Ch 3 Measurement And Density

Ch 3 Measurement and DensityCh 3 Measurement and Density

Types of Observations Types of Observations and Measurementsand Measurements

We makeWe make QUALITATIVEQUALITATIVE observations of reactions — observations of reactions — changes in color and physical state.changes in color and physical state.

We also makeWe also make QUANTITATIVE QUANTITATIVE MEASUREMENTSMEASUREMENTS, which involve , which involve numbersnumbers..

–UseUse SI unitsSI units — based on the — based on the metric systemmetric system

What is Scientific Notation?What is Scientific Notation?

Scientific notation is a way of Scientific notation is a way of expressing really big numbers or expressing really big numbers or really small numbers.really small numbers.

It is most often used in “scientific” It is most often used in “scientific” calculations where the analysis must calculations where the analysis must be very precise.be very precise.

For very large and very small For very large and very small numbers, scientific notation is more numbers, scientific notation is more concise.concise.

Scientific notation consists of Scientific notation consists of two parts:two parts:

A number between 1 and 10A number between 1 and 10

A power of 10A power of 10

N x 10N x 10xx

To change standard form to To change standard form to scientific notation…scientific notation…

Place the decimal point so that there is one non-Place the decimal point so that there is one non-zero digit to the left of the decimal point.zero digit to the left of the decimal point.

Count the number of decimal places the decimal Count the number of decimal places the decimal point has “moved” from the original number. This point has “moved” from the original number. This will be the exponent on the 10.will be the exponent on the 10.

If the original number was less than 1, then the If the original number was less than 1, then the exponent is negative. If the original number was exponent is negative. If the original number was greater than 1, then the exponent is positive.greater than 1, then the exponent is positive.

ExamplesExamples

Given: 289,800,000Given: 289,800,000 Use: 2.898 (moved 8 places)Use: 2.898 (moved 8 places) Answer:Answer: 2.898 x 102.898 x 1088

Given: 0.000567Given: 0.000567 Use: 5.67 (moved 4 places)Use: 5.67 (moved 4 places) Answer:Answer: 5.67 x 105.67 x 10-4-4

To change scientific notation To change scientific notation to standard form…to standard form…

Simply move the decimal point to the Simply move the decimal point to the right for positive exponent 10.right for positive exponent 10.

Move the decimal point to the left for Move the decimal point to the left for

negative exponent 10.negative exponent 10.

(Use zeros to fill in places.)(Use zeros to fill in places.)

ExampleExample

Given: 5.093 x 10Given: 5.093 x 1066

Answer: Answer: 5,093,0005,093,000 (moved 6 places (moved 6 places to the right)to the right)

Given: 1.976 x 10Given: 1.976 x 10-4-4

Answer: Answer: 0.00019760.0001976 (moved 4 (moved 4 places to the left)places to the left)

Learning CheckLearning Check

Express these numbers in Express these numbers in Scientific Notation:Scientific Notation:

1)1) 405789405789

2)2) 0.0038720.003872

3)3) 30000000003000000000

4)4) 22

5)5) 0.4782600.478260

4.05789 X 104.05789 X 1055

3.872 X 103.872 X 10-3-3

3 X 103 X 1099

2 X 102 X 1000

4.78260 X 104.78260 X 10-1-1

Accuracy Vs. PrecisionAccuracy Vs. Precision

What do you think What do you think the differences the differences

are?are?

Ideas anyone???Ideas anyone???

Three Three targets with targets with three arrows three arrows each to each to shoot.shoot.

Can you hit the bull's-eye?Can you hit the bull's-eye?

Both accurate and precise

Precise but not accurate

Neither accurate nor precise

How do How do they they compare?compare?

Can you define accuracy and precision?Can you define accuracy and precision?

Let’s use a golf anaolgy

Accurate? No Precise? Yes

10

Accurate? Yes Precise? Yes

12

Precise? No Accurate? Maybe?

13

Accurate? Yes Precise? We cant say!

18


18


18

Accuracy Precision ResolutionAccuracy Precision Resolution

subsequent samples

time

off

set

[arb

itrar

y un

its]

not accurate, not precise accurate, not precise not accurate, precise

accurate and precise accurate, low resolution

-2

-3

-1

0

1

2

3

In terms of measurementIn terms of measurement

Three students measure the Three students measure the room to be 10.2 m, 10.3 m room to be 10.2 m, 10.3 m and 10.4 m across.and 10.4 m across.

Were they precise?Were they precise? Were they accurate?Were they accurate?

