3.2 Units of Measurement >
Chapter 3
Scientific Measurement
3.1 Using and Expressing
Measurements
3.2 Units of Measurement
3.3 Solving Conversion Problems
1
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3.2 Units of Measurement >
CHEMISTRY
& YOU
What’s the forecast for tomorrow—hot
or cold?
Will the high
temperature tomorrow
be 28°C, which is
very warm? Or 28°F,
which is very cold?
Without the correct
units, you can’t be
sure.
2
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3.2 Units of Measurement > Using SI Units
Using SI Units
What makes metric units easy to use?
3
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3.2 Units of Measurement > Using SI Units
• The standards of measurement used in
science are those of the metric system.
All metric units are based on multiples
of 10. As a result, you can convert
between units easily.
4
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3.2 Units of Measurement > Using SI Units
• The metric system was originally
established in France in 1795.
• The International System of Units
(abbreviated SI after the French name, Le
Système International d’Unités) is a
revised version of the metric system.
• The SI was adopted by international
agreement in 1960.
5
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3.2 Units of Measurement > Using SI Units
• There are seven SI base
units.
• From these base units, all
other SI units of
measurement can be
derived.
• Derived units are used
for measurements
such as volume,
density, and pressure.
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SI Base Units
Quantity
SI base
unit
Symbol
Length
meter
m
Mass
kilogram
kg
Temperature
kelvin
K
Time
second
s
Amount of
substance
mole
mol
Luminous
intensity
candela
cd
Electric
current
ampere
A
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3.2 Units of Measurement > Using SI Units
Units of Length
• In SI, the basic unit of length, or linear
measure, is the meter (m).
• All measurements of length can be
expressed in meters.
• For very large and very small lengths,
however, it may be more convenient to use
a unit of length that has a prefix.
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3.2 Units of Measurement > Using SI Units
Units of Length
The table below lists the prefixes in common use.
Commonly Used Metric Prefixes
Prefix Symbol
8
Meaning
Factor
mega
M
1 million times larger than the unit it precedes
106
kilo
k
1000 times larger than the unit it precedes
103
deci
d
10 times smaller than the unit it precedes
10-1
centi
c
100 times smaller than the unit it precedes
10-2
milli
m
1000 times smaller than the unit it precedes
10-3
micro
μ
1 million times smaller than the unit it precedes
10-6
nano
n
1 billion times smaller than the unit it precedes
10-9
pico
p
1 trillion times smaller than the unit it precedes
10-12
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3.2 Units of Measurement > Using SI Units
Units of Length
• For example, the prefix milli- means 1/1000
(one-thousandth), so a millimeter (mm) is
1/1000 of a meter, or 0.001 m.
• A hyphen (-) measures about 1 mm.
• For large distances, it is most appropriate to
express measurements in kilometers (km).
• The prefix kilo- means 1000, so 1 km
equals 1000 m.
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3.2 Units of Measurement > Using SI Units
Units of Volume
• The space occupied by any sample of
matter is called its volume.
• You calculate the volume of any cubic or
rectangular solid by multiplying its length
by its width by its height.
• The unit for volume is thus derived from
the units of length.
10
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3.2 Units of Measurement > Using SI Units
Units of Volume
• The SI unit of volume is the amount of space
occupied by a cube that is 1 m along each
edge.
• This volume is a cubic meter (m3).
• A more convenient unit of volume for everyday
use is the liter, a non-SI unit.
• A liter (L) is the volume of a cube that is 10
centimeters (10 cm) along each edge (10
cm x 10 cm x 10 cm = 1000 cm3 = 1 L).
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3.2 Units of Measurement > Using SI Units
Units of Volume
• A smaller, non-SI unit of volume is the
milliliter (mL); 1 mL is 1/1000 of a liter.
• Thus, there are 1000 mL in 1 L.
• Because 1 L is defined as 1000 cm3, 1 mL
and 1 cm3 are the same volume.
• The units milliliter and cubic centimeter
are thus used interchangeably.
12
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3.2 Units of Measurement > Using SI Units
Units of Volume
These figures give you some idea of
the relative sizes of a liter and a
milliliter.
1L
1 mL
13
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3.2 Units of Measurement > Using SI Units
Units of Volume
• There are many devices for measuring liquid
volumes, including graduated cylinders,
pipets, burets, volumetric flasks, and
syringes.
