3.2 Units of Measurement > 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights...

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

3.2 Units of Measurement >3.2 Units of Measurement >

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Chapter 3Scientific Measurement

3.1 Using and Expressing Measurements

3.2 Units of Measurement

3.3 Solving Conversion Problems



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Will the high temperature tomorrow be 28°C, which is very warm? Or 28°F, which is very cold? Without the correct units, you can’t be sure.

CHEMISTRY & YOU

What’s the forecast for tomorrow—hot or cold?



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Using SI Units

What makes metric units easy to use?

Using SI UnitsUsing SI Units



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• The standards of measurement used in science are those of the metric system.

All metric units are based on multiples of 10. As a result, you can convert between units easily.




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• The metric system was originally established in France in 1795.

• The International System of Units (abbreviated SI after the French name, Le Système International d’Unités) is a revised version of the metric system.

• The SI was adopted by international agreement in 1960.




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• There are seven SI base units.

• From these base units, all other SI units of measurement can be derived.

• Derived units are used for measurements such as volume, density, and pressure.

SI Base UnitsQuantity SI base

unitSymbol

Length meter mMass kilogram kg

Temperature kelvin KTime second s

Amount of substance mole mol

Luminous intensity candela cd

Electric current ampere A



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• In SI, the basic unit of length, or linear measure, is the meter (m).

• All measurements of length can be expressed in meters.

• For very large and very small lengths, however, it may be more convenient to use a unit of length that has a prefix.

Units of Length




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The table below lists the prefixes in common use.

Units of Length

Commonly Used Metric PrefixesPrefix Symbol Meaning Factormega M 1 million times larger than the unit it precedes 106

kilo k 1000 times larger than the unit it precedes 103

deci d 10 times smaller than the unit it precedes 10-1

centi c 100 times smaller than the unit it precedes 10-2

milli m 1000 times smaller than the unit it precedes 10-3

micro μ 1 million times smaller than the unit it precedes 10-6

nano n 1 billion times smaller than the unit it precedes 10-9

pico p 1 trillion times smaller than the unit it precedes 10-12



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• For example, the prefix milli- means 1/1000 (one-thousandth), so a millimeter (mm) is 1/1000 of a meter, or 0.001 m.

• A hyphen (-) measures about 1 mm.

• For large distances, it is most appropriate to express measurements in kilometers (km).

• The prefix kilo- means 1000, so 1 km equals 1000 m.

Units of Length




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• The space occupied by any sample of matter is called its volume.

• You calculate the volume of any cubic or rectangular solid by multiplying its length by its width by its height.

• The unit for volume is thus derived from the units of length.

Units of Volume




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• The SI unit of volume is the amount of space occupied by a cube that is 1 m along each edge.

• This volume is a cubic meter (m3).

• A more convenient unit of volume for everyday use is the liter, a non-SI unit.

• A liter (L) is the volume of a cube that is 10 centimeters (10 cm) along each edge (10 cm x 10 cm x 10 cm = 1000 cm3 = 1 L).

Units of Volume




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• A smaller, non-SI unit of volume is the milliliter (mL); 1 mL is 1/1000 of a liter.

• Thus, there are 1000 mL in 1 L.

• Because 1 L is defined as 1000 cm3, 1 mL and 1 cm3 are the same volume.

• The units milliliter and cubic centimeter are thus used interchangeably.

Units of Volume




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These figures give you some idea of the relative sizes of a liter and a milliliter.

Units of Volume


1 mL

1 L



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• There are many devices for measuring liquid volumes, including graduated cylinders, pipets, burets, volumetric flasks, and syringes.

• The volume of substances will change with temperature, so accurate volume-measuring devices are calibrated at a given temperature—usually 20 degrees Celsius (20°C), which is about normal room temperature.

Units of Volume




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The relationships among common metric units of volume are shown in the table below.

Units of Volume

Metric Units of VolumeUnit Symbol Relationship ExampleLiter L base unit quart of milk ≈ 1 LMilliliter mL 103 mL = 1 L 20 drops of water ≈ 1 mLCubic centimeter cm3 1 cm3 = 1 mL cube of sugar ≈ 1 cm3

Microliter μL 103 μL = 1 L crystal of table salt ≈ 1 μL



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• The mass of an object is measured in comparison to a standard mass of 1 kilogram (kg), which is the basic SI unit of mass.

• A kilogram was originally defined as the mass of 1 L of liquid water at 4°C.

• A cube of water at 4°C measuring 10 cm on each edge would have a volume of 1 L and a mass of 1000 grams (g), or 1 kg.

• A gram (g) is 1/1000 of a kilogram; the mass of 1 cm3 of water at 4°C is 1 g.

Units of Mass




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The relationships among units of mass are shown in the table below.

