Christopher G. Hamaker, Illinois State University, Normal IL© 2008, Prentice Hall

Chapter 3The Metric System

INTRODUCTORY CHEMISTRYConcepts & Connections

Fifth Edition by Charles H. Corwin

Chapter 3 2

The Metric System• The English system was used primarily in the

British Empire and wasn’t very standardized.

• The French organized a committee to devise a universal measuring system.

• After about 10 years, the committee designed and agreed on the metric system.

• The metric system offers simplicity with a single base unit for each measurement.

Chapter 3 3

Metric System Basic Units

Chapter 3 4

Original Metric Unit Definitions• A meter was defined as 1/10,000,000 of the

distance from the North Pole to the equator.

• A kilogram (1000 grams) was equal to the mass of a cube of water measuring 0.1 m on each side.

• A liter was set equal to the volume of one kilogram of water at 4 C.

Chapter 3 5

Metric System Advantage• Another advantage of the metric system 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.

Chapter 3 6

Metric System Prefixes

• The following table lists the common prefixes used in the metric system:

Chapter 3 7

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:

–1 millimeter is 0.001 meters

Chapter 3 8

Metric Symbols• The names of metric units are abbreviated using

symbols. Use the prefix symbol followed by the symbol for the base unit, so:

–nanometer is abbreviated nm

–microgram is abbreviated mg

–deciliter is abbreviated dL

–gigasecond is abbreviated Gs

Chapter 3 9

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 1 mm = 0.001 m.

Chapter 3 10

Metric Unit Factors• Since 1000 m = 1 km, we can write the following

unit factors for converting between meters and kilometers:

1 km or 1000 m 1000 m 1 km

• Since 1 m = 0.001 mm, we can write the following unit factors.

1 mm or 0.001 m 0.001 m 1 mm

Chapter 3 11

Metric-Metric Conversions• We will use the unit analysis method we learned in

Chapter 2 to do metric-metric conversion problems.

• Remember, there are three steps:– Write down the unit asked for in the answer.

– Write down the given value related to the answer.

– Apply unit factor(s) to convert the given unit to the units desired in the answer.

Chapter 3 12

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 (1 mg = 0.001 g) and round to three significant figures.

325 mg × = 0.325 g1 mg

0.001 g

Chapter 3 13

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:

0.1 L and 0.001 mL1 dL 1 L .

Chapter 3 14

Problem, continued• Apply both unit factors, and round the answer to 3

significant digits.

• Notice that both dL and L units cancel, leaving us with units of mL.

125 dL × = 12,500 mL×1 dL0.1 L 1 mL

0.001 L

Chapter 3 15

Another Example

• The mass of the Earth’s moon is 7.35 × 1022 kg. What is the mass expressed in megagrams, Mg?

• We want Mg; we have 7.35 × 1022 kg.

• Convert kilograms to grams, and then grams to megagrams.

7.35 × 1022 kg × = 5.98 × 1019 Mg×1 kg

1000 g 1 Mg

1000000 g

Chapter 3 16

Metric and English Units• The English system is still very common in the

United States.

• We often have to convert between English and metric units.

Chapter 3 17

Metric-English Conversion

• 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 1 yd = 0.914 m.

120 yd × = 110 m1 yd

0.914 m

Chapter 3 18

English-Metric Conversion

• 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 mL1 qt

Chapter 3 19

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

– second, hours → seconds

Chapter 3 20

Compound Unit Problem• A motorcycle is traveling at 75 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.

= 21 m/s×1 km

1000 m 1 hr3600 s

75 kmhr

×

Chapter 3 21

Volume by Calculation

• The volume of an object is calculated by multiplying the length (l) by the width (w) by 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).

Chapter 3 22

Cubic Volume and Liquid Volume

• 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.

Chapter 3 23

Cubic & Liquid Volume Units• 1 liter is equal to 1000 cubic centimeters

–10 cm × 10 cm × 10 cm = 1000 cm3

• 1000 cm3 = 1 L = 1000 mL

• Therefore, 1 cm3 = 1 mL.

Chapter 3 24

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 ×

1 in2.54 cm

1 in2.54 cm

Chapter 3 25

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.

Chapter 3 26

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.

Chapter 3 27

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.

Chapter 3 28

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.

= densityvolumemass

Chapter 3 29

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.

Chapter 3 30

Densities of Common Substances

Chapter 3 31

Estimating Density• We can estimate the density of a

substance by comparing it to another object.

• A solid object will float on top 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.

Chapter 3 32

Calculating Density• What is the density of a platinum nugget that has a

mass of 224.50 g and a volume of 10.0 cm3 ?

• Recall, density is mass/volume.

= 22.5 g/cm3

10.0 cm3

224.50 g

Chapter 3 33

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 × = 2350 gmL

1.84 g

Chapter 3 34

Critical Thinking: Gasoline

• The density of gasoline is 730 g/L at 0 ºC (32 ºF) and 713 g/L at 25 ºC (77 ºF). What is the mass difference of 1.00 gallon of gasoline at these two temperatures (1 gal = 3.784L)?

• The difference is about 60 grams (about 2 %).

= 2760 g×At 0 ºC: 1.00 gal ×730 g

L3.784 L1 gal

= 2700 g×At 25 ºC: 1.00 gal ×713 g

L3.784 L1 gal

Chapter 3 35

Temperature• Temperature is a measure of the average kinetic

energy of the individual particles in a sample.

• There are three temperature scales:– Celsius

– Fahrenheit

– Kelvin

• Kelvin is the absolute temperature scale.

Chapter 3 36

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 273K and boils at 373K on the Kelvin scale.

Chapter 3 37

• 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 + 273 = K

Temperature Conversions

= °F°C ×100°C180°F( )

( )180°F100°C

= °C(°F - 32°F) ×

Chapter 3 38

Fahrenheit-Celsius Conversions

• Body temperature is 98.6 °F. What is body temperature in degrees Celsius? In Kelvin?

K = °C + 273 = 37.0 °C + 273 = 310 K

( )180°F100°C

= 37.0°C(98.6°F - 32°F) ×

Chapter 3 39

Heat

• Heat is the flow of energy from an object of higher temperature to an object of lower temperature.

• Heat measures the total energy of a system.

• Temperature measures the average energy of particles in a system.

• Heat is often expressed in terms of joules (J) or calories (cal).

Chapter 3 40

Heat vs. 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.

Chapter 3 41

Specific Heat

• The specific heat of a substance is the amount of heat required to bring about a change in temperature.

• 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.

Chapter 3 42

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.

Chapter 3 43

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.

Chapter 3 44

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.