chemistry chapter 2 measurementsandcalculations steps in the scientific method 1.observations -...
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Chemistry Chapter Chemistry Chapter 22
Measurements Measurements and and
CalculationsCalculations
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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 observationobservation
3.3. Performing experimentsPerforming experiments
- - gathering new information to gathering new information to decidedecide
whether the hypothesis is validwhether the hypothesis is valid
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Outcomes Over the Long-Outcomes Over the Long-TermTerm
Theory (Model)Theory (Model)
- - A set of tested hypotheses that give anA 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 systemsdifferent systems
-- Example - Law of Conservation of Example - Law of Conservation of MassMass
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Law vs. TheoryLaw vs. Theory
A A lawlaw summarizes what summarizes what happenshappens
A A theorytheory (model) is an attempt (model) is an attempt to explain to explain whywhy it happens. it happens.
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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
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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
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SI UnitsSI Units
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SI PrefixesSI PrefixesCommon to ChemistryCommon to Chemistry
Prefix Unit Abbr. ExponentKilo k 103
Deci d 10-1
Centi c 10-2
Milli m 10-3
Micro 10-6
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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.
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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?
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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
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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.
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Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details
Nonzero integersNonzero integers always count always count as significant figures.as significant figures.
34563456 hashas
44 sig figs.sig figs.
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Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details
ZerosZeros-- Leading zerosLeading zeros do not count do not count as as
significant figuressignificant figures..
0.04860.0486 has has
33 sig figs. sig figs.
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Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details
ZerosZeros-- Captive zeros Captive zeros always always
count ascount assignificant figures.significant figures.
16.07 16.07 hashas
44 sig figs. sig figs.
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Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details
ZerosZerosTrailing 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.
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Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details
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
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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
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Rules for Significant Figures in Rules for Significant Figures in Mathematical OperationsMathematical Operations
Multiplication and DivisionMultiplication and Division:: # sig # sig figs in the result equals the number figs in the result equals the number in the least precise measurement in the least precise measurement used in the calculation.used in the calculation.
6.38 x 2.0 =6.38 x 2.0 =
12.76 12.76 13 (2 sig figs)13 (2 sig figs)
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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
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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))
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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
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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
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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 kg91 kg x 602000000000000000000000x 602000000000000000000000
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Scientific Scientific Notation:Notation:A method of representing very large A method of representing very large or very small numbers in the form:or very small numbers in the form:
M x 10nM x 10n
MM is a number between is a number between 11 and and 1010 nn is an integer is an integer
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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
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2.5 x 102.5 x 1099
The exponent is the number of places we moved the decimal.
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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
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5.79 x 105.79 x 10-5-5
The exponent is negative because the number we started with was less than 1.
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PERFORMING PERFORMING CALCULATIONCALCULATION
S IN S IN SCIENTIFIC SCIENTIFIC NOTATIONNOTATION
ADDITION AND ADDITION AND SUBTRACTIONSUBTRACTION
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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
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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
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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
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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.
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4.00 x 104.00 x 1066
+ + 3.00 x 103.00 x 1055
Student AStudent A40.0 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!
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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!!
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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
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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
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Direct ProportionsDirect Proportions The quotient of two variables is a constant As the value of one variable increases, the other must also increase As the value of one variable decreases, the other must also decrease The graph of a direct proportion is a straight line
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Inverse ProportionsInverse Proportions The product of two variables is a constant As the value of one variable increases, the other must decrease As the value of one variable decreases, the other must increase The graph of an inverse proportion is a hyperbola