Chapter 2: Measurements Chapter 2: Measurements and Calculationsand Calculations
Chemistry isChemistry is
A natural science.A natural science.a language with its a language with its own vocabulary.own vocabulary.
a way of thinking.a way of thinking.
Scientific MethodScientific Method A way of solving problems or A way of solving problems or
answering questions.answering questions. Starts with observation- noting and Starts with observation- noting and
recording factsrecording facts Hypothesis- an Hypothesis- an educatededucated guess as guess as
to the cause of the problem or to the cause of the problem or answer to the question.answer to the question.
Scientific MethodScientific Method ExperimentExperiment- designed to test the - designed to test the
hypothesishypothesis only two possible answersonly two possible answers
hypothesis is righthypothesis is right hypothesis is wronghypothesis is wrong
Generates data observations from Generates data observations from experiments.experiments.
Modify hypothesis - repeat the cycleModify hypothesis - repeat the cycle
Observations
Hypothesis
Experiment
Cycle repeats many Cycle repeats many times.times.
The hypothesis The hypothesis gets more and gets more and more certain.more certain.
Becomes a Becomes a theorytheory A thoroughly tested A thoroughly tested
model that explains model that explains why things behave why things behave a certain way.a certain way.
Theory can never Theory can never be proven.be proven.
Useful because Useful because they predict they predict behaviorbehavior
Help us form Help us form mental pictures mental pictures of processes of processes ((modelsmodels))
Observations
Hypothesis
Experiment
Another outcome is Another outcome is that certain that certain behavior is behavior is repeated many repeated many timestimes
Scientific Scientific LawLaw is is developeddeveloped
Description of how Description of how things behave things behave
Law - howLaw - how Theory- whyTheory- why
Observations
Hypothesis
Experiment
Law
Theory(Model)
Prediction
Experiment
Modify
Observations
Hypothesis
Experiment
Scientific Method (Cont.)Scientific Method (Cont.)DataData
Qualitative:Qualitative: Descriptive Descriptive color, smell, taste, gas color, smell, taste, gas bubblesbubbles
Quantitative:Quantitative: Numerical Numerical mass, volume, mass, volume, temperaturetemperature
Scientific MethodScientific Method
Hypothesis: Hypothesis: testable testable statementstatement
Theory:Theory: A broad generalization A broad generalization that explains a body of facts of that explains a body of facts of phenomenaphenomena
Model: Model: Explanation of how Explanation of how phenomena occur and how phenomena occur and how data or events are related.data or events are related.
Natural LawNatural Law
Explanation Explanation of natural of natural phenomenonphenomenon
II: Units of MeasurementII: Units of Measurement
Quantity:Quantity: something that something that has magnitude, size, or has magnitude, size, or amountamount
SI measurement: SI measurement: International System.International System.
Base UnitsBase UnitsQuantityQuantity Unit Unit
SymbolSymbolUnit NameUnit Name
lengthlength m m metermeter
MassMass kgkg kilogramkilogram
timetime ss secondsecond
temperaturetemperature KK kelvinkelvin
amount of amount of substancesubstance
molmol molemole
electric electric currentcurrent
AA ampereampere
luminous luminous intensityintensity
cdcd candelacandela
PrefixesPrefixes
Prefixes are used to represent Prefixes are used to represent quantities that are larger or quantities that are larger or smaller than the base unit.smaller than the base unit. Ranges from “pico” (10Ranges from “pico” (10-12-12) to ) to
“tera” (10“tera” (101212). Can be applied to ). Can be applied to meters, grams, seconds, and meters, grams, seconds, and liters, etc.liters, etc.