Units of Mass

Metric Units of MassUnit Symbol Relationship ExampleKilogram (base unit) kg 1 kg = 103 g small textbook ≈ 1 kg

Gram g 1 g = 10-3 kg dollar bill ≈ 1 gMilligram mg 103 mg = 1 g ten grains of salt ≈ 1 mgMicrogram μg 106 μg = 1 g particle of baking powder ≈ 1 μg



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• Weight is a force that measures the pull on a given mass by gravity.

• Weight, a measure of force, is different from mass, which is a measure of the quantity of matter.

• The weight of an object can change with its location.

• An astronaut in orbit is weightless, but not massless.

Units of Mass




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• The capacity to do work or to produce heat is called energy.

• The SI unit of energy is the joule (J), named after the English physicist James Prescott Joule (1818–1889).

• A common non-SI unit of energy is the calorie.

• One calorie (cal) is the quantity of heat that raises the temperature of 1 g of pure water by 1°C.

Units of Energy




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• Conversions between joules and calories can be carried out using the following relationships.

• 1 J = 0.2390 cal

• 1 cal = 4.184 J

• A kilojoule is 1000 joules; a kilocalorie is 1000 calories.

Units of Energy




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What is the SI unit of volume?



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What is the SI unit of volume?

The SI unit of volume is the cubic meter (m3). A liter (L) can be converted to the SI unit of volume, because a liter is defined as 1000 cm3.



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Temperature Scales

What temperature units do scientists commonly use?

Temperature ScalesTemperature Scales



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• Temperature is a measure of how hot or cold an object is.

• An object’s temperature determines the direction of heat transfer.

• When two objects at different temperatures are in contact, heat moves from the object at the higher temperature to the object at the lower temperature.




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• Almost all substances expand with an increase in temperature and contract as the temperature decreases.

• A very important exception is water.

• These properties are the basis for the common bulb thermometer.




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The liquid in a thermometer expands and contracts more than the volume of the glass, producing changes in the column height of liquid.




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Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin.




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• The Celsius scale sets the freezing point of water at 0°C and the boiling point of water at 100°C.

• The distance between these two fixed points is divided into 100 equal intervals, or degrees Celsius (°C).




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• Another temperature scale used in the physical sciences is the Kelvin, or absolute, scale.• This scale is named for Lord Kelvin (1824–

1907), a Scottish physicist.

• On the Kelvin scale, the freezing point of water is 273.15 kelvins (K), and the boiling point is 373.15 (K). • Note that with the Kelvin scale, the degree

sign is not used.




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• The figure below compares the Celsius and Kelvin scales.

• The zero point on the Kelvin scale, 0 K, or absolute zero, is equal to –273.15°C.


Celsius

Kelvin

100 divisions

100 divisions

100°CBoiling point

of water373.15 K

0°CFreezing point

of water273.15 K



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• Because one degree on the Celsius scale is equivalent to one kelvin on the Kelvin scale, converting from one temperature to another is easy.

• You simply add or subtract 273, as shown in the following equations.


K = °C + 273°C = K – 273



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In a few countries, such as the United States, metric units are not commonly used in everyday measurements. What temperature units are used for a typical weather forecast in the United States? What about for a country that uses the metric system, such as Australia or Japan?

CHEMISTRY & YOU



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In a few countries, such as the United States, metric units are not commonly used in everyday measurements. What temperature units are used for a typical weather forecast in the United States? What about for a country that uses the metric system, such as Australia or Japan?

CHEMISTRY & YOU

In the United States, temperatures are usually given in degrees Fahrenheit. Countries that use the metric system forecast the weather in degrees Celsius.



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Sample Problem 3.7

Converting Between Temperature Scales Normal human body temperature is 37°C. What is this temperature in kelvins?



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Sample Problem 3.7

Analyze List the known and the unknown.

Use the known value and the equation K = °C + 273 to calculate the temperature in kelvins.

KNOWNTemperature in °C = 37°C

UNKNOWN Temperature in K = ? K

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Sample Problem 3.7

Calculate Solve for the unknown.

Substitute the known value for the Celsius temperature into the equation and solve.

K = °C + 273 = 37 + 273 = 310 K

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Sample Problem 3.7

Evaluate Does the result make sense?

You should expect a temperature in this range, since the freezing point of water is 273 K and the boiling point of water is 373 K; normal body temperature is between these two values.

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Is the change of one degree on the Celsius scale equivalent to one kelvin on the Kelvin scale?



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Is the change of one degree on the Celsius scale equivalent to one kelvin on the Kelvin scale?

Yes, a change of one degree on the Celsius scale is equivalent to a change of one kelvin on the Kelvin scale.



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Density

What determines the density of a substance?

