g
ddd=== 3
mL
cm
L
Density varies with temperature
d
d
4oC
H 2O
o
80 C
H 2O
1.0000 g
g
=
= 1.0000
1.0000 mL
mL
1.0000 g
g
=
= 0.97182
1.0290 mL
mL
A 13.5 mL sample of an unknown liquid has a mass of
12.4 g. What is the density of the liquid?
M 12.4 g
D 
 0.919 g/mL
V 13.5mL
A graduated cylinder is filled to the 35.0 mL mark with water.
A copper nugget weighing 98.1 grams is immersed into the
cylinder and the water level rises to the 46.0 mL. What is the
volume of the copper nugget? What is the density of copper?
Vcopper nugget = Vfinal -Vinitial = 46.0mL - 35.0mL = 11.0mL
M
98.1g
D

 8.92 g/mL
V 11.0 mL
46.0 mL
35.0 mL
98.1 g
The density of ether is 0.714 g/mL. What is the
mass of 25.0 milliliters of ether?
Method 1
(a) Solve the density equation for mass.
mass
d=
volume
mass = density x volume
(b) Substitute the data and calculate.
0.714 g
25.0 mL x
= 17.9 g
mL
The density of ether is 0.714 g/mL. What is the
mass of 25.0 milliliters of ether?
Method 2 Dimensional Analysis. Use density as
a conversion factor. Convert:
mL → g
g
=g
The conversion of units is mL x
mL
0.714 g
25.0 ml x
= 17.9 g
mL
The density of oxygen at 0oC is 1.429 g/L. What is
the volume of 32.00 grams of oxygen at this
temperature?
Method 1
(a) Solve the density equation for volume.
mass
d=
volume
mass
volume =
density
(b) Substitute the data and calculate.
32.00 g O2
volume =
= 22.40 L
1.429 g O2 /L
% error
• Measured value-accepted value
____________________________x 100
Accepted value
Measurement of
Temperature
Heat
• A form of energy that is associated with
the motion of small particles of matter.
• Heat refers to the quantity of this energy
associated with the system.
• The system is the entity that is being
heated or cooled.
Temperature
• A measure of the intensity of heat.
• It does not depend on the size of the
system.
• Heat always flows from a region of higher
temperature to a region of lower
temperature.
Temperature Measurement
• The SI unit of temperature is the Kelvin.
• There are three temperature scales: Kelvin,
Celsius and Fahrenheit.
• In the laboratory temperature is commonly
measured with a thermometer.
Degree Symbols
degrees Celsius =
oC
Kelvin (absolute) = K
degrees Fahrenheit = oF
To convert between the scales use the
following relationships.
o
K = C + 273.15
o
o
o
F = 1.8 x C + 32
o
F
32
o
o
o
o
= = 1.8 x C
FC- 32
1.8
180 Farenheit Degrees
= 100 Celcius degrees
180
=1.8
100
It is not uncommon for temperatures in the
Canadian plains to reach –60oF and below during
the winter. What is this temperature in oC and K?
o
o
o
F - 32
C=
1.8
60. - 32
o
C=
= -51 C
1.8
It is not uncommon for temperatures in the
Canadian planes to reach –60oF and below
during the winter. What is this temperature in oC
and K?
o
K = C + 273.15
o
K = -51 C + 273.15 = 222 K
The
Metric System
• The metric or International System (SI, Systeme
International) is a decimal system of units.
• It is built around standard units.
• It uses prefixes representing powers of 10 to
express quantities that are larger or smaller
than the standard units.
International System’s
Standard Units of Measurement
Quantity
Name of Unit
Abbreviation
Length
Mass
meter
kilogram
m
kg
Temperature
Kelvin
K
Time
second
Amount of substance m
s
mole
Electric Current
ampere
A
Luminous Intensity
candela
cd
Prefixes and Numerical Values for SI Units
Numerical Value
Power of 10
Equivalent
Prefix
Symbol
exa
peta
E
P
1,000,000,000,000,000,000 1018
1,000,000,000,000,000
1015
tera
T
1,000,000,000,000
1012
giga
G
1,000,000,000
109
mega
M
1,000,000
106
kilo
k
1,000
103
hecto
h
100
102
deca
da
10
101
—
—
1
100
Prefixes and Numerical Values for SI Units
Numerical Value
Power of 10
Equivalent
Prefix
Symbol
deci
d
0.1
10-1
centi
c
0.01
10-2
milli
m
0.001
10-3
micro

