Chemical Foundations 1. Nature of Measurement Part 1 - number Part 2 - scale (unit) Examples: 20...

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Chemical Chemical FoundationsFoundations

Nature of MeasurementNature of Measurement

Part 1 - Part 1 - numbernumberPart 2 - Part 2 - scale (unit)scale (unit)

Examples:Examples:2020 gramsgrams

6.63 x 106.63 x 10-34-34 Joule secondsJoule seconds

Measurement - quantitative Measurement - quantitative observation observation consisting of 2 partsconsisting of 2 parts

Uncertainty in MeasurementUncertainty in Measurement

A digit that must be A digit that must be estimatedestimated is called is called uncertainuncertain. A . A measurementmeasurement always has always has some degree of uncertainty.some degree of uncertainty.

Measurements are performed with instruments No instrument can read to an infinite number of decimal places

Ex: Reading a MeterstickEx: Reading a Meterstick

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

First digit (known)First digit (known) = 2 = 2 2.?? cm2.?? cm

Second digit (known)Second digit (known) = 0.7 = 0.7 2.7? 2.7? cmcm

Third digit (estimated) between 0.05- 0.07Third digit (estimated) between 0.05- 0.07

Length reportedLength reported == 2.75 cm 2.75 cm

oror 2.74 cm 2.74 cm

oror 2.76 cm2.76 cm

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details1. Nonzero integersNonzero integers always count as always count as significant figures.significant figures.

34563456 hashas

44 sig figs.sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

Note: “leading” means ANY zero that appears before the first nonzero digit, whether the zeros are before OR after a decimal.

ZerosZeros-- 2. 2. Leading zerosLeading zeros do not count do not count as as

significant figures.significant figures.

0.04860.0486 has has

33 sig figs. sig figs.

ZerosZeros-- 3. 3. Sandwiched zeros Sandwiched zeros always always

count ascount assignificant figures.significant figures.

16.07 16.07 hashas

44 sig figs. sig figs.Note: “sandwiched” means zeros that

appears between nonzero digits

ZerosZeros4. 4. Trailing zerosTrailing zeros are significant are significant only if the number contains a only if the number contains a decimal point.decimal point.

9.3009.300 has has

44 sig figs. sig figs.Note: “trailing” means ALL zeros that

appear after the last nonzero digit

5. Exact numbersExact numbers have an infinite have an infinite number of significant figures.number of significant figures.

11 inch = inch = 2.542.54 cm, exactlycm, exactly

Sig Fig Practice #1Sig Fig Practice #1How many significant figures in each of the following?

1.0070 m

5 sig figs

17.10 kg 4 sig figs

100,890 L 5 sig figs

3.29 x 103 s 3 sig figs

0.0054 cm 2 sig figs

3,200,000 2 sig figs

Rules for Significant Figures in Rules for Significant Figures in Mathematical OperationsMathematical Operations

#1.Multiplication and DivisionMultiplication and Division:: # # sig figs sig figs in the result equals the in the result equals the number in the least precise number in the least precise measurement used in the measurement used in the calculation.calculation.

6.38 x 2.0 =6.38 x 2.0 =

12.76 12.76 13 (2 sig figs)13 (2 sig figs)

Sig Fig Practice #2Sig Fig Practice #2

3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m2 23 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2

710 m ÷ 3.0 s 236.6666667 m/s 240 m/s

1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft

1.030 g x 2.87 mL 2.9561 g/mL 2.96 g/mL

Rules for Significant Figures Rules for Significant Figures in Mathematical Operationsin Mathematical Operations#2: Addition and SubtractionAddition and Subtraction: The : The number of number of decimal placesdecimal places in the result in the result equals the number of decimal places in equals the number of decimal places in the least precise measurement.the least precise measurement.

6.6.88 + 11.934 =18.734 + 11.934 =18.734 18. 18.77

((1 decimal place1 decimal place, , 3 sig figs3 sig figs))

Sig Fig Practice #3Sig Fig Practice #3

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Rules for Rounding AnswersRules for Rounding Answers

1. Complete all calculations, then round ONLY the final answer.

2. Identify the correct digit to round (the last sig fig).ex: 18.734

3. Look ONLY at the number immediately to the right of this digit: 18.734» If this number is 5 or greater, round

the last sig fig up.» If this number is less than 5, the last

sig fig remains the same. 18.7

The Fundamental SI UnitsThe Fundamental SI Units (le Système International, SI)(le Système International, SI)

Physical Quantity Name Abbreviation

Mass kilogram kg

Length meter m

Time second s

Temperature Kelvin K

Electric Current Ampere A

Amount of Substance mole mol

Luminous Intensity candela cd

SI UnitsSI Units

SI Prefixes Common to ChemistrySI Prefixes Common to Chemistry

Prefix Unit Abbr. Exponent

Mega M 106

Kilo k 103

Deci d 10-1

Centi c 10-2

Milli m 10-3

Micro 10-6

Nano n 10-9

Pico p 10-12

Precision and AccuracyPrecision and AccuracyAccuracyAccuracy refers to the agreement of a refers to the agreement of a particular value with the particular value with the truetrue value.value.

PrecisionPrecision refers to the degree of agreement refers to the degree of agreement among several measurements made in the among several measurements made in the same manner.same manner.

Neither accurate nor

precise

Precise but not accurate

Precise AND accurate

Types of ErrorTypes of Error

Random ErrorRandom Error (Indeterminate Error) - (Indeterminate Error) - measurement has an equal probability of measurement has an equal probability of being high or low.being high or low.

Systematic ErrorSystematic Error (Determinate Error) - (Determinate Error) - Occurs in the Occurs in the same directionsame direction each time each time (high or low), often resulting from poor (high or low), often resulting from poor technique or incorrect calibration. technique or incorrect calibration. This can This can result in measurements that are precise, result in measurements that are precise, but not accurate.but not accurate.

