3.2 Units of Measurement > 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Chapter 3 Scientific Measurement 3.1 Using and Expressing Measurements 3.2 Units of Measurement 3.3 Solving Conversion Problems
3.2 Units of Measurement >
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Chapter 3Scientific Measurement
3.1 Using and Expressing
Measurements
3.2 Units of Measurement
3.3 Solving Conversion Problems
3.2 Units of Measurement >
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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.
CHEMISTRY & YOU
What’s the forecast for tomorrow—hot or cold?
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Using SI Units
What makes metric units easy to use?
Using SI Units
3.2 Units of Measurement >
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• 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.
Using SI Units
3.2 Units of Measurement >
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• 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.
Using SI Units
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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.
SI Base Units
Quantity SI base
unit
Symbol
Length meter m
Mass kilogram kg
Temperature kelvin K
Time second s
Amount of
substancemole mol
Luminous
intensitycandela cd
Electric
currentampere A
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• 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.
Units of Length
Using SI Units
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Using SI Units
The table below lists the prefixes in common use.
Units of Length
Commonly Used Metric Prefixes
Prefix Symbol 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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• 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.
Units of Length
Using SI Units
3.2 Units of Measurement >
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• 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.
Units of Volume
Using SI Units
3.2 Units of Measurement >
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• 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).
Units of Volume
Using SI Units
3.2 Units of Measurement >
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• 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.
Units of Volume
Using SI Units
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These figures give you some idea of
the relative sizes of a liter and a
milliliter.
Units of Volume
Using SI Units
1 mL
1 L
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• 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.
Units of Volume
Using SI Units
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Using SI Units
The relationships among common metric units of volume
are shown in the table below.
Units of Volume
Metric Units of Volume
Unit Symbol Relationship Example
Liter L base unit quart of milk ≈ 1 L
Milliliter mL 103 mL = 1 L 20 drops of water ≈ 1 mL
Cubic centimeter cm3 1 cm3 = 1 mL cube of sugar ≈ 1 cm3
Microliter μL 103 μL = 1 L crystal of table salt ≈ 1 μL
3.2 Units of Measurement >
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• 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.
Units of Mass
Using SI Units
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Using SI Units
The relationships among units of mass are shown in the
table below.
Units of Mass
Metric Units of Mass
Unit 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
3.2 Units of Measurement >
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• Weight is a force that measures the pull on a given mass by gravity.
• Weight, a measure of force, is different frommass, which is a measure of the quantity ofmatter.
• The weight of an object can change with itslocation.
• An astronaut in orbit is weightless, but notmassless.
Units of Mass
Using SI Units
3.2 Units of Measurement >
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• The capacity to do work or to produce heat is called energy.
• The SI unit of energy is the joule (J), namedafter the English physicist James PrescottJoule (1818–1889).
• A common non-SI unit of energy is the calorie.
• One calorie (cal) is the quantity of heat thatraises the temperature of 1 g of pure waterby 1°C.
Units of Energy
Using SI Units
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• 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.
Units of Energy
Using SI Units
3.2 Units of Measurement >
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What is the SI unit of volume?
3.2 Units of Measurement >
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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.
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Temperature Scales
What temperature units do scientists
commonly use?
Temperature Scales
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• 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.
Temperature Scales
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• 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.
Temperature Scales
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The liquid in a thermometer expands and
contracts more than the volume of the glass,
producing changes in the column height of
liquid.
Temperature Scales
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Scientists commonly use two equivalent
units of temperature, the degree Celsius
and the kelvin.
Temperature Scales
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• 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).
Temperature Scales
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• 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.
Temperature Scales
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• 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.
Temperature Scales
Celsius
Kelvin
100
divisions
100
divisions
100°C
Boiling point
of water
373.15 K
0°C
Freezing point
of water
273.15 K
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• 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.
Temperature Scales
K = °C + 273°C = K – 273
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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?
CHEMISTRY & YOU
3.2 Units of Measurement >
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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?
CHEMISTRY & YOU
In the United States, temperatures are usually given
in degrees Fahrenheit. Countries that use the metric
system forecast the weather in degrees Celsius.
3.2 Units of Measurement >
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Sample Problem 3.7
Converting Between Temperature Scales
Normal human body temperature is
37°C. What is this temperature in
kelvins?
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Sample Problem 3.7
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
1
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Sample Problem 3.7
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
2
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Sample Problem 3.7
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.
3
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Is the change of one degree on the Celsius
scale equivalent to one kelvin on the Kelvin
scale?
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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.
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Density
What determines the density of a
substance?
Density
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• 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
massvolume
Density =
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• 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).
Density
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This figure compares the density of four
substances: lithium, water, aluminum, and lead.
Density
Increasing density (mass per unit volume)
10 g
0.53 g/cm3
19 cm3
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
3.2 Units of Measurement >
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Density is an intensive property that
depends only on the composition of a
substance, not the size of the sample.
Density
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• Because of differences in density, liquids separate into layers.
• As shown at right, corn oil floats on top of water because it is less dense.
• Corn syrup sinks below water because it is more dense.
Density
Corn oil
Water
Corn syrup
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Interpret Data
Densities of Some Common Materials
Solids and Liquids Gases
MaterialDensity 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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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.
Density
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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?
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Sample Problem 3.8
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
1
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Sample Problem 3.8
Density =mass
volume
Calculate Solve for the unknown.
Start with the equation for density.
2
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Calculate Solve for the unknown.
Substitute the known values for mass and
volume and then calculate.
Sample Problem 3.8
2
Density =31 g
0.35 cm3= 8.8571 g/cm3 = 8.9 g/cm3
The calculated answer must be
rounded to two significant figures.
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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.
3
3.2 Units of Measurement >
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Can you assume that something with a low
weight will float in water?
3.2 Units of Measurement >
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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.
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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.
Key Concepts
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K = °C + 273
°C = K – 273
Key Equations
Density =massvolume
3.2 Units of Measurement >
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• 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 cm3); 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 cm3
of water at 4°C
Glossary Terms
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• 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
Glossary Terms
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• 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
Glossary Terms
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END OF 3.2