christopher g. hamaker, illinois state university, normal il © 2008, prentice hall chapter 3 the...
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Christopher G. Hamaker, Illinois State University, Normal IL© 2008, Prentice Hall
Chapter 3The Metric System
INTRODUCTORY CHEMISTRYINTRODUCTORY CHEMISTRYConcepts & Connections
Fifth Edition by Charles H. Corwin
Chapter 3 2
Metric System Basic Units
Chapter 3 3
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 4
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 5
Metric System Prefixes
• The following table lists the common prefixes used in the metric system:
Know the common Prefix: k, c, m, µ
Chapter 3 6
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 7
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 8
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 9
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 10
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 11
Two Metric-Metric Conversions
• A hospital has 125 liters of blood plasma. What is the volume in milliliters?
• Step 1: We want the answer in mL.
• Step 2: We have 125 L.
• Step 3: We need to convert L to mL:
0.001 mL 1 L .
On your own, using dimensional analysis, set up and convert 125 L to mL in your notebook
Chapter 3 12
Metric and English Units
• The English system is still very common in the United States
All conversion factors are considered constants in our class. The constants have infinite significant digits
Chapter 3 13
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 14
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
On your own, using dimensional analysis, set up and convert 55 miles per hour to meters per second in your notebook
Chapter 3 15
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 16
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 17
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 18
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 19
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 20
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 21
The Density Concept
• The density of an object is a measure of its concentration of mass. It is an inherent property of a pure compound. Density does not change with the size or mass of the compound.
• Density is defined as the mass of an object divided by the volume of the object.
= densityvolumemass
Chapter 3 22
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 23
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 24
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 25
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 26
• 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 27
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 28
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 29
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 30
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.