Error Analysis PracticeError Analysis PracticeEx 1: The data collected when the same

sample of silver was weighed five times is as follows:

2.31g, 2.51g, 2.30g, 2.44g, 2.40g

The actual mass of the silver is 2.71.

Are the student’s measurements accurate?Are they precise?

Practice: Section 1.3 & 1.4 # 3, 4, 6.

Dimensional AnalysisDimensional AnalysisThere are times when you need to change the units

in which a measurement is expressed.

Ex: You might want to convert from hours to minutes.

6.2 hours = ? minutes

To do so, you must find the defined relationship between the 2 units.

1 hour = 60 minutes

Dimensional AnalysisDimensional Analysis

Then create a conversion factor that will cancel the units of your given value.

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 hr. = 60 min

Factors: 1 hr. and 60 min60 min 1 hr.

Which one of these conversion factors will cancel the units of our given value, 6.2 hours?

Conversion FactorsConversion Factors

6.2 hours x 1 hour = ? Minutes 60 min.

6.2 hours x 60 min = ? Minutes 1 hour

The second conv. factor allows us to cancel the hour units (since “hr” appears in numerator & denominator) so this is the one we want.

Multi-step ConversionsMulti-step Conversions

• Sometimes you must use more than one conversion factor.

• When there isn’t a direct relationship between the 2 units of interest.

Multi-step Conversions, cont.Multi-step Conversions, cont.

How many seconds are in 1.4 days?Unit plan: days hr min secondsDefined Relationships: 1 day = 24 hr

1 hr = 60 min1 min = 60 s

1.4 days x 24 hr x 60 min x 60 s = 1 day 1 hr 1 min

ANSWER: 120,960 s.

Complex ConversionsComplex Conversions• Sometimes it is necessary to convert with

measurements that involve more than one unit!

• Ex: convert 60 mi/hr into ft/sec• 1 mile=5280 ft 1 hr=60 min 1 min=60

60mi x 5280 ft 1 hr x 1 min = 90 ft/sec hr 1 mi 60 min 60 sec

Summary: Dimensional Summary: Dimensional AnalysisAnalysis

By using dimensional analysis the UNITS ensure By using dimensional analysis the UNITS ensure that you have the conversion right side up, and that you have the conversion right side up, and the UNITS are calculated as well as the numbers!the UNITS are calculated as well as the numbers!

ASSIGNMENT: Study Guide, Section 1.6, ASSIGNMENT: Study Guide, Section 1.6,

#15-18, 24-26#15-18, 24-26

p 16-17p 16-17

Steps in the Scientific MethodSteps in the Scientific Method

1.1. ObservationsObservations-- quantitativequantitative- - qualitativequalitative

2.2. Formulating hypothesesFormulating hypotheses- - possible explanation for the possible explanation for the

observationobservation3.3. Performing experimentsPerforming experiments

- - gathering new information to gathering new information to decidedecide

whether the hypothesis is validwhether the hypothesis is valid

Outcomes Over the Long-Outcomes Over the Long-TermTerm

Theory (Model)Theory (Model)

- - A set of tested hypotheses that give A set of tested hypotheses that give anan overall explanation of some natural overall explanation of some natural

phenomenon.phenomenon.

Natural LawNatural Law

-- The same observation applies to The same observation applies to manymany different systemsdifferent systems

-- Example - Law of Conservation of Example - Law of Conservation of MassMass

Law vs. TheoryLaw vs. Theory

A A lawlaw summarizes what happens summarizes what happens

A A theorytheory (model) is an attempt to explain (model) is an attempt to explain whywhy it happens.it happens.

Converting Celsius to KelvinConverting Celsius to Kelvin

33Kelvins = C + 273 °C = Kelvins - 273

DensityDensity

• Is a physical property of matter & can help you identify unknown element samples.

• Is the amount of mass per volume.• Often expressed in g/mL

Properties of Properties of MatterMatterExtensive propertiesExtensive properties

Intensive propertiesIntensive properties

Volume

MassEnergy Content (think Calories!)

depend on the amount of matter that is present.

do not depend on the amount of matter present.

Melting point

Boiling point

Density

Three PhasesThree Phases

Phase Phase DifferencesDifferences

SolidSolid – definite volume and shape; particles packed in fixed positions.LiquidLiquid – definite volume but indefinite shape; particles close together but not in fixed positionsGasGas – neither definite volume nor definite shape; particles are at great distances from one anotherPlasma – high temperature, ionized phase of matter as found on the sun.

Classification of Matter

Separation of a MixtureSeparation of a Mixture

The constituents of the mixture retain The constituents of the mixture retain their identity and may be separated by their identity and may be separated by physical means.physical means.

Separation of a MixtureSeparation of a Mixture

The components of dyes such as ink may be separated by paper chromatography.

Separation of a Separation of a Mixture By Mixture By DistillationDistillation

Organization of MatterOrganization of Matter

MatterMatter

Mixtures:a) Homogeneous (Solutions)b) Heterogeneous

Pure SubstancesPure Substances

Compounds ElementsElements

AtomsAtoms

NucleusNucleus ElectronsElectrons

Protons NeutronsNeutrons

QuarksQuarks QuarksQuarks

Separation of a CompoundSeparation of a CompoundThe Electrolysis of water

Water Hydrogen + Oxygen

H2O H2 + O2

Reactant Products

Compounds must be separated by chemical means.

With the application of electricity, water can be separated into its elements

Chemical Foundations 1. Nature of Measurement Part 1 - number Part 2 - scale (unit) Examples: 20...

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