Welcome to the World of Chemistry

Welcome to the Welcome to the World of World of ChemistryChemistry

The Language of The Language of ChemistryChemistry

• CHEMICAL ELEMENTCHEMICAL ELEMENT- - – pure substances that cannot be decomposed by pure substances that cannot be decomposed by

ordinary means to other substances.ordinary means to other substances.

Sodium Bromine

Aluminum

The Language of The Language of ChemistryChemistry

• The elements, The elements, their names, and their names, and symbols are given symbols are given on theon the PERIODIC PERIODIC TABLETABLE

• How many How many elements are elements are there? 118there? 118

The Periodic TableThe Periodic Table

Dmitri Mendeleev (1834 - 1907)Dmitri Mendeleev (1834 - 1907)

Glenn Glenn SeaborgSeaborg

(1912-1999)(1912-1999)• Discovered 8 Discovered 8

new elements.new elements.• Only living Only living

person for person for whom an whom an element was element was named.named.

Branches of Chemistry

• Many major areas of study for Many major areas of study for specializationspecialization

• Several career opportunitiesSeveral career opportunities• Also used in many other jobsAlso used in many other jobs

1. Organic Chemistry

• Organic is the study of Organic is the study of matter that contains carbon.matter that contains carbon.

• Organic chemists study the Organic chemists study the structure, function, structure, function, synthesis, and identity of synthesis, and identity of carbon compoundscarbon compounds

• Useful in petroleum Useful in petroleum industry, pharmaceuticals, industry, pharmaceuticals, polymerspolymers

2. Inorganic Chemistry

• Inorganic is the Inorganic is the study of matter that study of matter that does NOT contain does NOT contain carbon.carbon.

• Inorganic chemists Inorganic chemists study the structure, study the structure, function, synthesis, function, synthesis, and identity of non-and identity of non-carbon compoundscarbon compounds

• Polymers, Polymers, MetallurgyMetallurgy

3. Biochemistry• Biochemistry is Biochemistry is

the study of the study of chemistry in chemistry in living thingsliving things

• Cross between Cross between biology and biology and chemistrychemistry

• Pharmaceuticals Pharmaceuticals and geneticsand genetics

4. Physical Chemistry

• Physical Physical chemistry is the chemistry is the physics of physics of chemistry… the chemistry… the forces of matterforces of matter

• Much of p-chem Much of p-chem is computationalis computational

• Develop Develop theoretical ideas theoretical ideas for new for new compoundscompounds

5. Analytical Chemistry• Analytical Analytical

chemistry is the chemistry is the study of high study of high precision precision measurementmeasurement

• Find composition Find composition and identity of and identity of chemicalschemicals

• Forensics, quality Forensics, quality control, medical control, medical teststests

Types of Observations and Types of Observations and MeasurementsMeasurements

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

SI measurementSI measurement• Le Système international d'unitésLe Système international d'unités • The only countries that have not The only countries that have not

officiallyofficially adopted SI are Liberia adopted SI are Liberia (in western Africa) and Myanmar (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but (a.k.a. Burma, in SE Asia), but now these are reportedly using now these are reportedly using metric regularlymetric regularly

• Metrication is a process that does Metrication is a process that does not happen all at once, but is not happen all at once, but is rather a process that happens rather a process that happens over time. over time.

• Among countries with non-metric Among countries with non-metric usage, the U.S. is the usage, the U.S. is the only only country significantly holding outcountry significantly holding out.. The U.S. officially adopted SI in The U.S. officially adopted SI in 1866.1866.

Information from U.S. Metric Association

Stating a MeasurementStating a Measurement

In every measurement there is aIn every measurement there is a

Number Number followed by a followed by a

Unit Unit from a measuring devicefrom a measuring device

The number should also be as precise as the measurement!The number should also be as precise as the measurement!

