1. Chapter 2 The Metric System by Christopher G. Hamaker
Illinois State University
© 2014 Pearson Education, Inc. 1

2. The International System of Units (SI)
Chemists use the metric system and the International System of Units (SI) Système International for measurement when they
measure quantities.
do experiments.
solve problems.
Your weight on a bathroom scale is a measurement.

3. Metric System Basic Units

4. Length Length is measured in
units of meters (m) in both the metric and SI systems.
units of centimeters (cm) by chemists.

5. Length
Useful relationships between units of length include: 1 m = yd 1 m = in. 1 m = 100 cm 2.54 cm = 1 in.

6. Volume Volume, the space occupied by a substance,
is measured using units of m3 in the SI system.
is commonly measured in liters (L) and milliliters (mL) by chemists.

7. Volume
Useful relationships between units of volume include: 1 m3 = 1000 L 1 L = 1000 mL 1 mL = 1 cm3 1 L = qt mL = 1 qt

8. Mass
The mass of an object, a measure of the quantity of material it contains,
is measured on an electronic balance.
has the SI unit of kilogram (kg).
is often measured by chemists in grams (g).

9. Mass
Useful relationships between units of mass include: 1 kg = 1000 g 1 kg = lb g = 1 lb

10. Temperature Temperature, a measure of how hot or cold an object feels,
is measured on the Celsius (°C) scale.
is measured on the Kelvin (K) scale in the SI system.
is 18 °C or 64 °F on this thermometer.

11. Time
Time is based on an atomic clock and is measured in units of seconds (s) in both the metric and SI systems.

12. Metric Prefixes
The following table lists the common prefixes used in the metric system:

13. Metric Prefixes, Continued
For example, the prefix kilo- increases a base unit by 1000:
1 kilogram is 1000 grams.
The prefix milli- decreases a base unit by a factor of 1000:
1000 millimeters is 1 meter.

14. Metric Symbols
The names of metric units are abbreviated using symbols. Use the prefix symbol followed by the symbol for the base unit:
Kilometer is abbreviated km.
Milligram is abbreviated mg.
Microliter is abbreviated mL.
Nanosecond is abbreviated ns.

15. Critical Thinking: The International System of Units (SI)
An advantage of the metric system (i.e., International System of Units, SI) is that it is a decimal system.
It uses prefixes to enlarge or reduce the basic units.
For example:
A kilometer is 1000 meters.
A millimeter is 1/1000 of a meter.

16. Metric Conversion Factors
A unit equation relates two quantities that are equal.
For example:
1 kilometer = 1000 meters
1 km = 1000 m
Also, we can write:
1 centimeter = 1/100 of a meter
1 cm = 0.01 m

17. Unit Factors
A unit conversion factor, or unit factor, is a ratio of two equivalent quantities.
For the unit equation 1 m = 100 cm, we can write two unit factors:
1 m or cm
100 cm m

18. Metric–Metric Conversions
An effective method for solving problems in science is the unit analysis method.
It is also often called dimensional analysis or the factor-label method.
There are three steps to solving problems using the unit analysis method.
Read the problem and determine the unit required in the answer.
Analyze the problem and determine the given value that is related to the answer.
Write one or more unit factors to convert the unit in the given value to the unit in the answer.

19. Applying the Unit Analysis Method

20. Metric Equivalents
We can write unit equations for the conversion between different metric units.
The prefix kilo- means 1000 basic units, so 1 kilometer is 1000 meters.
The unit equation is 1 km = 1000 m.
Similarly, a millimeter is 1/1000 of a meter, so the unit equation is 1000 mm = 1 m.

21. Metric Unit Factors
Since 1000 m = 1 km, we can write the following unit factors for converting between meters and kilometers:
1 km or m
1000 m km
Since 1000 mm = 1 m, we can write the following unit factors:
1000 mm or m .
1 m mm

22. Metric–Metric Conversion Problem
What is the mass in grams of a 325-mg aspirin tablet?
Step 1: We want grams.
Step 2: We write down the given: 325 mg.
Step 3: We apply a unit factor (1000 mg = 1 g) and round to three significant figures.
325 mg ×
= g
1000 mg
1 g

23. Two Metric–Metric Conversions
A hospital has 125 deciliters of blood plasma. What is the volume in milliliters?
Step 1: We want the answer in mL.
Step 2: We have 125 dL.
Step 3: We need to first convert dL to L and then convert L to mL:
1 L and mL
10 dL L

