Chemistry Ch 2 Notes

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