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

Meters (m)Meters (m)

Kilogram, kgKilogram, kg

Seconds, sSeconds, sCelsius degrees, ˚CCelsius degrees, ˚Ckelvins, Kkelvins, K

Liters (L)Liters (L)

Mass vs. WeightMass vs. Weight

• Mass: Amount Mass: Amount of Matter (grams, of Matter (grams, measured with a measured with a BALANCE)BALANCE)

• Weight: Force Weight: Force exerted by the exerted by the mass, only mass, only present with 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 to would you use to measure:measure:A.A. temperature temperatureB.B. volume volumeC.C. time timeD.D. weight weight

Learning Check

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

Learning CheckLearning Check

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

A. length A. length

B. volume B. volume

C. weightC. weight

D. temperatureD. temperature

SolutionSolution

Some possible answers areSome possible answers are

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

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

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

D.D. temperature temperature FF

Metric PrefixesMetric Prefixes• 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

Units of Units of LengthLength

• ? 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

Learning Check

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) kilometers2. 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) millimeters b) metersb) meters c) kilometers c) kilometers

4. The width of an artery4. The width of an arterya) millimetersa) millimeters b) metersb) meters c) kilometers c) kilometers

Solution

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 arterya) millimetersa) millimeters

Equalities

State the same measurement in two different State the same measurement in two different unitsunits

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

Learning Check

Conversion FactorsConversion Factors

Fractions in which the numerator and Fractions in which the numerator and denominator are EQUAL quantities expressed denominator are EQUAL quantities expressed in different unitsin different units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

Learning Check

Write conversion factors that relate each of Write conversion factors that relate each of the following pairs of units:the following pairs of units:

1. Liters and mL1. Liters and mL

2. Hours and minutes2. Hours and minutes

3. Meters and kilometers3. Meters and kilometers

How many minutes are in 2.5 hours?

Conversion factor

2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min 1 hr1 hr

cancelBy using dimensional analysis / factor-label method, By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the side up, and the UNITS are calculated as well as the

numbers!numbers!

Sample Problem

• You have $7.25 in your pocket in You have $7.25 in your pocket in quarters. How many quarters do you quarters. How many quarters do you have?have?

7.25 dollars 4 quarters7.25 dollars 4 quarters 1 dollar1 dollar X = 29 quarters= 29 quarters

Learning Check

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

a) a) 2440 cm2440 cmb)b) 244 cm244 cmc)c) 24.4 cm24.4 cm

Learning Check

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x 24 hr x ?? 1 day

Solution

Unit plan: days hr min seconds

1.4 day x 24 hr x 60 min x 60 sec 1 day 1 hr 1 min

= 1.2 x 105 sec

Wait a minute!

What is What is wrongwrong with the following setup? with the following setup?

1.4 day x 1.4 day x 1 day 1 day x x 60 min 60 min x x 60 sec 60 sec 24 hr 1 hr 1 min24 hr 1 hr 1 min

English and Metric English and Metric ConversionsConversions

• If you know ONE conversion for If you know ONE conversion for each type of measurement, you can each type of measurement, you can convert anything!convert anything!

• You must You must memorizememorize and use these and use these conversions:conversions:–Mass: 454 grams = 1 poundMass: 454 grams = 1 pound–Length: 2.54 cm = 1 inchLength: 2.54 cm = 1 inch–Volume: 0.946 L = 1 quartVolume: 0.946 L = 1 quart


An adult human has 4.65 L of blood. How An adult human has 4.65 L of blood. How many gallons of blood is that?many gallons of blood is that?

Unit plan: L qt gallon

Equalities: 1 quart = 0.946 L 1 gallon = 4 quarts

Your Setup:

Steps to Problem SolvingSteps to Problem Solving

Read problemRead problem Identify data Identify data Make a unit plan from the initial unit to the Make a unit plan from the initial unit to the

desired unitdesired unit Select conversion factorsSelect conversion factors Change initial unit to desired unitChange initial unit to desired unit Cancel units and checkCancel units and check Do math on calculator Do math on calculator Give an answer using significant figuresGive an answer using significant figures

Dealing with Two Units – Honors Dealing with Two Units – Honors OnlyOnly

If your pace on a treadmill is 65 meters If your pace on a treadmill is 65 meters per minute, how many seconds will it per minute, how many seconds will it take for you to walk a distance of 8450 take for you to walk a distance of 8450 feet?feet?