24. Two Metric–Metric Conversions, Continued
Apply both unit factors, and round the answer to three significant digits.
Notice that both dL and L units cancel, leaving us with units of mL.
125 dL ×
= 12,500 mL ×
10 dL
1 L
1000 mL

25. Another Example
The mass of the Earth’s moon is 7.35 × 1022 kg. What is the mass expressed in nanograms, ng?
We want ng; we have 7.35 × 1022 kg.
Convert kilograms to grams, and then grams to nanograms.
7.35 × 1022 kg ×
= 7.35 × 1031 ng ×
1 kg
1000 g
1 × 106 ng
1 g

26. Metric–English Conversions
The English system is still very common in the United States.
We often have to convert between English and metric units.

27. Metric–English Conversions, Continued
The length of an American football field, including the end zones, is 120 yards. What is the length in meters?
Convert 120 yd to meters (given that yd = m).
120 yd ×
= 110 m
1 yd
0.914 m

28. Metric–English Conversions, Continued
A half-gallon carton contains 64.0 fl oz of milk. How many milliliters of milk are in a carton?
We want mL; we have 64.0 fl oz.
Use 1 qt = 32 fl oz, and 1 qt = 946 mL.
64.0 fl oz ×
= 1,890 mL ×
32 fl oz
1 qt
946 mL

29. Another English–Metric Problem
A marathon is 26.2 miles. What is the distance in kilometers (1 km = 0.62 mi)?
Step 1: We want km.
Step 2: We write down the given: 26.2 mi.
Step 3: We apply a unit factor (1 km = 0.62 mi) and round to three significant figures.

30. Compound Units Some measurements have a ratio of units.
For example, the speed limit on many highways is 55 miles per hour. How would you convert this to meters per second?
Convert one unit at a time using unit factors.
First, miles → meters
Next, hours → seconds

31. Compound Unit Problem
A motorcycle is traveling at 105 km/hour. What is the speed in meters per second?
We have km/h; we want m/s.
Use 1 km = 1000 m and 1 h = 3600 s.
= 29.2 m/s ×
1 km
1000 m
1 hr
3600 s
105 km hr

32. Chemistry Connection: The Olympics
While the United States still uses English units of measure (mile, gallon, pounds), most of the rest of the world uses the metric system.
The distances in Olympic events are in metric units: 100-m dash; 30-km cross-country skiing; m steeplechase.
The 1600-m run is approximately 1 mile in length.

33. The Percent Concept
A percent, %, expresses the amount of a single quantity compared to an entire sample.
A percent is a ratio of parts per 100 parts.
The formula for calculating percent is shown below:

34. Calculating Percentages
Bronze is an allow of copper and tin. If a sample of bronze contains 79.2 g of copper and 10.8 g of tin, what is the percent copper in bronze?
= 88.0% ×
( ) g
79.2 g
100%

35. Percent Unit Factors
A percent can be expressed as parts per 100 parts.
25% can be expressed as 25/100 and 10% can be expressed as 10/100.
We can use a percent expressed as a ratio as a unit factor.
A rock is 4.70% iron, so

36. Percent Unit Factor Calculation
The Earth and Moon have a similar composition; each contains 4.70% iron. What is the mass of iron in a lunar sample that weighs 92 g?
Step 1: We want g iron.
Step 2: We write down the given: 92 g sample.
Step 3: We apply a unit factor (4.70 g iron = 100 g sample) and round to three significant figures.

37. Volume by Calculation
The volume of an object is calculated by multiplying the length (l) times the width (w) times the thickness (t).
volume = l × w × t
All three measurements must be in the same units.
If an object measures 3 cm by 2 cm by 1 cm, the volume is 6 cm3 (cm3 is cubic centimeters).

38. Volumes of Solids, Liquids, and Gases
The liter (L) is the basic unit of volume in the metric system.
One liter is defined as the volume occupied by a cube that is 10 cm on each side.