• The volume of substances will change with
temperature, so accurate volume-measuring
devices are calibrated at a given
temperature—usually 20 degrees Celsius
(20°C), which is about normal room
temperature.
14
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3.2 Units of Measurement > Using SI Units
Units of Volume
The relationships among common metric units of volume
are shown in the table below.
Metric Units of Volume
Unit
Symbol
Liter
L
base unit
quart of milk ≈ 1 L
Milliliter
mL
103 mL = 1 L 20 drops of water ≈ 1 mL
Cubic centimeter
cm 3
1 cm 3 = 1 mL cube of sugar ≈ 1 cm 3
Microliter
15
Relationship Example
μL
103 μL = 1 L
crystal of table salt ≈ 1 μL
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3.2 Units of Measurement > Using SI Units
Units of Mass
• The mass of an object is measured in comparison to
a standard mass of 1 kilogram (kg), which is the
basic SI unit of mass.
• A kilogram was originally defined as the mass of 1 L
of liquid water at 4°C.
• A cube of water at 4°C measuring 10 cm on
each edge would have a volume of 1 L and a
mass of 1000 grams (g), or 1 kg.
• A gram (g) is 1/1000 of a kilogram; the mass of 1
cm3 of water at 4°C is 1 g.
16
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3.2 Units of Measurement > Using SI Units
Units of Mass
The relationships among units of mass are shown in the
table below.
Metric Units of Mass
Unit
17
Symbol
Relationship Example
Kilogram
(base unit)
kg
1 kg = 103 g
small textbook ≈ 1 kg
Gram
g
1 g = 10-3 kg
dollar bill ≈ 1 g
Milligram
mg
103 mg = 1 g ten grains of salt ≈ 1 mg
Microgram
μg
106 μg = 1 g
particle of baking powder ≈ 1 μg
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3.2 Units of Measurement > Using SI Units
Units of Mass
• Weight is a force that measures the pull on a
given mass by gravity.
• Weight, a measure of force, is different from
mass, which is a measure of the quantity of
matter.
• The weight of an object can change with its
location.
• An astronaut in orbit is weightless, but not
massless.
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3.2 Units of Measurement > Using SI Units
Units of Energy
• The capacity to do work or to produce heat is
called energy.
• The SI unit of energy is the joule (J), named
after the English physicist James Prescott
Joule (1818–1889).
• A common non-SI unit of energy is the calorie.
• One calorie (cal) is the quantity of heat that
raises the temperature of 1 g of pure water
by 1°C.
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3.2 Units of Measurement > Using SI Units
Units of Energy
• Conversions between joules and calories
can be carried out using the following
relationships.
• 1 J = 0.2390 cal
• 1 cal = 4.184 J
• A kilojoule is 1000 joules; a kilocalorie is
1000 calories.
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3.2 Units of Measurement >
What is the SI unit of volume?
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3.2 Units of Measurement >
What is the SI unit of volume?
The SI unit of volume is the cubic meter (m3). A
liter (L) can be converted to the SI unit of
volume, because a liter is defined as 1000 cm3.
22
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3.2 Units of Measurement > Temperature Scales
Temperature Scales
What temperature units do scientists
commonly use?
23
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3.2 Units of Measurement > Temperature Scales
• Temperature is a measure of how hot or
cold an object is.
• An object’s temperature determines the
direction of heat transfer.
• When two objects at different
temperatures are in contact, heat moves
from the object at the higher
temperature to the object at the lower
temperature.
24
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3.2 Units of Measurement > Temperature Scales
• Almost all substances expand with an
increase in temperature and contract as
the temperature decreases.
• A very important exception is water.
• These properties are the basis for the
common bulb thermometer.
25
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3.2 Units of Measurement > Temperature Scales
The liquid in a thermometer expands and
contracts more than the volume of the glass,
producing changes in the column height of
liquid.
26
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3.2 Units of Measurement > Temperature Scales
Scientists commonly use two equivalent
units of temperature, the degree Celsius
and the kelvin.
27
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3.2 Units of Measurement > Temperature Scales
• The Celsius scale sets the freezing point of
water at 0°C and the boiling point of water at
100°C.
• The distance between these two fixed
points is divided into 100 equal intervals, or
degrees Celsius (°C).
28
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3.2 Units of Measurement > Temperature Scales
• Another temperature scale used in the
physical sciences is the Kelvin, or absolute,
scale.
