Chapter 1-part 2Chapter 1-part 2Measurements

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 cm10-2 m = 1cm1 m = 1000 mm10-3m = 1 mm

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Conversion FactorsConversion Factors

A 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. = 1 = 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.

Unit 1 x Unit 2 = Unit 2Unit 1

Given x Conversion = Needed unit factor unitExample:

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.)

ExamplesExamples

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

1) 2440 cm2) 244 cm3) 24.4 cm

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ExamplesExamples

If 189.0 mL of orange juice is prepared from orange juice concentrate, how many liters of orange juice is that ?

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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 10

ExamplesExamples

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

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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 mass

and 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

Using Density as a Conversion Using Density as a Conversion FactorFactor The units of density is an derived unit where

they are written as a ratio. Knowing the density we can calculate the mass

or volume of an object Write the two possible conversion factors for

density

If the mass is known, what is the set up for calculating the volume ?

ExamleExamle A thermometer containing 8.3 g of mercury has

broken. If mercury has a density of 13.6 g/ml, what volume (ml) spilled?

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

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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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

Reference solution is waterDensity of water is 1.00 g/ml

ExampleExample What is the specific gravity of ice if 35.0 g of ice

has a volume of 38.2 mL?