InitialInitial8450 ft x 8450 ft x 12 in. 12 in. x x 2.54 cm 2.54 cm x x 1 m 1 m

1 ft1 ft 1 in. 1 in. 100 cm 100 cm

x x 1 min 1 min x x 60 sec 60 sec = 2400 sec = 2400 sec 65 m65 m 1 min 1 min

Solution

What about Square and Cubic What about Square and Cubic units? – Honors Onlyunits? – Honors Only

• Use the conversion factors you already Use the conversion factors you already know, but when you square or cube the know, but when you square or cube the unit, don’t forget to cube the number unit, don’t forget to cube the number also!also!

• Best way: Square or cube the ENITRE Best way: Square or cube the ENITRE conversion factorconversion factor

• Example: Convert 4.3 cmExample: Convert 4.3 cm33 to mm to mm33

4.3 cm4.3 cm33 10 mm 10 mm 33

1 cm 1 cm ( ) = 4.3 cm4.3 cm33 10 1033 mm mm33

1133 cm cm33

= 4300 mm3


• A Nalgene water A Nalgene water bottle holds 1000 bottle holds 1000 cmcm33 of dihydrogen of dihydrogen monoxide monoxide (DHMO). How (DHMO). How many cubic many cubic decimeters is decimeters is that?that?

SolutionSolution

1000 cm1000 cm33 1 dm 1 dm 33

10 cm10 cm( ) = 1 dm= 1 dm33

So, a dmSo, a dm33 is the same as a Liter ! is the same as a Liter !

A cmA cm33 is the same as a milliliter. is the same as a milliliter.

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 Generally require temp’s in kelvinskelvins

• T (K) = t (˚C) + 273.15T (K) = t (˚C) + 273.15• Body temp = 37 ˚C + 273 = 310 KBody temp = 37 ˚C + 273 = 310 K

• Liquid nitrogen = -196 ˚C + 273 = 77 KLiquid nitrogen = -196 ˚C + 273 = 77 K

Fahrenheit Formula – Honors OnlyFahrenheit Formula – Honors Only

180°F180°F = = 9°F 9°F == 1.8°F 1.8°F 100°C 100°C 5°C 5°C 1°C1°C

Zero point: 0°C = 32°FZero point: 0°C = 32°F

°F = 9/5 °C + 32°F = 9/5 °C + 32

Celsius Formula – Honors OnlyCelsius Formula – Honors Only

Rearrange to find T°CRearrange to find T°C°F °F = = 9/5 °C + 329/5 °C + 32

°F - 32 = °F - 32 = 9/5 °C ( +32 - 32)9/5 °C ( +32 - 32)

°F - 32°F - 32 = = 9/5 °C9/5 °C 9/5 9/5 9/5 9/5

(°F - 32) * 5/9 = (°F - 32) * 5/9 = °C°C

Temperature Conversions – Honors OnlyTemperature Conversions – Honors Only

A person with hypothermia has a body A person with hypothermia has a body temperature of 29.1°C. What is the body temperature of 29.1°C. What is the body temperature in °F? temperature in °F?

°F °F = = 9/5 (29.1°C) + 329/5 (29.1°C) + 32 = = 52.4 + 3252.4 + 32

= = 84.4°F84.4°F

Learning Check – Honors OnlyLearning Check – Honors Only

The normal temperature of a chickadee is The normal temperature of a chickadee is 105.8°F. What is that temperature in °C?105.8°F. What is that temperature in °C? 1) 73.8 °C 1) 73.8 °C 2) 58.8 °C2) 58.8 °C3) 41.0 °C3) 41.0 °C

Learning Check – Honors Only

Pizza is baked at 455°F. What is that in °C?1) 437 °C1) 437 °C2) 235°C2) 235°C3) 221°C3) 221°C

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

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

Scientific notation consists Scientific notation consists of two parts:of 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

Are the following in scientific notation?

http://ellerbruch.nmu.edu/classes/cs255w03/cs255students/jeericks/p12/yes.pdf

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

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

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

• If the original number was less than 1, If the original number was less than 1, then the exponent is negative. If the then the exponent is negative. If the original number was greater than 1, original number was greater than 1, then the exponent is positive.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 To change scientific notation to standard notation to standard

form…form…• Simply move the decimal point to Simply move the decimal point to

the right for positive exponent 10. the right for positive exponent 10. • Move the decimal point to the left Move the decimal point to the left

for negative exponent 10.for 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 places (moved 4 places to the left)to the left)

Learning Check

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

1)1) 4057894057892)2) 0.0038720.0038723)3) 300000000030000000004)4) 225)5) 0.4782600.478260

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?