Significant FiguresSignificant Figures

The numbers reported in a The numbers reported in a measurement are limited by the measurement are limited by the measuring toolmeasuring tool

Significant figures in a Significant figures in a measurement include the known measurement include the known digits plus one estimated digitdigits plus one estimated digit

Counting Significant FiguresCounting Significant Figures

RULE 1. All non-zero digits in a measured number are RULE 1. All non-zero digits in a measured number are

significant. Only a zero could indicate that rounding significant. Only a zero could indicate that rounding occurred.occurred.

Number of Significant FiguresNumber of Significant Figures

38.15 cm38.15 cm 44

5.6 ft5.6 ft 22

65.6 lb65.6 lb ______

122.55 m122.55 m ______

33

55

Leading ZerosLeading Zeros

RULE 2. Leading zeros in decimal numbers are RULE 2. Leading zeros in decimal numbers are NOTNOT

significant.significant.


0.008 mm0.008 mm 11

0.0156 oz0.0156 oz 33

0.0042 lb0.0042 lb ________

0.000262 mL 0.000262 mL ________

22

33

Sandwiched ZerosSandwiched Zeros

RULE 3. Zeros between nonzero numbers are significant. RULE 3. Zeros between nonzero numbers are significant.

(They can not be rounded unless they are on an end of a (They can not be rounded unless they are on an end of a

number.)number.)


50.8 mm50.8 mm 33

2001 min2001 min 44

0.702 lb0.702 lb ________

0.00405 m0.00405 m ____ ____

33

33

Trailing ZerosTrailing Zeros

RULE 4. Trailing zeros in numbers without RULE 4. Trailing zeros in numbers without

decimals are NOT significant. They are only decimals are NOT significant. They are only

serving as place holders.serving as place holders.


25,000 in. 25,000 in. 22

200. yr200. yr 33

48,600 gal48,600 gal ________

25,005,000 g 25,005,000 g ________

33

55


A. Which answers contain 3 significant figures?A. Which answers contain 3 significant figures?

1)1) 0.4760 2) 0.004760.4760 2) 0.00476 3) 4760 3) 4760

B. All the zeros are significant inB. All the zeros are significant in

1) 0.00307 1) 0.00307 2) 25.300 2) 25.300 3) 2.050 x 3) 2.050 x 101033

C. 534,675 rounded to 3 significant figures isC. 534,675 rounded to 3 significant figures is

1) 535 1) 535 2) 535,000 2) 535,000 3) 5.35 x 10 3) 5.35 x 1055

SolutionSolution

A. Which answers contain 3 significant figures?A. Which answers contain 3 significant figures?

1) 0.47601) 0.4760 2) 0.004762) 0.00476 3) 4760 3) 4760

B. All the zeros are significant inB. All the zeros are significant in

1) 0.003071) 0.00307 2) 25.3002) 25.300 3) 2.050 x 10 3) 2.050 x 1033

C. 534,675 rounded to 3 significant figures isC. 534,675 rounded to 3 significant figures is

1) 5351) 535 2) 535,000 3) 5.35 x 102) 535,000 3) 5.35 x 1055


In which set(s) do both numbers In which set(s) do both numbers contain the contain the samesame number of number of significant figures?significant figures?

1) 22.0 and 22.00 1) 22.0 and 22.00

2) 400.0 and 40 2) 400.0 and 40

3) 0.000015 and 150,0003) 0.000015 and 150,000

Solution Solution

In which set(s) do both numbers In which set(s) do both numbers contain the contain the samesame number of number of significant figures?significant figures?

3) 0.000015 and 150,0003) 0.000015 and 150,000

State the number of significant figures in each of State the number of significant figures in each of the following:the following:

A. 0.030 mA. 0.030 m 1 1 2 2 3 3

B. 4.050 LB. 4.050 L 2 2 3 3 4 4

C. 0.0008 gC. 0.0008 g 1 1 2 2 4 4

D. 3.00 mD. 3.00 m 1 1 2 2 3 3

E. 2,080,000 beesE. 2,080,000 bees 3 3 5 5 7 7


State the number of significant figures in State the number of significant figures in each of the following:each of the following:

A. 0.030 mA. 0.030 m 1 1 22 3 3

B. 4.050 LB. 4.050 L 2 2 3 3 44

C. 0.0008 gC. 0.0008 g 11 2 2 4 4

D. 3.00 mD. 3.00 m 1 1 2 2 33

E. 2,080,000 beesE. 2,080,000 bees 33 5 5 7 7


UNITS OF UNITS OF MEASUREMENTMEASUREMENT

Use Use SI unitsSI units — based on the metric — based on the metric systemsystem