39. Volumes of Solids, Liquids, and Gases, Continued
1 liter is equal to 1000 cubic centimeters.
10 cm × 10 cm × 10 cm = cm3
1000 cm3 = 1 L = 1000 mL
Therefore, 1 cm3 = 1 mL

40. Cubic-Liquid Volume Conversion
An automobile engine displaces a volume of 498 cm3 in each cylinder. What is the displacement of a cylinder in cubic inches, in3?
We want in3; we have 498 cm3.
Use 1 in = 2.54 cm three times.
= 30.4 in3 ×
1 in
2.54 cm
498 cm3 ×

41. Volume by Displacement
If a solid has an irregular shape, its volume cannot be determined by measuring its dimensions.
You can determine its volume indirectly by measuring the amount of water it displaces.
This technique is called volume by displacement.
Volume by displacement can also be used to determine the volume of a gas.

42. Solid Volume by Displacement
You want to measure the volume of an irregularly shaped piece of jade.
Partially fill a volumetric flask with water and measure the volume of the water.
Add the jade, and measure the difference in volume.
The volume of the jade is 10.5 mL.

43. Gas Volume by Displacement
You want to measure the volume of gas given off in a chemical reaction.
The gas produced displaces the water in the flask into the beaker The volume of water displaced is equal to the volume of gas.

44. The Density Concept
The density of an object is a measure of its concentration of mass.
Density is defined as the mass of an object divided by the volume of the object.
= density
volume
mass

45. Density
Density is expressed in different units. It is usually grams per milliliter (g/mL) for liquids, grams per cubic centimeter (g/cm3) for solids, and grams per liter (g/L) for gases.

46. Densities of Common Substances

47. Estimating Density
We can estimate the density of a substance by comparing it to another object.
A solid object will float on top of a liquid with a higher density.
Object S1 has a density less than that of water, but larger than that of L1.
Object S2 has a density less than that of L2, but larger than that of water.

48. Calculating Density
What is the density of a platinum nugget that has a mass of g and a volume of 10.0 cm3 ? Recall, density is mass/volume.
= g/cm3
10.0 cm3 g

49. Density as a Unit Factor
We can use density as a unit factor for conversions between mass and volume.
An automobile battery contains 1275 mL of acid. If the density of battery acid is 1.84 g/mL, how many grams of acid are in an automobile battery?
– We have 1275 mL; we want grams:
1275 mL ×
= g mL
1.84 g

50. Temperature
Temperature is a measure of the average kinetic energy of individual particles in motion.
There are three temperature scales:
Fahrenheit
Celsius
Kelvin
Kelvin is the absolute temperature scale.

51. Temperature Scales
On the Fahrenheit scale, water freezes at 32 °F and boils at 212 °F.
On the Celsius scale, water freezes at 0 °C and boils at 100 °C. These are the reference points for the Celsius scale.
Water freezes at 273 K and boils at 373 K on the Kelvin scale.

52. Temperature Conversions
This is the equation for converting °C to °F.
This is the equation for converting °F to °C.
To convert from °C to K, add 273.
°C = K

53. Fahrenheit-Celsius Conversions
Body temperature is 98.6 °F. What is body temperature in degrees Celsius? In Kelvin?
K = °C = °C = 310 K

54. The Heat Concept Heat is a measure of total energy.
Temperature measures the average energy of particles in a system.
Heat is often expressed in terms of joules (J) or calories (cal).

55. Heat Versus Temperature
Although both beakers below have the same temperature (100 ºC), the beaker on the right has twice the amount of heat because it has twice the amount of water.

56. Specific Heat
The specific heat of a substance is the amount of heat required to raise the temperature of one gram of substance one degree Celsius.
It is expressed with units of calories per gram per degree Celsius.
The larger the specific heat, the more heat is required to raise the temperature of the substance.

57. Chapter Summary
The basic units in the metric system are grams for mass, liters for volume, and meters for distance.
The base units are modified using prefixes to reduce or enlarge the base units by factors of 10.
We can use unit factors to convert between metric units.
We can convert between metric and English units using unit factors.

58. Chapter Summary, Continued
A unit equation is a statement of two equivalent quantities.
A unit factor is a ratio of two equivalent quantities.
Unit factors can be used to convert measurements between different units.
A percent is the ratio of parts per 100 parts.

59. Chapter Summary, Continued
Volume is defined as length × width × thickness.
Volume can also be determined by displacement of water.
Density is mass divided by volume.

60. Chapter Summary, Continued
Temperature is a measure of the average energy of the particles in a sample.
Heat is a measure of the total energy of a substance.
Specific heat is a measure of how much heat is required to raise the temperature of a substance.