scientific measurement - pittsfield high school

3.2 Units of Measurement >

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

Chapter 3Scientific Measurement

3.1 Using and Expressing

Measurements

3.2 Units of Measurement

3.3 Solving Conversion Problems



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?



Using SI Units

What makes metric units easy to use?

Using SI Units



• 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.

Using SI Units



• 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.

Using SI Units



Using SI Units

• 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 Units

Quantity SI base

unit

Symbol

Length meter m

Mass kilogram kg

Temperature kelvin K

Time second s

Amount of

substancemole mol

Luminous

intensitycandela cd

Electric

currentampere A



• 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

Using SI Units



Using SI Units

The table below lists the prefixes in common use.

Units of Length

Commonly Used Metric Prefixes

Prefix Symbol Meaning Factor

mega 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



• 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

Using SI Units



• 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

Using SI Units



• 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

Using SI Units



• 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

Using SI Units



These figures give you some idea of

the relative sizes of a liter and a

milliliter.

Units of Volume

Using SI Units

1 mL

1 L



• 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

Using SI Units



Using SI Units

The relationships among common metric units of volume

are shown in the table below.

Units of Volume

Metric Units of Volume

Unit Symbol Relationship Example

Liter L base unit quart of milk ≈ 1 L

Milliliter mL 103 mL = 1 L 20 drops of water ≈ 1 mL

Cubic centimeter cm3 1 cm3 = 1 mL cube of sugar ≈ 1 cm3

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



• 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

Using SI Units



Using SI Units

The relationships among units of mass are shown in the

table below.

Units of Mass

Metric Units of Mass

Unit Symbol Relationship Example

Kilogram

(base unit)kg 1 kg = 103 g small textbook ≈ 1 kg

Gram g 1 g = 10-3 kg dollar bill ≈ 1 g

Milligram mg 103 mg = 1 g ten grains of salt ≈ 1 mg

Microgram μg 106 μg = 1 g particle of baking powder ≈ 1 μg



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

• Weight, a measure of force, is different frommass, which is a measure of the quantity ofmatter.

• The weight of an object can change with itslocation.

• An astronaut in orbit is weightless, but notmassless.

Units of Mass

Using SI Units



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

• The SI unit of energy is the joule (J), namedafter the English physicist James PrescottJoule (1818–1889).

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

• One calorie (cal) is the quantity of heat thatraises the temperature of 1 g of pure waterby 1°C.

Units of Energy

Using SI Units



• 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

Using SI Units



What is the SI unit of volume?



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.



Temperature Scales

What temperature units do scientists

commonly use?

Temperature Scales



• 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.

Temperature Scales



• 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.

Temperature Scales



The liquid in a thermometer expands and

contracts more than the volume of the glass,

producing changes in the column height of

liquid.

Temperature Scales



Scientists commonly use two equivalent

units of temperature, the degree Celsius

and the kelvin.

Temperature Scales



• 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).

Temperature Scales



• 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.

Temperature Scales



• 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.

Temperature Scales

Celsius

Kelvin

100

divisions

100

divisions

100°C

Boiling point

of water

373.15 K

0°C

Freezing point

of water

273.15 K



• 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.

Temperature Scales

K = °C + 273°C = K – 273



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 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.



Sample Problem 3.7

Converting Between Temperature Scales

Normal human body temperature is

37°C. What is this temperature in

kelvins?



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.

KNOWN

Temperature in °C = 37°C

UNKNOWN

Temperature in K = ? K

1



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

2



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.

3



Is the change of one degree on the Celsius

scale equivalent to one kelvin on the Kelvin

scale?



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.



Density

What determines the density of a

substance?

Density



• 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.

Density

massvolume

Density =



• 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).

Density



This figure compares the density of four

substances: lithium, water, aluminum, and lead.

Density

Increasing density (mass per unit volume)

10 g

0.53 g/cm3

19 cm3

10 g

10 cm3

10 g

3.7 cm3

10 g

0.88 cm3

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



Density is an intensive property that

depends only on the composition of a

substance, not the size of the sample.

Density



• 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.

Density

Corn oil

Water

Corn syrup



Interpret Data

Densities of Some Common Materials

Solids and Liquids Gases

MaterialDensity at

20°C (g/cm3)Material

Density at

20°C (g/L)

Gold 19.3 Chlorine 2.95

Mercury 13.6 Carbon dioxide 1.83

Lead 11.3 Argon 1.66

Aluminum 2.70 Oxygen 1.33

Table sugar 1.59 Air 1.20

Corn syrup 1.35–1.38 Nitrogen 1.17

Water (4°C) 1.000 Neon 0.84

Corn oil 0.922 Ammonia 0.718

Ice (0°C) 0.917 Methane 0.665

Ethanol 0.789 Helium 0.166

Gasoline 0.66–0.69 Hydrogen 0.084



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.

Density



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?



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 g

volume = 0.35 cm3

UKNOWN

density = ? g/cm3

1



Sample Problem 3.8

Density =mass

volume


Start with the equation for density.

2




Substitute the known values for mass and

volume and then calculate.

Sample Problem 3.8

2

Density =31 g

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

The calculated answer must be

rounded to two significant figures.



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.

3



Can you assume that something with a low

weight will float in water?



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.



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 Concepts



K = °C + 273

°C = K – 273

Key Equations

Density =massvolume



• 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 Terms



• 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

Glossary Terms



• 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

Glossary Terms



END OF 3.2

scientific measurement - pittsfield high school

Documents