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

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

Number of Significant Figures

38.15 cm38.15 cm 445.6 ft5.6 ft 2265.6 lb65.6 lb ______122.55 m122.55 m ___

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 ____

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 ____

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. Number of Significant Figures

25,000 in. 25,000 in. 22

200. yr200. yr 33

48,600 gal48,600 gal ________

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


A. Which answers contain 3 significant figures?A. Which answers contain 3 significant figures?1) 0.47601) 0.4760 2) 0.00476 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 10 3) 2.050 x 1033

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


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

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


Significant Numbers in CalculationsSignificant Numbers in Calculations

A calculated answer cannot be more precise than A calculated answer cannot be more precise than the measuring tool. the measuring tool.

A calculated answer must match the least precise A calculated answer must match the least precise measurement.measurement.

Significant figures are needed for final answers Significant figures are needed for final answers fromfrom 1) adding or subtracting1) adding or subtracting

2) multiplying or dividing2) multiplying or dividing

Adding and SubtractingAdding and Subtracting

The answer has the same number of decimal The answer has the same number of decimal places as the measurement with the fewest places as the measurement with the fewest decimal places.decimal places.

25.25.22 one decimal placeone decimal place

+ 1.+ 1.3434 two decimal placestwo decimal places 26.5426.54answer 26.5answer 26.5 one decimal placeone decimal place


In each calculation, round the answer to the In each calculation, round the answer to the correct number of significant figures.correct number of significant figures.A. 235.05 + 19.6 + 2.1 = A. 235.05 + 19.6 + 2.1 =

1) 256.751) 256.75 2) 256.8 2) 256.8 3) 2573) 257

B. 58.925 - 18.2B. 58.925 - 18.2 ==1) 40.7251) 40.725 2) 40.73 2) 40.73 3) 40.73) 40.7

Multiplying and Dividing

Round (or add zeros) to the calculated Round (or add zeros) to the calculated answer until you have the same number answer until you have the same number of significant figures as the measurement of significant figures as the measurement with the fewest significant figures.with the fewest significant figures.


A. 2.19 X 4.2 =A. 2.19 X 4.2 = 1) 91) 9 2) 9.2 2) 9.2 3) 9.1983) 9.198

B. 4.311 ÷ 0.07 =B. 4.311 ÷ 0.07 = 1)1) 61.5861.58 2) 62 2) 62 3) 603) 60

C. C. 2.54 X 0.00282.54 X 0.0028 = = 0.0105 X 0.060 0.0105 X 0.060 1) 11.31) 11.3 2) 112) 11 3) 0.041 3) 0.041

Reading a MeterstickReading a Meterstick

. l. l22. . . . I . . . . I. . . . I . . . . I33 . . . .I . . . . I . . . .I . . . . I44. . cm. . cm

First digit (known)First digit (known) = 2 = 2 2.?? cm2.?? cmSecond digit (known)Second digit (known) = 0.7 = 0.7 2.7? cm2.7? cmThird digit (estimated) between 0.05- 0.07Third digit (estimated) between 0.05- 0.07Length reportedLength reported == 2.75 cm 2.75 cm

oror 2.74 cm 2.74 cm oror 2.76 cm2.76 cm

Known + Estimated DigitsKnown + Estimated Digits

In 2.76 cm…In 2.76 cm…

• Known digitsKnown digits 2 andand 7 are 100% certainare 100% certain

• The third digit 6 is estimated (uncertain)The third digit 6 is estimated (uncertain)

• In the reported length, all three digits In the reported length, all three digits (2.76 cm) are significant including the (2.76 cm) are significant including the estimated oneestimated one


. l8. . . . I . . . . I9. . . .I . . . . I10. . cm

What is the length of the line?What is the length of the line?