DensityDensity



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• The relationship between an object’s mass and its volume tells you whether it will float or sink.

• This relationship is called density.

• Density is the ratio of the mass of an object to its volume.

DensityDensity

massvolumeDensity =



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• When mass is measured in grams, and volume in cubic centimeters, density has units of grams per cubic centimeter (g/cm3).

• The SI unit of density is kilograms per cubic meter (kg/m3).

DensityDensity



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This figure compares the density of four substances: lithium, water, aluminum, and lead.

DensityDensity

Increasing density (mass per unit volume)

10 g

0.53 g/cm3

19 cm3

10 g10 cm3

10 g3.7 cm3

10 g0.88 cm3

1.0 g/cm3 2.7 g/cm3 0.88 g/cm3



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Density is an intensive property that depends only on the composition of a substance, not the size of the sample.

DensityDensity



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• Because of differences in density, liquids separate into layers.

• As shown at right, corn oil floats on top of water because it is less dense.

• Corn syrup sinks below water because it is more dense.

DensityDensity

Corn oilWater

Corn syrup



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Interpret Data

Densities of Some Common MaterialsSolids and Liquids Gases

Material Density at 20°C (g/cm3) Material Density at

20°C (g/L)Gold 19.3 Chlorine 2.95

Mercury 13.6 Carbon dioxide 1.83Lead 11.3 Argon 1.66

Aluminum 2.70 Oxygen 1.33Table sugar 1.59 Air 1.20

Corn syrup 1.35–1.38 Nitrogen 1.17

Water (4°C) 1.000 Neon 0.84Corn oil 0.922 Ammonia 0.718Ice (0°C) 0.917 Methane 0.665Ethanol 0.789 Helium 0.166

Gasoline 0.66–0.69 Hydrogen 0.084



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What happens to the density of a substance as its temperature increases?

• The volume of most substances increases as the temperature increases, while the mass remains the same.

• Since density is the ratio of an object’s mass to its volume, the density of a substance generally decreases as its temperature increases.

• Water is an important exception.

DensityDensity



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Sample Problem 3.8

Calculating Density

A copper penny has a mass of 3.1 g and a volume of 0.35 cm3. What is the density of copper?



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Sample Problem 3.8

Analyze List the knowns and the unknown.

Use the known values and the equation for density to solve the problem.

KNOWNS mass = 3.1 gvolume = 0.35 cm3

UKNOWN density = ? g/cm3

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Sample Problem 3.8

Density = mass volume


Start with the equation for density.

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Substitute the known values for mass and volume and then calculate.

Sample Problem 3.8

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Density =31 g

0.35 cm3= 8.8571 g/cm3 = 8.9 g/cm3

The calculated answer must be rounded to two significant figures.



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Sample Problem 3.8

Evaluate Does the result make sense?

A piece of copper with a volume of about 0.3 cm3 has a mass of about 3 grams. About three times that volume of copper, 1 cm3, should have a mass three times larger, about 9 grams. This estimate is close to the calculated result.

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Can you assume that something with a low weight will float in water?



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Can you assume that something with a low weight will float in water?

No, it is the relationship between an object’s mass and its volume, its density, that tells you whether it will float or sink.



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All metric units are based on multiples of 10. As a result, you can convert between units easily.

Scientists commonly use two equivalent units of temperature, the degree Celsius and the kelvin.

Density is an intensive property that depends only on the composition of a substance.

Key ConceptsKey Concepts



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K = °C + 273

°C = K – 273

Key EquationsKey Equations

Density = mass volume



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• International System of Units (SI): the revised version of the metric system, adopted by international agreement in 1960

• meter (m): the base unit of length in SI

• liter (L): the volume of a cube measuring 10 centimeters on each edge (1000 cm3); it is the common unprefixed unit of volume in the metric system

• kilogram (kg): the mass of 1 L of water at 4°C; it is the base unit of mass in SI

• gram (g): a metric mass unit equal to the mass of 1 cm3 of water at 4°C

Glossary TermsGlossary Terms



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• weight: a force that measures the pull of gravity on a given mass

• energy: the capacity for doing work or producing heat

• Joule (J): the SI unit of energy; 4.184 J equals one calorie

• calorie (cal): the quantity of heat needed to raise the temperature of 1 g of pure water 1°C

• temperature: a measure of the average kinetic energy of particles in matter; temperature determines the direction of heat transfer




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• Celsius scale: the temperature scale in which the freezing point of water is 0°C and the boiling point is 100°C

• Kelvin scale: the temperature scale in which the freezing point of water is 273 K and the boiling point is 373 K; 0 K is absolute zero

• absolute zero: the zero point on the Kelvin temperature scale, equivalent to –273.15°C

• density: the ratio of the mass of an object to its volume




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END OF 3.2END OF 3.2

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