1. Chapter 3 Scientific Measurement 3.2 Units of Measurement
3.1 Using and Expressing
Measurements
3.2 Units of Measurement
3.3 Solving Conversion Problems
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2. What’s the forecast for tomorrow—hot or cold?
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.
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3. Using SI Units What makes metric units easy to use?
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.
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4. Derived units are used for measurements such as
Using SI Units
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
The International System of Units (abbreviated SI after the French name, Le Système International d’Unités) is a revised version of the metric system.
There are seven SI base units, and from these all other 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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5. In SI, the basic unit of length, or linear measure, is the meter (m).
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 is more convenient to use a unit of length that has a prefix.
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6. Commonly Used Metric Prefixes
Using SI Units
Units of Length
The table below lists the prefixes in common use.
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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7. The space occupied by any sample of matter is called its volume.
Using SI Units
Units of Length
For example, the prefix milli- means 1/1000, so a millimeter (mm) is 1/1000 of a meter, or m.
For large distances, it is most appropriate to express measurements in km (1000 m.).
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 x width, x height.
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8. This volume is a cubic meter (m3).
Using SI Units
Units of Volume
The unit for volume is thus derived from the units of length. 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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9. The units milliliter and cubic centimeter are used interchangeably.
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 used interchangeably.
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10. Using SI Units
Units of Volume
These figures give you some idea of the relative sizes of a liter and a milliliter.
1 L
1 mL
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11. 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 (20⁰ C), which is about normal room temperature.
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12. Units of Volume Using SI Units
The relationships among common metric units of volume are shown in the table below.
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
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13. Units of Mass Using SI Units
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 4⁰ C.
A cube of water at 4⁰ 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 4⁰ C is 1 g.
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14. Units of Mass Using SI Units
The relationships among units of mass are shown in the table below.
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
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15. Weight is a force that measures the pull on a given mass by gravity.
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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16. The capacity to do work or to produce heat is called energy.
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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17. A kilojoule is 1000 joules; a kilocalorie is 1000 calories.
Using SI Units
Units of Energy
Conversions between joules and calories can be carried out using the following relationships.
1 J = cal
1 cal = J
A kilojoule is 1000 joules; a kilocalorie is 1000 calories.
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18. What is the SI unit of volume?
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19. 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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20. Temperature Scales What temperature units do scientists commonly use?
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21. Temperature is a measure of how hot or cold an object is.
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.
Almost all substances expand with an increase in temperature and contract as the temperature decreases.
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22. A very important exception is water. The liquid in a thermometer
Temperature Scales
A very important exception is
water.
The liquid in a thermometer
expands and contracts more
than the volume of the glass,
producing changes in the
column height of liquid.
These properties are the
basis for the common bulb
thermometer.
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23. Temperature Scales
Scientists commonly use two equivalent units of temperature, the degree Celsius and the Kelvin.
The Celsius scale sets the freezing point of water at 0⁰ C and the boiling point of water at 100⁰ C.
The distance between these two fixed points is divided into 100 equal intervals, or degrees Celsius (⁰ C).
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24. This scale is named for Lord Kelvin (1824–1907), a Scottish physicist.
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 kelvin (K), and the boiling point is (K).
Note that with the Kelvin scale, the degree sign is not used.
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25. The figure below compares the Celsius and Kelvin scales.
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 –273.15⁰ C.
Celsius
Kelvin
100
divisions
100⁰ C
Boiling point
of water K
0⁰ C
Freezing point K
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26. You simply add or subtract 273, as shown in the following equations.
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 = ⁰ C + 273
⁰ C = K – 273
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27. Converting Between Temperature Scales
Sample Problem 3.7
Converting Between Temperature Scales
Normal human body temperature is 37⁰ C. What is this temperature in kelvins?
Analyze List the known and the unknown.
Use the known value and the equation
K = ⁰ C to calculate the temperature in kelvins. KNOWN Temperature in °C = 37⁰ C
UNKNOWN Temperature in K = ? K
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28. 2. Calculate Solve for the unknown.
Sample Problem 3.7
2. Calculate Solve for the unknown.
Substitute the known value for the Celsius
temperature into the equation and solve.
K = ⁰ C = = 310 K
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.
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29. Is the change of one degree on the Celsius scale equivalent to one kelvin on the Kelvin scale?
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30. 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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31. What determines the density of a substance?
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.
mass
volume
Density =
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32. The SI unit of density is kilograms per cubic meter (kg/m3).
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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33. Density
This figure compares the density of four substances: lithium, water, aluminum, and lead.
Increasing density (mass per unit volume)
10 g
0.53 g/cm3
19 cm3
10 cm3
3.7 cm3
0.88 cm3
1.0 g/cm3
2.7 g/cm3
0.88 g/cm3
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34. Density
Density is an intensive property that depends only on the composition of a substance, not the size of the sample.
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35. 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.
Corn oil
Water
Corn syrup
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36. Densities of Some Common Materials
Interpret Data
Densities of Some Common Materials
Solids and Liquids
Gases
Material
Density at 20°C (g/cm3)
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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37. Water is an important exception.
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.
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38. Analyze List the knowns and the unknown.
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?
Analyze List the knowns and the
unknown.
KNOWNS mass = 3.1 g volume = 0.35 cm3
UKNOWN density = ? g/cm3
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39. Calculate Solve for the unknown. Start with the equation for density.
Sample Problem 3.8
Calculate Solve for the unknown.
Start with the equation for density. 2
Density =
mass
volume
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40. Calculate Solve for the unknown.
Sample Problem 3.8
Calculate Solve for the unknown.
Substitute the known values for mass and volume and then calculate. 2
Density =
31 g
0.35 cm3
= g/cm3 = 8.9 g/cm3
The calculated answer must be rounded to two significant figures.
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41. Evaluate Does the result make sense?
Sample Problem 3.8 3
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.
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42. Can you assume that something with a low weight will float in water?
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43. 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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44. 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.
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45. K = °C + 273 °C = K – 273 Key Equations mass Density = volume
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46. meter (m): the base unit of length in SI
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 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
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47. weight: a force that measures the pull of gravity on a given mass
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; 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
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48. density: the ratio of the mass of an object to its volume
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
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