• This scale is named for Lord Kelvin (1824–
1907), a Scottish physicist.
• On the Kelvin scale, the freezing point of
water is 273.15 kelvins (K), and the boiling
point is 373.15 (K).
• Note that with the Kelvin scale, the degree
sign is not used.
29
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3.2 Units of Measurement > Temperature Scales
• The figure below compares the Celsius and Kelvin
scales.
• The zero point on the Kelvin scale, 0 K, or absolute
zero, is equal to –273.15°C.
Celsius
100
divisions
100°C
Boiling point
of water
373.15 K
0°C
Freezing point
of water
273.15 K
Kelvin
30
100
divisions
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3.2 Units of Measurement > Temperature Scales
• Because one degree on the Celsius scale
is equivalent to one kelvin on the Kelvin
scale, converting from one temperature to
another is easy.
• You simply add or subtract 273, as shown
in the following equations.
K = °C + 273
°C = K – 273
31
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3.2 Units of Measurement >
CHEMISTRY
& YOU
In a few countries, such as the United
States, metric units are not commonly
used in everyday measurements. What
temperature units are used for a typical
weather forecast in the United States?
What about for a country that uses the
metric system, such as Australia or
Japan?
32
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3.2 Units of Measurement >
CHEMISTRY
& YOU
In a few countries, such as the United
States, metric units are not commonly
used in everyday measurements. What
temperature units are used for a typical
weather forecast in the United States?
What about for a country that uses the
metric system, such as Australia or
Japan?
In the United States, temperatures are usually given
in degrees Fahrenheit. Countries that use the metric
system forecast the weather in degrees Celsius.
33
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3.2 Units of Measurement >
Sample Problem 3.7
Converting Between Temperature Scales
Normal human body temperature is
37°C. What is this temperature in
kelvins?
34
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3.2 Units of Measurement >
Sample Problem 3.7
1 Analyze List the known and the unknown.
Use the known value and the equation K = °C +
273 to calculate the temperature in kelvins.
KNOWN
Temperature in °C = 37°C
UNKNOWN
Temperature in K = ? K
35
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3.2 Units of Measurement >
Sample Problem 3.7
2 Calculate Solve for the unknown.
Substitute the known value for the Celsius
temperature into the equation and solve.
K = °C + 273 = 37 + 273 = 310 K
36
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3.2 Units of Measurement >
Sample Problem 3.7
3 Evaluate Does the result make sense?
You should expect a temperature in this range,
since the freezing point of water is 273 K and
the boiling point of water is 373 K; normal body
temperature is between these two values.
37
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3.2 Units of Measurement >
Is the change of one degree on the Celsius
scale equivalent to one kelvin on the Kelvin
scale?
38
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3.2 Units of Measurement >
Is the change of one degree on the Celsius
scale equivalent to one kelvin on the Kelvin
scale?
Yes, a change of one degree on the Celsius
scale is equivalent to a change of one kelvin on
the Kelvin scale.
39
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3.2 Units of Measurement > Density
Density
What determines the density of a
substance?
40
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3.2 Units of Measurement > Density
• The relationship between an object’s mass
and its volume tells you whether it will float
or sink.
• This relationship is called density.
• Density is the ratio of the mass of an
object to its volume.
Density =
41
mass
volume
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3.2 Units of Measurement > Density
• When mass is measured in grams, and
volume in cubic centimeters, density has
units of grams per cubic centimeter
(g/cm3).
• The SI unit of density is kilograms per
cubic meter (kg/m3).
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3.2 Units of Measurement > Density
This figure compares the density of four
substances: lithium, water, aluminum, and lead.
Increasing density (mass per unit volume)
10 g
19 cm3
0.53 g/cm3
43
10 g
10 cm3
10 g
3.7 cm3
10 g
0.88 cm3
1.0 g/cm3
2.7 g/cm3
0.88 g/cm3
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3.2 Units of Measurement > Density
Density is an intensive property that
depends only on the composition of a
substance, not the size of the sample.
44
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3.2 Units of Measurement > Density
• Because of differences in
density, liquids separate into
layers.
Corn oil
• As shown at right, corn oil
floats on top of water
because it is less dense.
Water
Corn syrup
• Corn syrup sinks below
water because it is more
dense.