ConversionsConversions
Change 5.6 m to millimetersChange 5.6 m to millimeters
k h D d c m
starts at the base unit and move three to the right.move the decimal point three to the right
56 00
PrefixesPrefixes
Number Line MethodNumber Line Method
Convert 5.21 kg to cgConvert 5.21 kg to cgConvert 13478 nm to mConvert 13478 nm to mConvert 6478.92 dL to hlConvert 6478.92 dL to hlConvert 312.7 dag to mgConvert 312.7 dag to mg
AnswersAnswers
5.21 kg = 521000 cg5.21 kg = 521000 cg 13478 nm = 0.000013478 13478 nm = 0.000013478
mm 6478.92 dL = 6.47892 hL6478.92 dL = 6.47892 hL 312.7 dag = 3127000 mg312.7 dag = 3127000 mg
Derived UnitsDerived Units
Derived Units:Derived Units: combinations combinations of SI base unitsof SI base unitsArea: Square meters: mArea: Square meters: m22
Volume: cubic meters: mVolume: cubic meters: m33
Density: kilograms/ cubic Density: kilograms/ cubic meters: meters:
kg/ mkg/ m33
Molar Mass: kilograms/mole: Molar Mass: kilograms/mole: kg/molkg/mol
Molar volume: cubic meters/ Molar volume: cubic meters/ mole: mmole: m33/ mol/ mol
Energy: Joule: J = kgEnergy: Joule: J = kg··mm22/s/s22Pressure: Pascal: Pa: Pressure: Pascal: Pa:
kg/m x skg/m x s22
More Commonly Used UnitsMore Commonly Used Units
Volume:Volume: 1cm 1cm33 = 1mL = 1mL
1 L = 1dm1 L = 1dm33
Density:Density: g/cm g/cm33 = g/mL = g/mL Molar mass:Molar mass: g/mol g/mol Molar volume:Molar volume: liters/mol liters/mol
CalculationsCalculations
Calculate density of a sample Calculate density of a sample of Al that has a mass of 16.8 of Al that has a mass of 16.8 g and a volume of 6.2 cmg and a volume of 6.2 cm33
Density = mass / volume Density = mass / volume D = 16.8 g / 6.2 cmD = 16.8 g / 6.2 cm3 3
D = 2.71 g/cmD = 2.71 g/cm3 3 = 2.7 g/cm= 2.7 g/cm33
Conversion FactorsConversion Factors
A ratio derived from the A ratio derived from the equality between two equality between two different units that can different units that can be used to convert from be used to convert from one unit to the other.one unit to the other.
Examples:Examples: 1 cal/4.184 J1 cal/4.184 J 1 mL/1 cm1 mL/1 cm33
1 ft/12 in1 ft/12 in 2.54 cm/1 in2.54 cm/1 in
Dimensional AnalysisDimensional Analysis A mathematical technique A mathematical technique
that allows you to use that allows you to use units to solve problems units to solve problems involving measurements.involving measurements.Convert 7.21 weeks to Convert 7.21 weeks to seconds:seconds:
7.2 weeks x 7 days/1 7.2 weeks x 7 days/1 week x 24 hr/1 day x week x 24 hr/1 day x 60 min/1 hr x 60s/1 60 min/1 hr x 60s/1 min = min = 4,360,608 s4,360,608 s
Dimensional AnalysisDimensional Analysis
Convert 65 Convert 65 mi/hr to mi/hr to km/sec:km/sec:
65 mi/hr x 1.6 km/mi 65 mi/hr x 1.6 km/mi x 1 hr/60 min x 1 x 1 hr/60 min x 1 min/60 s = min/60 s = 0.029 0.029 km/skm/s
III: Using Scientific MeasurementsIII: Using Scientific Measurements
Accuracy: refers to the Accuracy: refers to the closeness of measurement to closeness of measurement to the correct or accepted value the correct or accepted value of the quantity measuredof the quantity measured Accepted value: 1.57 gAccepted value: 1.57 g Your Measurements: 1.52 g Your Measurements: 1.52 g
and 1.31 g NOT ACCURATE!!and 1.31 g NOT ACCURATE!!
PrecisionPrecision
Refers to the closeness of a Refers to the closeness of a set of measurements of the set of measurements of the same quantity made in the same quantity made in the same waysame way 2.11, 2.12, 2.11 = precise2.11, 2.12, 2.11 = precise 2.11, 2.57, 2.72 = not precise2.11, 2.57, 2.72 = not precise 2.33, 2.35, 2.34 = precise2.33, 2.35, 2.34 = precise
Precision and AccuracyPrecision and Accuracy
Accepted Value: 2.79 kgAccepted Value: 2.79 kg
Measurements: 3.01 kg, 3.02 kg, Measurements: 3.01 kg, 3.02 kg, 3.01 kg3.01 kg These are precise but not accurateThese are precise but not accurate
Let’s use a golf anaolgy
Accurate? No
Precise? Yes
Accurate? Yes
Precise? Yes
Precise? No
Accurate? Maybe?