Length Length

MassMass

VolumeVolume

TimeTime

TemperatureTemperature

Meter, mMeter, m

Kilogram, kgKilogram, kg

Seconds, sSeconds, s

Celsius degrees, ˚CCelsius degrees, ˚Ckelvins, Kkelvins, K

Liter, LLiter, L

Mass vs. WeightMass vs. Weight Mass: Amount of Mass: Amount of

Matter (grams, Matter (grams, measured with a measured with a BALANCE)BALANCE)

Weight: Force Weight: Force exerted by the mass, exerted by the mass, only present with only present with gravity (pounds, gravity (pounds, measured with a measured with a SCALE)SCALE)

Can you hear Can you hear me now?me now?

Some Tools for Some Tools for MeasurementMeasurement

Which tool(s) Which tool(s) would you use would you use to measure:to measure:

A.A. temperature temperature

B.B. volume volume

C.C. time time

D.D. weight weight

SolutionSolution

AA. . temperaturetemperature thermometerthermometer

B.B. volume volume measuring cupmeasuring cup, , graduated cylindergraduated cylinder

C.C. timetime watchwatch

DD. . weightweight scalescale


Match Match L) lengthL) length M) mass M) mass V) volume V) volume

____ A. A bag of tomatoes is 4.6 kg.____ A. A bag of tomatoes is 4.6 kg.

____ B. A person is 2.0 m tall.____ B. A person is 2.0 m tall.

____ C. A medication contains 0.50 g Aspirin.____ C. A medication contains 0.50 g Aspirin.

____ D. A bottle contains 1.5 L of water.____ D. A bottle contains 1.5 L of water.

M

L

M

V


What are some U.S. units that are used What are some U.S. units that are used to measure each of the following?to measure each of the following?

A. length A. length

B. volume B. volume

C. weightC. weight

D. temperatureD. temperature

Solution Solution

Some possible answers areSome possible answers are

A.A. length length inch, foot, yard, mile inch, foot, yard, mile

B. volume B. volume cup, teaspoon, gallon, pint, quartcup, teaspoon, gallon, pint, quart

C. weight C. weight ounce, pound (lb), tonounce, pound (lb), ton

D. temperature D. temperature FF

Metric Metric PrefixesPrefixes

Kilo-Kilo- means 1000 of that unit means 1000 of that unit

– 1 kilometer (km) = 1000 meters (m)1 kilometer (km) = 1000 meters (m)

Centi-Centi- means 1/100 of that unit means 1/100 of that unit

– 1 meter (m) = 100 centimeters (cm)1 meter (m) = 100 centimeters (cm)

– 1 dollar = 100 cents1 dollar = 100 cents

Milli-Milli- means 1/1000 of that unit means 1/1000 of that unit

– 1 Liter (L) = 1000 milliliters (mL)1 Liter (L) = 1000 milliliters (mL)

Metric PrefixesMetric Prefixes

Metric PrefixesMetric Prefixes

Units of LengthUnits of Length

? kilometer (km) = 500 meters (m)? kilometer (km) = 500 meters (m)

2.5 meter (m) = ? centimeters (cm)2.5 meter (m) = ? centimeters (cm)

1 centimeter (cm) = ? millimeter (mm)1 centimeter (cm) = ? millimeter (mm)

1 nanometer (nm) = 1.0 x 101 nanometer (nm) = 1.0 x 10-9-9 meter meter

O—H distance =O—H distance =9.4 x 109.4 x 10-11 -11 mm9.4 x 109.4 x 10-9 -9 cmcm0.094 nm0.094 nm

O—H distance =O—H distance =9.4 x 109.4 x 10-11 -11 mm9.4 x 109.4 x 10-9 -9 cmcm0.094 nm0.094 nm


Select the unit you would use to measure Select the unit you would use to measure

1. Your height1. Your height

a) millimeters a) millimeters b) metersb) meters c) kilometers c) kilometers

2. Your mass2. Your mass

a) milligramsa) milligrams b) gramsb) grams c) kilograms c) kilograms

3. The distance between two cities3. The distance between two cities

a) millimetersa) millimetersb) metersb) meters c) kilometers c) kilometers

4. The width of an artery4. The width of an artery

a) millimetersa) millimetersb) metersb) meters c) kilometers c) kilometers

SolutionSolution

1. Your height1. Your height

b) metersb) meters

2. Your mass2. Your mass

c) kilogramsc) kilograms

3. The distance between two cities3. The distance between two cities

c) kilometersc) kilometers

4. The width of an artery4. The width of an artery

a) millimetersa) millimeters

EqualitiesEqualities

State the same measurement in two State the same measurement in two different unitsdifferent units

lengthlength

10.0 in.10.0 in.

