Chapter 3: 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.
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Metric System Basic Units
Base units:
-temperature: kelvin (K)
-amount of substance: mole (mol)
-heat: joules (J) - (1 cal = 4.184 J )
-power: watts (W) - (J/s)
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1
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.
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Chapter 3
Metric System Advantage
• Another advantage of the metric system is that it is
a decimal system.
• It uses prefixes
.
• For example: base unit is meters.
– A kilometer is 1000 meters.
– A millimeter is 1/1000 of a meter.
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2
Metric System Prefixes
• The following table lists the common prefixes
used in the metric system:
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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:
– There are 1000 millimeters in 1 meter.
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3
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. (nanotechnology)
– Microgram is abbreviated μg.
– Deciliter is abbreviated dL.
– Gigasecond is abbreviated Gs.
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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.
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4
Metric Unit Factors
• Since 1000 m = 1 km, we can write the following
unit factors for converting between meters and
kilometers:
1 km
1000 m
or
1000 m
1 km
• Since 1000 mm = 1 m, we can write the following
unit factors:
1000 mm
1m
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or
1m .
1000 mm
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Chapter 3
Metric–Metric Conversions
•
Unit analysis method - learned in Chapter 2 for
metric–metric conversion.
•
Remember, there are three steps:
1.
.
2.
.
3.
.
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5
Metric–Metric Conversion Problem
What is the mass in grams of a 325 mg aspirin
tablet?
• Step 1: We want
.
• Step 2: We write down the given:
.
• Step 3: We apply a unit factor (
and round to three significant figures.
)
=
x
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Chapter 3
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
• Step 2: We have
.
• Step 3: We need to first convert
convert
:
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Chapter 3
and then
12
6
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.
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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 x 1022 kg.
• Convert kilograms to grams, and then grams to
megagrams.
7.35 x 1022 kg ×
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1000 g
1 Mg
x
= 7.35 x 1019 Mg
1000000 g
1 kg
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7
Metric and English Units
• The English system is very common in the US.
• We often have to convert between English and
metric units.
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Chapter 3
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Metric–English Conversion
The length of an American football field,
including the end zones, is 120 yards. What is
the length in meters?
• We want meters
• We have 120 yd
• Given 1 yd = 0.914 m).
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8
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.
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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.
1. First, miles → meters
2. Next, hours → seconds
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9
Compound Unit Problem
A motorcycle is traveling at 75 km/hour. What is
the speed in meters per second?
• We want m/s
• Have km/hr
• Use 1 km = 1000 m and 1 h = 3600 s.
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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 x w x 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).
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10
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.
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Cubic and Liquid Volume Units
• 1 liter is equal to 1000 cubic centimeters.
– 10 cm x 10 cm x 10 cm = 1000 cm3
• 1000 cm3 = 1 L = 1000 mL.
• Therefore, 1 cm3 = 1 mL.
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11
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?
• We want in3;
• we have 498 cm3.
• Use 1 in = 2.54 cm three times.
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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.
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12
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.
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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.
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13
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.
mass
= density
volume
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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.
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14
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.
224.50 g
= 22.5 g/cm3
10.0 cm3
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Densities of Common Substances
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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.
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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 want grams; have 1275 mL
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16
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 %
how?).
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Temperature
•
Temperature is a measure of the average kinetic
energy of the individual particles in a sample.
•
There are three temperature scales:
1. Celsius
2. Fahrenheit
3. Kelvin
•
Kelvin is the absolute temperature scale.
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17
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.
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Chapter 3
Temperature Conversions
• This is the equation for converting °C to °F.
°C x
(
180°F
100°C
) = °F + 32°F = °F
• This is the equation for converting °F to °C.
(
)
100°C
= °C
(°F - 32°F) x 180°F
• To convert from °C to K, add 273.
°C + 273 = K
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18
Fahrenheit–Celsius Conversions
• Body temperature is 98.6 °F. What is body
temperature in degrees Celsius? In Kelvin?
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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 in SI units of joules(J) or calories(cal) the
more familiar everyday unit. 1 cal heat required to
raise the temperature of 1 g water 1°C
• 1 cal = 4.184 J
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Calorie in food is kcal(1000cal)
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19
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.
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Energy conversion
• When 1.00 g of gasoline burns and yields about
10.3 kcal what is the energy in SI units?
• Unit Analysis: [1000 cal/1 kcal & 4.184 J/1 cal ]
• want SI energy joules (J).
• Given 10.3 kcal per g gasoline
• =
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20