Chapter 3 Scientific Measurement. Measurements 2 types: Qualitative measurements (words) Heavy, hot, or long Quantitative measurements (#’s) &

Chapter 3Chapter 3Scientific Scientific

MeasuremMeasurementent

MeasurementsMeasurements 2 types: Qualitative measurements (words)

Heavy, hot, or long Quantitative measurements (#’s) &

depend on:1) Reliability of measuring instrument2) Care w/ which it’s read – determined

by YOU! Scientific Notation Coefficient raised to power 10

(ex. 1.3 x 107) Review: Textbook pages R56 & R57

Accuracy, Precision, and ErrorAccuracy, Precision, and Error Necessary for reliable lab reliable lab

measurements measurements Accuracy –

Precision –

Reproducible Reproducible For #’s w/ decimal pt……… decimal For #’s w/ decimal pt……… decimal place right-most digit is inplace right-most digit is in

134.90134.90 0.01570.0157

how close measurement is to true valuehow close measurements to each other

Accuracy, Precision, and ErrorAccuracy, Precision, and Error

For #’s For #’s w/ow/o decimal decimal pt…...right-most non-zero pt…...right-most non-zero ##3420034200

120390120390

Precision and AccuracyPrecision and Accuracy

Accuracy, Precision, and Accuracy, Precision, and ErrorError

Accepted value – based on reliable references (Density Table page 90)

Experimental value - measured in lab

Accuracy, Precision, and Accuracy, Precision, and ErrorError

Error = accepted value – experimental value

can be + or - Percent error = absolute value of error divided by accepted value, & multiplied by 100%

| error |

accepted value

x 100%% error =

NFL Flyovers 4:53

Significant Figures in Significant Figures in MeasurementsMeasurements

Significant figures all known digits + one estimated digit

Measurements must be recorded to correct # sig figs

Figure 3.5 Significant Figures - Page 67

Which measurement is the best?

What is the measured value?



Rules for Counting Sig FigsRules for Counting Sig Figs

Non-zerosNon-zeros alwaysalways count as count as sig figs:sig figs:

34563456 hashas 44 sig figssig figs


ZerosZerosLeading zeroes Leading zeroes do notdo not count as sig figs:count as sig figs:

0.04860.0486 has has33 sig figs sig figs


ZerosZerosCaptive zeroesCaptive zeroes alwaysalways count as sig figs:count as sig figs:

16.0716.07 hashas44 sig figs sig figs


ZerosZeros

Trailing zerosTrailing zeros significant significant only only w/ written decimal w/ written decimal point:point:

9.3009.300 has has44 sig figs sig figs


Two special situationsTwo special situations have have

unlimited #unlimited # sig figs: sig figs:1. Counted items1. Counted items

a)a) 23 people, or 425 23 people, or 425 thumbtacksthumbtacks

2. Exactly defined quantities2. Exactly defined quantitiesb)b) 60 minutes = 1 hour60 minutes = 1 hour

Big Sig Fig Gig (2:27) – Mark Rosengarten

Sig Fig Practice #1Sig Fig Practice #1How many significant figures in 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 mL 2 sig figs5 dogs unlimited

These all come from some measurements

This is a counted value

Sig Figs in CalculationsSig Figs in Calculations answer cannot be more precise than least precise measurement.

Sometimes, calculated values need rounded off

Rounding Calculated Rounding Calculated AnswersAnswers

RoundingDecide how many sig figs needed Round to that many digits, counting from the leftIs next digit less than 5? Drop it. Is next digit 5+? Add 1

- Page 69

Be sure to answer the question completely!


Addition and Subtractionanswer rounded to same # decimal places as least # decimal places in problem

- Page 70


Multiplication and Divisionanswer rounded to same # of sig figs as least # of sig figs in problem

- Page 71

Rules for Sig Figs in Mathematical Rules for Sig Figs in Mathematical OperationsOperations

• Multiplication and DivisionMultiplication and Division:: # sig figs in result = # in # sig figs in result = # in least least preciseprecise measurement used in measurement used in calculation.calculation.

• 6.38 x 2.0 =6.38 x 2.0 =• 12.76 12.76 13 13 (2 sig figs)(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 Sig Figs in Rules for Sig Figs in Mathematical OperationsMathematical Operations

• Addition and SubtractionAddition and Subtraction: # : # decimal places in result = # decimal places in result = # decimal places in decimal places in least preciseleast 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

*Note the zero that has been added.