25.4 cm25.4 cm

1. 1000 m = 1 1. 1000 m = 1 ______ a) mm b) km c) dma) mm b) km c) dm

2. 0.001 g = 1 2. 0.001 g = 1 ___ ___ a) mg b) kg c) dga) mg b) kg c) dg

3. 0.1 L = 1 3. 0.1 L = 1 ______ a) mL b) cL c) dLa) mL b) cL c) dL

4. 0.01 m = 1 ___ 4. 0.01 m = 1 ___ a) mm b) cm c) dma) mm b) cm c) dm


1. 1000 m = 1 1. 1000 m = 1 ______ a) mm a) mm b) kmb) km c) dm c) dm

2. 0.001 g = 1 2. 0.001 g = 1 ___ ___ a) mga) mg b) kg c) dg b) kg c) dg

3. 0.1 L = 1 3. 0.1 L = 1 ______ a) mL b) cL a) mL b) cL c) dLc) dL

4. 0.01 m = 1 ___ 4. 0.01 m = 1 ___ a) mm a) mm b) cmb) cm c) dm c) dm


Instruments for Measuring VolumeInstruments for Measuring Volume

Graduatedcylinder

Syringe Volumetric flaskBuret Pipet

Units of Measuring VolumeUnits of Measuring Volume

1 L = 1000 mL

1 qt = 946 mL

Timberlake, Chemistry 7th Edition, page 3

Reading a MeniscusReading a Meniscus

Units for Measuring MassUnits for Measuring Mass

1 kg = 2.20 lb

Timberlake, Chemistry 7th Edition, page 3

Quantities of Quantities of MassMass

Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25

Earth’s atmosphere to 2500 km

Ocean liner

Indian elephant

Average human

1.0 liter of water

Grain of table salt

Typical protein

Uranium atomWater molecule

1024 g

1021 g

1018 g

1015 g

1012 g

109 g

106 g

103 g

100 g

10-3 g

10-6 g

10-9 g

10-12 g

10-15 g

10-18 g

10-21 g

10-24 g

Giga- Mega-

Kilo-Kilo-

base

milli-milli-

micro-

nano-

pico-

femto-

atomo-

DENSITYDENSITY - an important - an important and useful physical propertyand useful physical property

Density mass (g)volume (cm3)


Mercury

13.6 g/cm13.6 g/cm33 21.5 g/cm21.5 g/cm33

Aluminum

2.7 g/cm2.7 g/cm33

Platinum

ProblemProblem A piece of copper has a A piece of copper has a mass of 57.54 g. It is 9.36 cm long, mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. 7.23 cm wide, and 0.95 mm thick. Calculate density (g/cmCalculate density (g/cm33).).



StrategyStrategy1. Get dimensions in common units.1. Get dimensions in common units.

2.2. Calculate volume in cubic Calculate volume in cubic centimeters.centimeters.

3. Calculate the density.3. Calculate the density.

DENSITYDENSITYDENSITYDENSITY Density is anDensity is an

INTENSIVEINTENSIVE property property of matter.of matter.– does does NOTNOT depend on depend on

quantity of matter.quantity of matter.– temperaturetemperature

Contrast withContrast with EXTENSIVEEXTENSIVE – depends on quantity depends on quantity

of matter. of matter. – mass and volume.mass and volume.

StyrofoamStyrofoam BrickBrick

PROBLEM: Mercury (Hg) has a PROBLEM: Mercury (Hg) has a density of 13.6 g/cmdensity of 13.6 g/cm33. What is the . What is the mass of 95 mL of Hg in grams? In mass of 95 mL of Hg in grams? In pounds?pounds?

PROBLEM: Mercury (Hg) has a PROBLEM: Mercury (Hg) has a density of 13.6 g/cmdensity of 13.6 g/cm33. What is the . What is the mass of 95 mL of Hg in grams? In mass of 95 mL of Hg in grams? In pounds?pounds?

Solve the problem usingSolve the problem using DIMENSIONAL DIMENSIONAL ANALYSIS.ANALYSIS.