0.000001
10-6
nano
n
0.000000001
10-9
pico
p
0.000000000001
10-12
femto
f
0.00000000000001
10-15
atto
a
0.000000000000000001
10-18
Dimensional Analysis
Dimensional analysis converts one unit to
another by using conversion factors.
unit1 x conversion factor = unit2
Basic Steps
1. Read the problem carefully. Determine
what is to be solved for and write it
down.
2. Tabulate the data given in the problem.
–
Label all factors and measurements with
the proper units.
Basic Steps
3. Determine which principles are
involved and which unit relationships
are needed to solve the problem.
–
You may need to refer to tables for
needed data.
4. Set up the problem in a neat,
organized and logical fashion.
–
–
Make sure unwanted units cancel.
Use sample problems in the text as
guides for setting up the problem.
Basic Steps
5. Proceed with the necessary mathematical
operations.
–
Make certain that your answer contains the
proper number of significant figures.
6. Check the answer to make sure it is
reasonable.
Metric Units of Length
Unit
Abbreviation Metric Equivalent
Exponential
Equivalent
kilometer
meter
km
m
1,000 m
1m
103 m
100 m
decimeter
dm
0.1 m
10-1 m
centimeter
cm
0.01 m
10-2 m
millimeter
mm
0.001 m
10-3 m
micrometer
m
0.000001 m
10-6 m
nanometer
nm
0.000000001 m
10-9 m
angstrom
Å
0.0000000001 m
10-10 m
How many millimeters are there in 2.5 meters?
The
conversion
factor
must
unit1 x conversion factor = unit2
accomplish two things:
m x conversion factor = mm
• It must cancel
meters.
• It must introduce
millimeters
The conversion factor takes a fractional
form.
mm
mx
= mm
m
The conversion factor
is derived from the
equality.
1 m = 1000 mm
Divide both sides by 1000 mm
1m
1000 mm
conversion
=

1
factor
1000m 1000 mm
Divide both sides by 1 m
1 m 1000 mm
conversion
=
 1
factor
1m
1m
How many millimeters are there in 2.5 meters?
Use the conversion factor with millimeters in the
numerator and meters in the denominator.
1000 mm
= 2500 mm
2.5 m x
1m
3
2.5 x 10 mm
Convert 16.0 inches to centimeters.
Use this
conversio
n factor
2.54 cm
1 in
2.54 cm
16.0 in x
= 40.6 cm
1 in
Convert 3.7 x 103 cm to micrometers.
Centimeters can be converted to micrometers by
writing down conversion factors in succession.
cm  m  meters
1m
10 μm
7
x
3.7 x 10 cm x
= 3.7 x 10 μm
100 cm
1m
6
3
Metric Units of mass
Unit
Abbreviation Gram Equivalent
Exponential
Equivalent
kilogram
gram
kg
g
1,000 g
1g
103 g
100 g
decigram
dg
0.1 g
10-1 g
centigram
cg
0.01 g
10-2 g
milligram
mg
0.001 g
10-3 g
microgram
g
0.000001 g
10-6 g
Convert 45 decigrams to grams.
1 g = 10 dg
1g
45 dg x
= 4.5 g
10 dg
An atom of hydrogen weighs 1.674 x 10-24 g.
How many ounces does the atom weigh?
Grams can be converted to ounces by a series of
stepwise conversions.
1 lb = 454 g
-24
1.674 x 10
1 lb
-27
gx
 3.69 x 10 lb
454 g
16 oz = 1 lb
-27
3.69 x 10
16 oz
-26
x
 5.90 x 10 oz
lb
1 lb
An atom of hydrogen weighs 1.674 x 10-24 g.
How many ounces does the atom weigh?
Grams can be converted to ounces using a linear
expression by writing down conversion factors
in succession.
1 lb
16 oz
-26
x
x
 5.90 x 10 oz
1.674 x 10 g
454 g
1 lb
-24