Chapter 1-part 2Chapter 1-part 2

Metric EqualitiesMetric EqualitiesAn equality

states the same measurement in two different units.

can be written using the relationships between two metric units.

Example: 1 meter is the same as 100 cm and 1000 mm.

1 m = 100 cm1 m = 1000 mm

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Conversion FactorsConversion FactorsA conversion factor is• obtained from an equality.

• E.g Metric – U.S system

Equality: 1 in. = 2.54 cm

• written as a fraction (ratio) with a numerator and denominator.

• inverted to give two conversion factors for every equality. 1 in. and 2.54 cm

2.54 cm 1 in.

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Conversion Factors in a Conversion Factors in a ProblemProblemA conversion factor

• may be obtained from information in a word problem.

• is written for that problem only.

Example : The cost of one gallon (1 gal) of gas is $4.29.

1 gallon of gas and $4.29$4.29 1 gallon of gas

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Conversion Factors for a Conversion Factors for a Percentage, ppm, and ppbPercentage, ppm, and ppb The term percent (%) means parts per 100 parts

E.g 18% body fat by massEquality : 18 kg body fat = 100 kg body mass

Conversion factors:

18 kg body fat100 kg body mass

100 kg body mass

18 kg body fatand/or

Different mass units such as grams (g), kilograms (kg), or pounds (lb) can be used, but both units in the factors must be the same

Smaller Percents: ppm and Smaller Percents: ppm and ppbppb

Small percents are shown as ppm and ppb.

• Parts per million (ppm) = mg part/kg whole

Example: The EPA allows 15 ppm cadmium in food colors15 mg cadmium = 1 kg food color

• Parts per billion ppb = g part/kg whole

Example: The EPA allows10 ppb arsenic in public water10 g arsenic = 1 kg water

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1.7 Problem Solving1.7 Problem SolvingTo solve a problem,• identify the given unit.• identify the needed unit.

Example: A person has a height of 2.0 meters. What is that height in inches?

The given unit is the initial unit of height.

given unit = meters (m)

The needed unit is the unit for the answer.

needed unit = inches (in.)

Problem SetupProblem Setup

Unit 1 x Unit 2 = Unit 2

Unit 1Given x Conversion = Needed

unit factor unit

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ExamplesExamples

An injured person loses 0.30 pints of blood. How

many milliliters of blood would that be?

Identify the given and needed units given in this

problem.

Given unit = _______

Needed unit = _______

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ExamplesExamplesA bucket contains 4.65 L of water. Write the setup for the problem and calculate the gallons of water

in the bucket.

plan:

Equalities:

Set Up Problem:

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ExamplesExamples

A rattlesnake is 2.44 m long. How many cm long is the snake?

1) 2440 cm2) 244 cm3) 24.4 cm

How many in2 in 1.5 cm2?

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Using Two or More FactorsUsing Two or More Factors

• Often, two or more conversion factors are required to obtain the unit needed for the answer.Unit 1 Unit 2 Unit 3

• Additional conversion factors are placed in the setup problem to cancel each preceding unit.

Given unit x factor 1 x factor 2 = needed unitUnit 1 x Unit 2 x Unit 3 = Unit 3

Unit 1 Unit 2 12

ExamplesExamples

If a ski pole is 3.0 feet in length, how long is the ski pole in mm?

If your pace on a treadmill is 65 meters per minute,

how many minutes will it take for you to walk a

distance of 7500 feet?

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ExamplesExamples

How many lb of sugar are in 120 g of candy if the candy is 25% (by mass) sugar?

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1.8 Density1.8 Density

Density

• compares the mass of an object to its volume.

• is the mass of a substance divided by its volume.

Density ExpressionDensity = mass = g or g = g/cm3 volume mL cm3

Note: 1 mL = 1 cm3

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Densities of Common Densities of Common SubstancesSubstances

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(at 4 °C)

ExampleExample

Osmium is a very dense metal. What is its density in g/cm3 if 50.0 g of osmium has a volume of 2.22 cm3?

1) 2.25 g/cm3

2) 22.5 g/cm3

3) 111 g/cm3

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Volume by DisplacementVolume by Displacement

• A solid completely submerged in water displaces its own volume of water.

• The volume of the object is calculated from the difference in volume.

45.0 mL - 35.5 mL = 9.5 mL = 9.5 cm3

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Density Using Volume Density Using Volume DisplacementDisplacement

The density of the zinc object is

then calculated from its massand volume. Density =

mass = 68.60 g = 7.2 g/cm3 volume 9.5 cm3

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ExamplesExamples

What is the density (g/cm3) of 48.0 g of a metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added?

1) 0.17 g/cm3 2) 6.0 g/cm3 3) 380 g/cm3

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object

33.0 mL 25.0 mL

Sink or FloatSink or Float

• Ice floats in water because the density of ice is less than the density of water.

• Aluminum sinks because its density is greater than the density of water.

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ExamplesExamples

The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?

1) 0.614 kg

2) 614 kg

3) 1.25 kg

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ExamplesExamples

If olive oil has a density of 0.92 g/mL, how many liters of olive oil are in 285 g of olive oil?

1) 0.26 L2) 0.31 L3) 310 L

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ExamplesExamples

A group of students collected 125 empty aluminum cans to take to the recycling center. If 21 cans make 1.0 lb aluminum, how many liters of aluminum (D=2.70 g/cm3) are obtained from the cans?

1) 1.0 L 2) 2.0 L 3) 4.0 L

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Learning CheckLearning Check

Which of the following samples of metals will displace the greatest volume of water?

1 2 3

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25 g of aluminum2.70 g/mL

45 g of gold19.3 g/mL

75 g of lead11.3 g/mL

Specific gravitySpecific gravity The ratio of the density of a substance compare

to the density (mass of the same unit volume) of a reference substance.◦ A Hydrometer is used as a tool to measure

specific gravity

Specif ic Gravity =Density of a substance

Density of a reference