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CH 3: The Metric System

Renee Y. BeckerCHM 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

Physical Quantity Name of Unit Abbreviation Mass kilogram kg

Length meter m Temperature kelvin K

Amount of substance mole mol Time second s

Electric current ampere A Luminous intensity candela cd

SI Units

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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 meter1 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

Always start with the original quantityThen multiply by the conversion factor

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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 = .30

44 g CO2

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 = L x w x hLength, 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 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.

Temperature

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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.