1. A measurement is a quantity that has both a number and a unit.
Scientific Notation
A measurement is a quantity that has both a number and a unit.
Your height (66 inches), your age (15 years), and your body temperature (37°C) are examples of measurements.
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2. Scientific Notation
In chemistry, you will often encounter very large or very small numbers.
A single gram of hydrogen, for example, contains approximately 602,000,000,000,000,000,000,000 hydrogen atoms.
You can work more easily with very large or very small numbers by writing them in scientific notation.
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3. Scientific Notation
In scientific notation, a given number is written as the product of two numbers: a coefficient and 10 raised to a power.
For example, the number 602,000,000,000,000,000,000,000 can be written in scientific notation as 6.02 x 1023.
The coefficient in this number is The power of 10, or exponent, is 23.
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4. Scientific Notation
In scientific notation, the coefficient is always a number greater than or equal to one and less than ten. The exponent is an integer.
A positive exponent indicates how many times the coefficient must be multiplied by 10.
A negative exponent indicates how many times the coefficient must be divided by 10.
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5. Scientific Notation
When writing numbers greater than ten in scientific notation, the exponent is positive and equals the number of places that the original decimal point has been moved to the left.
6,300,000. = 6.3 x 106
94,700. = 9.47 x 104
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6. Scientific Notation
Numbers less than one have a negative exponent when written in scientific notation. The value of the exponent equals the number of places the decimal has been moved to the right.
= 8 x 10–6
= 7.36 x 10–3
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7. Accuracy, Precision, and Error
How do you evaluate accuracy and precision?
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8. Accuracy, Precision, and Error
Accuracy and Precision
In chemistry, the meanings of accuracy and precision are quite different.
Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured.
Precision is a measure of how close a series of measurements are to one another, irrespective of the actual value.
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9. Accuracy, Precision, and Error
Accuracy and Precision
To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.
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10. Accuracy, Precision, and Error
Accuracy and Precision
Darts on a dartboard illustrate the difference between accuracy and precision.
Good Accuracy, Good Precision
Poor Accuracy, Good Precision
Poor Accuracy, Poor Precision
The closeness of a dart to the bull’s-eye corresponds to the degree of accuracy. The closeness of several darts to one another corresponds to the degree of precision.
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11. Accuracy, Precision, and Error
Determining Error
Suppose you use a thermometer to measure the boiling point of pure water at standard pressure.
The thermometer reads 99.1°C.
You probably know that the true or accepted value of the boiling point of pure water at these conditions is actually
100.0°C.
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12. Accuracy, Precision, and Error
Determining Error
There is a difference between the accepted value, which is the correct value for the measurement based on reliable references, and the experimental value, the value measured in the lab.
The difference between the experimental value and the accepted value is called the error.
Error = experimental value – accepted value
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13. Accuracy, Precision, and Error
Determining Error
Error can be positive or negative, depending on whether the experimental value is greater than or less than the accepted value.
For the boiling-point measurement, the error is 99.1°C – 100°C, or –0.9°C.
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14. Are precise measurements always accurate?
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15. Are precise measurements always accurate?
No, measurements are precise if they are easily reproducible, but not accurate if they do not reflect the accepted value.
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16. Using SI Units What makes metric units easy to use? Using SI Units
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17. 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.
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18. There are seven SI base units.
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 substance
mole
mol
Luminous intensity
candela cd
Electric current
ampere A
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19. 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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20. 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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21. 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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22. Temperature Scales What temperature units do scientists commonly use?
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23. 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.
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24. A very important exception is water.
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.
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25. 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.
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26. Temperature Scales
Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin.
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27. 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).
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28. 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 kelvins (K), and the boiling point is (K).
Note that with the Kelvin scale, the degree sign is not used.
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29. 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 –273.15°C.
Celsius
Kelvin
100
divisions
100°C
Boiling point
of water K
0°C
Freezing point K
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30. 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 = °C + 273
°C = K – 273
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31. Converting Between Temperature Scales
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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32. Is the change of one degree on the Celsius scale equivalent to one kelvin on the Kelvin scale?
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33. 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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34. Density What determines the density of a substance? Density
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35. This relationship is called 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.
mass
volume
Density =
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36. 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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37. 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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38. 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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39. 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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40. 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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41. Can you assume that something with a low weight will float in water?
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42. 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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