Unit 1:Unit 1:Observation,Observation,MeasurementMeasurement

and and CalculationsCalculations

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Steps in the Scientific MethodSteps in the Scientific Method

► 1.1. ObservationsObservations

-- quantitative quantitative

- - qualitative qualitative

2.2. Formulating hypotheses Formulating hypotheses

- - possible explanation for the possible explanation for the observation observation

3.3. Performing experiments Performing experiments

- - gathering new information to gathering new information to decide decide

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 an A set of tested hypotheses that give an overall explanation of some natural overall explanation of some natural

phenomenonphenomenon.. ► Natural LawNatural Law

-- The same observation applies to many The same observation applies to many different systems different systems

► -- Example - Law of Conservation Example - Law of Conservation of Massof Mass

Law vs. TheoryLaw vs. Theory

A A lawlaw summarizes what summarizes what happens happens

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

Nature of MeasurementNature of Measurement

►

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

Examples: Examples: 2020 grams grams

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

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 PrefixesSI PrefixesCommon to ChemistryCommon to Chemistry

PrefixPrefix Unit Abbr.Unit Abbr. ExponentExponentKiloKilo kk 101033

DeciDeci dd 1010-1-1

CentiCenti cc 1010-2-2

MilliMilli mm 1010-3-3

MicroMicro 1010-6-6

Uncertainty in MeasurementUncertainty in Measurement

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

Why Is there Uncertainty?Why Is there Uncertainty? Measurements are performed with instruments No instrument can read to an infinite number of decimal placesWhich of these balances has the greatest

uncertainty in measurement?

Precision and AccuracyPrecision and Accuracy► AccuracyAccuracy 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.

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

► Nonzero integersNonzero integers always always count as significant figures. count as significant figures.

34563456 hashas

44 sig figs.sig figs.

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

► Zeros Zeros -- Leading zerosLeading zeros do not count do not count as as

significant figuressignificant figures..

► 0.04860.0486 has has

33 sig figs. sig figs.

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

► Zeros Zeros -- Captive zeros Captive zeros always always

count as count as significant figures.significant figures.

► 16.07 16.07 has has

44 sig figs. sig figs.

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

► Zeros Zeros 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.

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

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

► Multiplication and DivisionMultiplication and Division:: # # sig figs in the result equals the sig figs 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 ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Rules for Significant Figures Rules for Significant Figures in Mathematical Operationsin Mathematical Operations

► Addition and SubtractionAddition and Subtraction: The : The number of decimal places in the number of decimal places in the result equals the number of decimal result equals the number of decimal places in the least precise places in the least precise measurement. measurement.

6.8 + 11.934 = 6.8 + 11.934 =

18.734 18.734 18.7 ( 18.7 (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

In science, we deal with some In science, we deal with some very very LARGELARGE numbers: numbers:

1 mole = 6020000000000000000000001 mole = 602000000000000000000000

In science, we deal with some In science, we deal with some very very SMALLSMALL numbers: numbers:

Mass of an electron = Mass of an electron = 0.000000000000000000000000000000091 kg0.000000000000000000000000000000091 kg

Scientific NotationScientific Notation

Imagine the difficulty of Imagine the difficulty of calculating the mass of 1 mole calculating the mass of 1 mole of electrons!of electrons!

0.00000000000000000000000000000000.000000000000000000000000000000091 kg 91 kg x 602000000000000000000000x 602000000000000000000000

???????????????????????????????????

Scientific Scientific Notation:Notation:A method of representing very large A method of representing very large

or very small numbers in the or very small numbers in the form: form:

M x 10n M x 10n MM is a number between is a number between 11 and and 10 10 nn is an integer is an integer

2 500 000 000

Step #1: Insert an understood decimal pointStep #1: Insert an understood decimal point

.

Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal point

123456789

Step #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn

2.5 x 102.5 x 1099

The exponent is the number of places we moved the decimal.

0.00005790.0000579

Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal pointStep #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn

1 2 3 4 5

5.79 x 105.79 x 10-5-5

The exponent is negative because the number we started with was less than 1.

PERFORMING PERFORMING CALCULATIONCALCULATION

S IN S IN SCIENTIFIC SCIENTIFIC NOTATIONNOTATION

ADDITION AND ADDITION AND SUBTRACTIONSUBTRACTION

ReviewReview::Scientific notation Scientific notation expresses a number in the expresses a number in the form:form: M x 10M x 10nn

1 1 M M 1010

n is an n is an integerinteger

4 x 104 x 1066

+ 3 x 10+ 3 x 1066

IFIF the exponents the exponents are the same, we are the same, we simply add or simply add or subtract the subtract the numbers in front numbers in front and bring the and bring the exponent down exponent down unchanged.unchanged.

77 x 10x 1066

4 x 104 x 1066

- 3 x 10- 3 x 1066 The same holds The same holds true for true for subtraction in subtraction in scientific scientific notation.notation.

11 x 10x 1066

Scientific Notation #10Scientific Notation #10

4 x 104 x 1066

+ 3 x 10+ 3 x 1055

If the exponents If the exponents are NOT the are NOT the same, we must same, we must move a decimal to move a decimal to makemake them the them the same.same.

4.00 x 104.00 x 1066

+ + 3.00 x 103.00 x 1055

Student AStudent A

40.0 x 1040.0 x 1055

43.0043.00 x 10x 1055 Is this Is this good good

scientific scientific notation? notation?

NO!NO!

== 4.300 x 104.300 x 1066

To avoid To avoid this this problem, problem, move the move the decimal on decimal on the the smallersmaller number!number!

4.00 x 104.00 x 1066

+ + 3.00 x 103.00 x 1055

Student BStudent B

.30 x 10.30 x 1066

4.304.30 x 10x 1066 Is this Is this good good

scientific scientific notation? notation?

YESYES!!

A Problem for A Problem for you…you…

2.37 x 102.37 x 10-6-6

+ 3.48 x 10+ 3.48 x 10-4-4

Scientific Notation #14Scientific Notation #14

2.37 x 102.37 x 10-6-6

+ 3.48 x 10+ 3.48 x 10-4-4

Solution…Solution…002.37 x 10002.37 x 10--

66

0.0237 x 100.0237 x 10--

44

3.5037 x 103.5037 x 10-4-4

Data RepresentationsData Representations

What are different What are different ways to display ways to display data?data?

What are the key What are the key components to a components to a graph?graph?

Titration curve for Monoprotic Acid

Graph EssentialsGraph Essentials

► In your notebook, In your notebook, use complete use complete sentences to sentences to describe the describe the essential essential components to a components to a graph.graph.

► Also, describe how Also, describe how a graph needs to a graph needs to be displayedbe displayedRemember: Don’t play connect the

dots unless instructed to do so!

What Makes a Graph?What Makes a Graph?

► Objective: Graph Objective: Graph the following data. the following data. What information What information should be included should be included on a graph? Use on a graph? Use your prior your prior knowledge and knowledge and group members to group members to create a create a perfectperfect graph from the graph from the data.data.

Mass Mass (g)(g)

Volume Volume (mL)(mL)

2.352.35 2.302.30

1.251.25 1.221.22

3.653.65 3.573.57

0.960.96 0.940.94

4.564.56 4.474.47

4.004.00 3.923.92

2.332.33 2.272.27

Density of H2O @ 0.4 ۫C