1. 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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2. Density Volume generally increases with temperature
Density increases with temperature
Water is an important exception.

3. 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?

4. 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

5. 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.

6. Can you assume that something with a low weight will float in water?

7. 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.

8. 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.

9. Key Equations
K = °C + 273
°C = K – 273
Density =
mass
volume

10. 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

11. 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

12. 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

13. Conversion Problems

14. Conversion Factors
If you think about any number of everyday situations, you will realize that a quantity can usually be expressed in several different ways.
For example:
1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies
These are all expressions, or measurements, of the same amount of money.

15. The same is true of scientific quantities. For example:
1 meter = 10 decimeters = 100 centimeters = 1000 millimeters

16. Whenever two measurements are equivalent, a ratio will equal 1,
For example, you can divide both sides of the equation 1 m = 100 cm by 1 m or by 100 cm.
1 m =
100 cm 1 or

17. A conversion factor is a ratio of equivalent measurements.
The ratios 100 cm/1 m and 1 m/100 cm are examples of conversion factors.
A conversion factor is a ratio of equivalent measurements.
conversion factors
1 m =
100 cm 1 or

18. 1 meter
100 centimeters
Larger unit
Smaller unit
100 1 m cm
Smaller number
Larger number
The figure above illustrates another way to look at the relationships in a conversion factor.

19. The figure at right shows a scale that can be used to measure mass in grams or kilograms.
If you read the scale in terms of grams, you can convert the mass to kilograms by multiplying by the conversion factor 1 kg/1000 g.

20. The relationship between nanometers and meters is given by the equation 109 nm = 1 m.
The possible conversion factors are
109 nm
1 m
and

21. The relationship 1 L = 106μL yields the following conversion factors:
Common volumetric units used in chemistry include the liter and the microliter.
The relationship 1 L = 106μL yields the following conversion factors:
1 L
106 μL
and

22. Dimensional Analysis
Many problems in chemistry are conveniently solved using dimensional analysis, rather than algebra.
Dimensional analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements.

23. Using Dimensional Analysis
Sample Problem 3.9
Using Dimensional Analysis
How many seconds are in a workday that lasts exactly eight hours?

24. Calculate Solve for the unknown.
Sample Problem 3.9
Calculate Solve for the unknown.
Multiply the time worked by the conversion factors. 2
60 s
1 min
60 min
1 h
8 h x =
28,000 s
x 104 s

25. Using Dimensional Analysis
Sample Problem 3.10
Using Dimensional Analysis
The directions for an experiment ask each student to measure 1.84 g of copper (Cu) wire. The only copper wire available is a spool with a mass of 50.0 g. How many students can do the experiment before the copper runs out?

26. Calculate Solve for the unknown.
Sample Problem 3.10
Calculate Solve for the unknown.
Because the desired unit for the answer is students, use the second conversion factor. Multiply the mass of copper by the conversion factor. 2
50.0 g Cu x
1.84 g Cu
1 student =
students
27 students

27. The conversion factor to convert from U.S. dollars to euros would be
CHEMISTRY & YOU
If the exchange rate between U.S. dollars and euros is 0.7 euro to every dollar, what is the conversion factor that allows you to convert from U.S. dollars to euros?
The conversion factor to convert from U.S. dollars to euros would be
0.7 euro
1 U.S. dollar

28. Using Density as a Conversion Factor
Sample Problem 3.12
Using Density as a Conversion Factor
What is the volume of a pure silver coin that has a mass of 14 g? The density of silver (Ag) is 10.5 g/cm3.

29. Calculate Solve for the unknown.
Sample Problem 3.12
Calculate Solve for the unknown.
Multiply the mass of the coin by the conversion factor. 2
14 g Ag x
= 1.3 cm3 Ag
1 cm3 Ag
10.5 g Ag

30. Dimensional Analysis
Multistep Problems
Many complex tasks in your life are best handled by breaking them down into smaller, manageable parts.
Similarly, many complex word problems are more easily solved by breaking the solution down into steps.

31. Converting Between Metric Units
Sample Problem 3.13
Converting Between Metric Units
The diameter of a sewing needle is cm. What is the diameter in micrometers?

32. Calculate Solve for the unknown.
Sample Problem 3.13
Calculate Solve for the unknown.
Multiply the known length by the conversion factors. 2
7.3 x 10-2 cm x =
7.3 x 102 μm
1 m
102 cm
106 μm x

33. Converting Ratios of Units
Sample Problem 3.14
Converting Ratios of Units
The density of manganese (Mn), a metal, is 7.21 g/cm3. What is the density of manganese expressed in units of kg/m3?

34. Calculate Solve for the unknown.
Sample Problem 3.14
Calculate Solve for the unknown.
Multiply the known density by the correct conversion factors. 2
7.21 g
1 cm3 x
1 kg
103 g
106 cm3
1 m3
= 7.21 x 103 kg/m3

35. Key Concepts
When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same.
Dimensional analysis is a powerful tool for solving conversion problems in which a measurement with one unit is changed to an equivalent measurement with another unit.

36. Glossary Terms
conversion factor: a ratio of equivalent measurements used to convert a quantity from one unit to another
dimensional analysis: a technique of problem-solving that uses the units that are part of a measurement to help solve the problem