StrategyStrategy

1.1. Use density to calc. mass (g) from Use density to calc. mass (g) from volume.volume.

2.2. Convert mass (g) to mass (lb)Convert mass (g) to mass (lb)

Need to know conversion factorNeed to know conversion factor

= 454 g / 1 lb= 454 g / 1 lb

PROBLEM: Mercury (Hg) has a PROBLEM: Mercury (Hg) has a density of 13.6 g/cmdensity of 13.6 g/cm33. What is the . What is the mass of 95 mL of Hg?mass of 95 mL of Hg?

PROBLEM: Mercury (Hg) has a PROBLEM: Mercury (Hg) has a density of 13.6 g/cmdensity of 13.6 g/cm33. What is the . What is the mass of 95 mL of Hg?mass of 95 mL of Hg?

First, note thatFirst, note that 1 cm1 cm33 = 1 mL = 1 mL

1.1. Convert volume to massConvert volume to mass

PROBLEM: Mercury (Hg) has a density PROBLEM: Mercury (Hg) has a density of 13.6 g/cmof 13.6 g/cm33. What is the mass of 95 . What is the mass of 95 mL of Hg?mL of Hg?

PROBLEM: Mercury (Hg) has a density PROBLEM: Mercury (Hg) has a density of 13.6 g/cmof 13.6 g/cm33. What is the mass of 95 . What is the mass of 95 mL of Hg?mL of Hg?

95 cm3 • 13.6 g

cm3 = 1.3 x 103 g

1.3 x 103 g • 1 lb

454 g = 2.8 lb

2.2. Convert mass (g) to mass (lb)Convert mass (g) to mass (lb)


Osmium is a very dense metal. What is its Osmium is a very dense metal. What is its

density in g/cmdensity in g/cm3 3 if 50.00 g of the metal occupiesif 50.00 g of the metal occupies

a volume of 2.22cma volume of 2.22cm33??

1) 2.25 g/cm1) 2.25 g/cm33

2)2) 22.5 g/cm22.5 g/cm33

3)3) 111 g/cm111 g/cm33

Volume DisplacementVolume Displacement

A solid displaces a matching volume A solid displaces a matching volume of water when the solid is placed in of water when the solid is placed in water.water.

33 mL33 mL

25 mL 25 mL


What is the density (g/cmWhat is the density (g/cm33) of 48 g of a metal if the metal ) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL raises the level of water in a graduated cylinder from 25 mL to 33 mL? to 33 mL?

1) 0.2 g/ cm1) 0.2 g/ cm33 2) 6 g/m 2) 6 g/m33 3) 252 g/cm3) 252 g/cm33

33 mL33 mL

25 mL25 mL


Which diagram represents the liquid Which diagram represents the liquid layers in the cylinder?layers in the cylinder?

(K) Karo syrup (1.4 g/mL), (V) vegetable (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)oil (0.91 g/mL,) (W) water (1.0 g/mL)

1)1) 2) 2) 3) 3)

K

K

W

W

W

V

V

V

K

SolutionSolution

(K) Karo syrup (1.4 g/mL), (V) (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)water (1.0 g/mL)

1)1)

K

W

V

Temperature ScalesTemperature Scales

FahrenheitFahrenheit CelsiusCelsius KelvinKelvin

Anders Celsius1701-1744

Lord Kelvin(William Thomson)1824-1907

Temperature ScalesTemperature Scales

Notice that 1 kelvin = 1 degree Celsius1 kelvin = 1 degree Celsius

Boiling point Boiling point of waterof water

Freezing point Freezing point of waterof water

CelsiusCelsius

100 ˚C100 ˚C

0 ˚C0 ˚C

100˚C100˚C

KelvinKelvin

373 K373 K

273 K273 K

100 K100 K

FahrenheitFahrenheit

32 ˚F32 ˚F

212 ˚F212 ˚F

180˚F180˚F

Calculations Calculations Using Using TemperatureTemperature

Generally require temp’s in kelvinsGenerally require temp’s in kelvins

T (K) = t (˚C) + 273.15T (K) = t (˚C) + 273.15

Body temp = 37 ˚C + 273 =Body temp = 37 ˚C + 273 = 310 K 310 K

Liquid nitrogen = -196 ˚C + 273 Liquid nitrogen = -196 ˚C + 273

= 77 K= 77 K

Generally require temp’s in kelvinsGenerally require temp’s in kelvins

T (K) = t (˚C) + 273.15T (K) = t (˚C) + 273.15

Body temp = 37 ˚C + 273 =Body temp = 37 ˚C + 273 = 310 K 310 K

Liquid nitrogen = -196 ˚C + 273 Liquid nitrogen = -196 ˚C + 273

= 77 K= 77 K

Technology

Ch 3 Measurement And Density