1) 9.6 cm 1) 9.6 cm

2) 9.62 cm 2) 9.62 cm

3) 9.63 cm3) 9.63 cm

How does your answer compare with your How does your answer compare with your neighbor’s answer? Why or why not?neighbor’s answer? Why or why not?

Zero as a Measured NumberZero as a Measured Number

. l3. . . . I . . . . I4 . . . . I . . . . I5. . cm

What is the length of the line?What is the length of the line?First digitFirst digit 5.?? cm5.?? cmSecond digitSecond digit 55.0? cm.0? cmLast (estimated) digit isLast (estimated) digit is 5.05.00 cm0 cm

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).).

Density mass (g)volume (cm3)

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

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

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

SOLUTIONSOLUTION1. Get dimensions in common units.1. Get dimensions in common units.

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

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

0.95 mm • 1cm 10 mm

= 0.095 cm

57.54 g6.4 cm3 = 9.0 g / cm3

(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm(9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm33

Note only 2 significant figures in the answer!Note only 2 significant figures in the answer!

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 mL . What is the mass of 95 mL of Hg in grams? In pounds?of Hg in grams? In pounds?

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

StrategyStrategy1.1. 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 density of PROBLEM: Mercury (Hg) has a density of 13.6 g/cm13.6 g/cm33. What is the mass of 95 mL of Hg?. What is the 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 of 13.6 PROBLEM: Mercury (Hg) has a density of 13.6 g/cmg/cm33. What is the mass of 95 mL of Hg?. What is the mass of 95 mL of Hg?

95 cm3 • 13.6 gcm3 = 1.3 x 103 g

1.3 x 103 g • 1 lb454 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 occupiesa 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

Solution

2) Placing the mass and volume of the osmium 2) Placing the mass and volume of the osmium metal into the density setup, we obtainmetal into the density setup, we obtain

D = D = massmass = = 50.00 g 50.00 g = = volumevolume2.22 cm2.22 cm33

= 22.522522 g/cm= 22.522522 g/cm3 3 == 22.5 g/cm22.5 g/cm33

Volume DisplacementVolume Displacement

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

33 mL33 mL25 mL 25 mL


What is the density (g/cmWhat is the density (g/cm33) of 48 g of a metal if ) of 48 g of a metal if the metal raises the level of water in a graduated the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? cylinder from 25 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 layers in the Which diagram represents the liquid layers in the cylinder?cylinder?(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)g/mL,) (W) water (1.0 g/mL)

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

K

K

W

W

W

V

V

VK

SolutionSolution

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

1)1)

KW

V


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

1) 0.614 kg1) 0.614 kg

2) 614 kg2) 614 kg

3) 1.25 kg3) 1.25 kg


If blood has a density of 1.05 g/mL, how If blood has a density of 1.05 g/mL, how many liters of blood are donated if 575 g many liters of blood are donated if 575 g of blood are given?of blood are given?

1) 1) 0.548 L0.548 L2) 2) 1.25 L1.25 L3) 3) 1.83 L1.83 L


A group of students collected 125 empty A group of students collected 125 empty aluminum cans to take to the recycling center. aluminum cans to take to the recycling center. If 21 cans make 1.0 pound of aluminum, how If 21 cans make 1.0 pound of aluminum, how many liters of aluminum (D=2.70 g/cmmany liters of aluminum (D=2.70 g/cm33) are ) are obtained from the cans?obtained from the cans?

1) 1.0 L1) 1.0 L 2) 2.0 L2) 2.0 L 3) 4.0 L3) 4.0 L

Scientific Method1.1. State the problem clearly.State the problem clearly.2.2. Gather information.Gather information.3.3. Form a hypothesis.Form a hypothesis.4.4. Test the hypothesis.Test the hypothesis.5.5. Evaluate the data to form a conclusion.Evaluate the data to form a conclusion.

If the conclusion is valid, then it becomes a If the conclusion is valid, then it becomes a theorytheory. If the theory is found to be true over . If the theory is found to be true over along period of time (usually 20+ years) with along period of time (usually 20+ years) with no counter examples, it may be considered a no counter examples, it may be considered a lawlaw..

6. Share the results.6. Share the results.

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