45
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3.2 Units of Measurement >
Interpret Data
Densities of Some Common Materials
Solids and Liquids
46
Gases
Material
Density at
20°C (g/cm3)
Material
Density at
20°C (g/L)
Gold
19.3
Chlorine
2.95
Mercury
13.6
Carbon dioxide
1.83
Lead
11.3
Argon
1.66
Aluminum
2.70
Oxygen
1.33
Table sugar
1.59
Air
1.20
Corn syrup
1.35–1.38
Nitrogen
1.17
Water (4°C)
1.000
Neon
0.84
Corn oil
0.922
Ammonia
0.718
Ice (0°C)
0.917
Methane
0.665
Ethanol
0.789
Helium
0.166
Gasoline
0.66–0.69
Hydrogen
0.084
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3.2 Units of Measurement > Density
What happens to the density of a substance as its
temperature increases?
• The volume of most substances increases as the
temperature increases, while the mass remains the
same.
• Since density is the ratio of an object’s mass to its
volume, the density of a substance generally
decreases as its temperature increases.
• Water is an important exception.
47
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3.2 Units of Measurement >
Sample Problem 3.8
Calculating Density
A copper penny has a mass of 3.1 g
and a volume of 0.35 cm3. What is
the density of copper?
48
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3.2 Units of Measurement >
Sample Problem 3.8
1 Analyze List the knowns and the unknown.
Use the known values and the equation for density
to solve the problem.
KNOWNS
mass = 3.1 g
volume = 0.35 cm3
UKNOWN
density = ? g/cm3
49
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3.2 Units of Measurement >
Sample Problem 3.8
2 Calculate Solve for the unknown.
Start with the equation for density.
Density =
50
mass
volume
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3.2 Units of Measurement >
Sample Problem 3.8
2 Calculate Solve for the unknown.
Substitute the known values for mass and
volume and then calculate.
Density =
31 g
0.35 cm3
= 8.8571 g/cm3 = 8.9 g/cm3
The calculated answer must be
rounded to two significant figures.
51
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3.2 Units of Measurement >
3
Sample Problem 3.8
Evaluate Does the result make sense?
A piece of copper with a volume of about 0.3
cm3 has a mass of about 3 grams. About three
times that volume of copper, 1 cm3, should have
a mass three times larger, about 9 grams. This
estimate is close to the calculated result.
52
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3.2 Units of Measurement >
Can you assume that something with a low
weight will float in water?
53
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3.2 Units of Measurement >
Can you assume that something with a low
weight will float in water?
No, it is the relationship between an object’s
mass and its volume, its density, that tells you
whether it will float or sink.
54
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3.2 Units of Measurement > Key Concepts
All metric units are based on multiples of
10. As a result, you can convert between
units easily.
Scientists commonly use two equivalent
units of temperature, the degree Celsius
and the kelvin.
Density is an intensive property that
depends only on the composition of a
substance.
55
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3.2 Units of Measurement > Key Equations
K = °C + 273
°C = K – 273
Density = mass
volume
56
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3.2 Units of Measurement > Glossary Terms
• International System of Units (SI): the revised version
of the metric system, adopted by international
agreement in 1960
• meter (m): the base unit of length in SI
• liter (L): the volume of a cube measuring 10 centimeters
on each edge (1000 cm 3); it is the common unprefixed
unit of volume in the metric system
• kilogram (kg): the mass of 1 L of water at 4°C; it is the
base unit of mass in SI
• gram (g): a metric mass unit equal to the mass of 1 cm 3
of water at 4°C
57
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3.2 Units of Measurement > Glossary Terms
• weight: a force that measures the pull of gravity on a
given mass
• energy: the capacity for doing work or producing heat
• Joule (J): the SI unit of energy; 4.184 J equals one
calorie
• calorie (cal): the quantity of heat needed to raise the
temperature of 1 g of pure water 1°C
• temperature: a measure of the average kinetic energy of
particles in matter; temperature determines the direction
of heat transfer
58
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3.2 Units of Measurement > Glossary Terms
• Celsius scale: the temperature scale in which the
freezing point of water is 0°C and the boiling point is
100°C
• Kelvin scale: the temperature scale in which the freezing
point of water is 273 K and the boiling point is 373 K; 0 K
is absolute zero
• absolute zero: the zero point on the Kelvin temperature
scale, equivalent to –273.15°C
• density: the ratio of the mass of an object to its volume
59
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3.2 Units of Measurement >
END OF 3.2
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