Accurate? Yes
Precise? We cant say!
ErrorError
Percentage Error:Percentage Error: (Experimental Value– Accepted Value)(Experimental Value– Accepted Value) x x 100%100%
Accepted ValueAccepted Value Experimental Value = 87.9 g/cmExperimental Value = 87.9 g/cm33
Accepted = 89.1 g/cmAccepted = 89.1 g/cm33
[(87.9 – 89.1)/89.1] x 100 = -1.3%[(87.9 – 89.1)/89.1] x 100 = -1.3% Error in Measurement:Error in Measurement: Go to Go to
packet (+)packet (+)
Significant FiguresSignificant Figures All the digits known with certainty All the digits known with certainty
plus one final digit that is plus one final digit that is somewhat uncertain or is somewhat uncertain or is estimatedestimated
Atlantic – Pacific RuleAtlantic – Pacific Rule Atlantic: if the decimal is Atlantic: if the decimal is aabsent, start bsent, start
counting from the right (Atlantic) side counting from the right (Atlantic) side with the first non-zero numberwith the first non-zero number
Pacific: start counting from the left Pacific: start counting from the left (Pacific) side with the first non-zero (Pacific) side with the first non-zero number if the decimal is number if the decimal is ppresent.resent.
Significant figures (sig figs)Significant figures (sig figs) How many numbers mean anythingHow many numbers mean anything When we measure something, we When we measure something, we
can (and do) always estimate can (and do) always estimate between the smallest marks.between the smallest marks.
21 3 4 5
Significant figures (sig figs)Significant figures (sig figs) The better marks the better we The better marks the better we
can estimate.can estimate. Scientist always understand that Scientist always understand that
the last number measured is the last number measured is actually an estimateactually an estimate
21 3 4 5
Which zeros count?Which zeros count? Those at the end of a number Those at the end of a number
before the decimal point don’t before the decimal point don’t countcount
12400 12400 If the number is smaller than one, If the number is smaller than one,
zeroes before the first number zeroes before the first number don’t countdon’t count
0.045 0.045
Which zeros count?Which zeros count? Zeros between other sig figs do.Zeros between other sig figs do. 10021002 zeroes at the end of a number after zeroes at the end of a number after
the decimal point do countthe decimal point do count 45.830045.8300 If they are holding places, they don’t.If they are holding places, they don’t. If they are measured (or estimated) If they are measured (or estimated)
they dothey do
Sig figs.Sig figs. How many sig figs in the following How many sig figs in the following
measurements?measurements? 458 g458 g 4085 g4085 g 4850 g4850 g 0.0485 g0.0485 g 0.004085 g0.004085 g 40.004085 g40.004085 g
Sig. Fig. ExamplesSig. Fig. Examples 3440:3440: 0.007987: 0.007987: 0.07650: 0.07650: 200: 200: 200. : 200. :
Rounding:Rounding: Table 6 on page 48. Table 6 on page 48. If the number after you want If the number after you want
to round is greater than 5, to round is greater than 5, then round up: 42.68 then round up: 42.68 42.7 42.7
If the number after you want If the number after you want to round is less than 5, leave to round is less than 5, leave the same: 17.32 the same: 17.32 17.3 17.3
RoundingRounding
If the number after the one If the number after the one you want to round is a 5 you want to round is a 5 followed by non-zero digits followed by non-zero digits then round up: 2.78512 then round up: 2.78512 2.79 2.79
RoundingRounding
If the number after the one you want If the number after the one you want to round is a 5, not followed by non-to round is a 5, not followed by non-zero digits and preceded by an odd zero digits and preceded by an odd digit, round up: 4.635digit, round up: 4.635 4.64 4.64
If the number after the one you want If the number after the one you want to round is a 5, not followed by non-to round is a 5, not followed by non-zero digits and preceded by and zero digits and preceded by and even digit, then leave the same: even digit, then leave the same: 78.65 78.65 78.6 78.6
Addition and Subraction with S.F.Addition and Subraction with S.F.
