CH 3: The Metric System
Renee Y. Becker
CHM 1025
Valencia Community College
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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
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SI unit
• SI units
– In 1960 International System of Units (SI) adopted
– This system has 7 SI base units that all other units
can be derived from
– Metric system is a decimal system
• We use SI prefixes
• Indicates a power of 10
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Measurement and Units
SI Units
Physical Quantity
Mass
Length
Temperature
Amount of substance
Time
Electric current
Luminous intensity
Name of Unit
kilogram
meter
kelvin
mole
second
ampere
candela
Abbreviation
kg
m
K
mol
s
A
cd
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Metric Prefixes
Unit
Symbol
Value
meter
m
1
decimeter
dm
10 = 1 x 101
centimeter
cm
100 = 1 x 102
millimeter
mm
1000= 1 x 103
micrometer
m
1 x 106
nanometer
nm
1 x 109
picometer
pm
1 x 1012
1 kilometer = 1 x103 meter
1 km = 1000 m
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Measurements and Units
• Dimensional-Analysis method uses a conversion
factor to express the relationship between units.
Original quantity x conversion factor = equivalent quantity
Example: express 2.50 kg  lb.
Conversion factor: 1.00 kg = 2.205 lb
2.50 kg x 2.205 lb = 6.00 lb
1.00 kg
Then multiply by the conversion factor
Always start with the original quantity
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Measurements and Units
• Remember that anything divided by itself =1
• This is how we can get rid of units!!! They cancel
out!!
• So remember when setting up dimensional analysis
to always divide the units you are trying to get rid of.
And multiply by the unit you want to keep!
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Example 1
• What unit will the answer have for the following?
12 bird x 3 dog x 12 cat = 108
4 bird
1 dog
13 g CO2 x 1 mole CO2
44 g CO2
= .30
56 clowns x 2 doctors x 10 doctors = 3 x 101
12 clowns
3 cops
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Example 2: Metric Conversion
a) 1.267 km  m  cm
b) .784 L  mL
c) 3.67 x 105 cm  mm
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Example 3: English Conversion
a) 79 oz  lb.
b) 9.63 x 10-3 ft  in
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Example 4: Metric-English Conversion
a) 1.34 x 1012 in  cm
b) 4.67 x 10-7 lb  g
c) 10.5 gal  L
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Example 5: Measurement with Compound Units
I am traveling 32 mi/hr, how fast am I traveling
in km/hr?
1 mi = 1.61 km
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Volume by Calculations
V=Lxwxh
Length, width, and height have to be in the same
unit
Example: a box has L = 12 cm, w = 42 cm, h = 32 cm
• What is the volume of the box?
V = L x w x h = 12 cm x 42 cm x 32 cm = 1.6 x 104 cm3
– don’t forget to multiply the units as well as the
#’s!!!
– If the units are not the same you will have to
convert so that they are!!
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Volumes of Solids, Liquids, Gases
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Volume by Displacement
• How we can find density in the lab!!
• If the jade has a mass of 21.3 g what is the density?
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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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Density
• 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 = Mass/Volume
• M = DxV
• V = M/D
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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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Density
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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.
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Example 6: Density
• What is the density(in g/mL) of unknown
substance that has a volume of 20 mL and a
mass of 10 g?
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Example 7: Density
• What is the density (in g/cm3) of a platinum
nugget that has a mass of 224.50 g and a
volume of 10.0 cm3 ?
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Example 8: Volume
• What is the volume (in mL) of an unknown
substance if it’s mass is 0.125 g and it’s density
is 1.873 g/mL?
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Example 9: Mass
• What is the mass (in g) of an unknown
substance if it’s density is 2.578 g/mL and it’s
volume is 4.23 mL?
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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:
– Celsius
– Fahrenheit
– Kelvin
• Kelvin is the absolute temperature scale.
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Temperature
Temperature Conversions:
The Kelvin and Celsius degree
are essentially
the same because both
are one hundredth of the
interval between freezing
and boiling points of water.
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Temperature
• Temperature Conversions:
– Celsius (°C) — Kelvin temperature conversion:
Kelvin (K) = °C + 273.15
– Fahrenheit (°F) — Celsius temperature conversions:
C = 5/9 (F -32)
F = (9/5 * C) + 32
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Example 10: Temperature
Carry out the indicated temperature conversions:
(a) –78°C = ? K
(b) 158°C = ? °F
(c) 375 K = ? °C
(d) 98.6°F = ? °C
(e) 98.6°F = ? K
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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.
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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 is often expressed in terms of joules (J) or
calories (cal).
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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.
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