The answer must have the same The answer must have the same number of digits to the right of number of digits to the right of the decimal point as there are in the decimal point as there are in the measurement having the the measurement having the fewest digits to the right of the fewest digits to the right of the decimal point.decimal point.
For example
27.93 6.4+ First line up the decimal places
27.936.4+
Then do the adding
34.33Find the estimated numbers in the problem
27.936.4
This answer must be rounded to the tenths place
37.284 + 114.2 = 37.284 + 114.2 = 89.25 – 17.111 = 89.25 – 17.111 = 522 + 38.7 =522 + 38.7 =
37.284 + 114.2 = 37.284 + 114.2 = 151.484 = 151.484 = 151.5151.5
89.25 – 17.111 = 72.139 89.25 – 17.111 = 72.139 ==72.1472.14
522 + 38.7 = 560.7 = 522 + 38.7 = 560.7 = 561561
Multiplying and Dividing with S.F.Multiplying and Dividing with S.F.
The answer can have The answer can have no more significant no more significant figures than are the figures than are the measurement with measurement with the fewest number of the fewest number of significant figuressignificant figures..
5.27 x 3477.6 = 5.27 x 3477.6 = 8.2 / 7.666 =8.2 / 7.666 =32.103 x 6.23 =32.103 x 6.23 =
5.27 x 3477.6 = 5.27 x 3477.6 = 18326.952 = 18326.952 = 18,30018,300
8.2 / 7.666 = 8.2 / 7.666 = 1.06965823 = 1.06965823 = 1.11.1
32.103 x 6.23 = 32.103 x 6.23 = 200.00169 =200.00169 =200.200.
Scientific NotationScientific Notation Numbers are written in the form Numbers are written in the form
M x 10M x 10nn where M is a number where M is a number between one and ten and n is a between one and ten and n is a whole number.whole number. Determine M by moving the decimal Determine M by moving the decimal
point in the original number to the point in the original number to the left or right so that only one nonzero left or right so that only one nonzero digit remains to the left of the digit remains to the left of the decimal point.decimal point.
Determine n by counting the number Determine n by counting the number of places that you moved the decimal of places that you moved the decimal point.point.
Scientific NotationScientific Notation
5,856,000 = 5.856 x 105,856,000 = 5.856 x 1066
0.02560 = 2.560 x 100.02560 = 2.560 x 10-2-2
4.77 x 104.77 x 1044 = 47700 = 477008.952 x 108.952 x 10-3-3 = 0.008952 = 0.008952
Examples of Scientific NotationExamples of Scientific Notation
756320 = 756320 = 5856000 = 5856000 = 4.50 x 104.50 x 10-4-4 = =7.834 x 107.834 x 1066= =
More ExamplesMore Examples
0.001760 = 0.001760 = 4.25 x 104.25 x 1044 = =3.60 x 103.60 x 10-3-3 = =
Answers to ExamplesAnswers to Examples
756320 = 7.5632 x 10756320 = 7.5632 x 1055
5856000 = 5.856 x 105856000 = 5.856 x 1066
4.50 x 104.50 x 10-4-4 =0.000450 =0.000450 7.834 x 107.834 x 1066= 7834000= 7834000 0.001760 = 1.760 x 100.001760 = 1.760 x 10-3-3
4.25 x 104.25 x 1044 = 42500 = 42500 3.60 x 103.60 x 10-3-3 = 0.00360 = 0.00360
Direct ProportionsDirect Proportions Two quantities are directly Two quantities are directly
proportional to each other if proportional to each other if dividing one by the other gives a dividing one by the other gives a constant value.constant value. Y/X = kY/X = k Y = kxY = kx K = proportionality constantK = proportionality constant Graph is a straight line with a Graph is a straight line with a
positive slopepositive slope Ex= density, speedEx= density, speed
Inverse ProportionsInverse Proportions
Two quantities are inversely Two quantities are inversely proportional to each other if proportional to each other if their product is constant.their product is constant.
K = xyK = xy Example:Example:
Increase Pressure of a gas Increase Pressure of a gas Decrease Volume of a gasDecrease Volume of a gas