International System of International System of Units Units p. 73p. 73

Measurements depend on units

The standards of measurement of science is Metric System

Why science uses the metrics 2:30

International System of International System of UnitsUnits

Metric system now revised & named International System of Units (SI), (1960)

multiples of 105 common base units in 5 common base units in chemistrychemistry

meter, kilogram, kelvin, meter, kilogram, kelvin, second & molesecond & mole

Nature of MeasurementsNature of Measurements

•

Part 1 – Part 1 – numbernumber Part 2 - Part 2 - unitunit

Examples:Examples: 2222 gramsgrams

3.55 x 103.55 x 1033 molesmoles

Measurement - quantitative observation -Measurement - quantitative observation -2 parts2 parts::

International System of International System of UnitsUnits

Sometimes, non-SI units usedLiter, Celsius, calorie

Derived unitsjoining unitsSpeed = kilometers/hour (distance/time)

Density = grams/mL (mass/volume)

LengthLength

SI basic unit - meter (m)distance btwn 2 objects

use prefixes for larger/smaller units

SI Prefixes – Page 74 - Common to SI Prefixes – Page 74 - Common to ChemistryChemistry

Prefix Abbreviation Meaning Exponent

Mega- M Million 106

Kilo- k thousand 103

Deci- d tenth 10-1

Centi- c hundredth 10-2

Milli- m thousandth 10-3

Micro- millionth 10-6

Nano- n billionth 10-9

Pico- P trillionth 10-12

VolumeVolume Space occupied by matter Calculated for solid…length x width x heightderived from units of length

SI unit = cubic meter (m3) Everyday unit = Liter (L), non-SI

(Note: 1mL = 1cm3)

Devices for Measuring Devices for Measuring Liquid VolumeLiquid Volume

Graduated cylindersPipetsBuretsVolumetric FlasksSyringes

Volume Changes!Volume Changes! Volumes of a solid, liquid, or gas generally increases w/ temp

More prominent for GASES Therefore, measuring instruments calibrated for specific temp usually 20 oC, which is about room temp

Ex. Volumetric flask

Units of MassUnits of Mass

Mass - quantity of matter presentMass constant, regardless of location

Weight - force of “g”- changes w/ location

Working with MassWorking with Mass

SI unit - kilogram (kg)everyday unit is gram (g)measuring instrument: triple beam balance

Units of TemperatureUnits of TemperatureTemp - measures how hot/cold object is.

Heat moves from hi - low temp2 temp scales:

◦Celsius – named after Anders Celsius

◦Kelvin – named after Lord Kelvin

(Measured with a thermometer.)

Units of TemperatureUnits of TemperatureCelsius scale

◦Water Freezing point = 0 oC◦Water Boiling point = 100 oC

Kelvin scale does not use degree sign, just K• absolute zero = 0 K (no negative

values)

• formula to convert: K = oC + 273

- Page 78

Units of EnergyUnits of Energy Energy - ability to do work,

or produce heat energy can be measured

2 common units:1) Joule (J) = SI unit of energy,

named after James Prescott Joule2) calorie (cal) = heat needed to

raise 1g of water 1 oC

Units of EnergyUnits of EnergyConversions btwn joules & calories carried out by using following relationship:

1 cal = 4.184 J

Sec 3.3 Conversion factorsSec 3.3 Conversion factorsA “ratio” of equivalent measurementsStart with two things that are the same: one meter is one hundred centimeters write it as an equation 1 m = 100 cmDivide on each side of equation to come up with 2 ways of writing the number “1”

Conversion factorsConversion factors

100 cm1 m =100 cm 100 cm


11 m =100 cm


11 m =100 cm

100 cm=1 m1 m 1 m


11 m =100 cm

100 cm=1 m

1

Conversion factorsConversion factorsunique way of writing the # 1In same system they are defined quantities so unlimited number of sig figs

big # small unit = small # big unit 100 cm = 1 m

Practice writing Practice writing two possible two possible conversion factorsconversion factors for the for the following:following:

Between kilograms and grams

between feet and inchesusing 1.096 qt. = 1.00 L

What are they good for?What are they good for?

We can multiply by # “one” creatively to change units

Question: 13 inches is how many yards?

We know that 36 inches = 1 yard 1 yard = 1

36 inches13 inches x 1 yard =

36 inches

What are they good for?What are they good for?

We can multiply by a conversion factor to We can multiply by a conversion factor to change the units .change the units .

Problem: 13 inches is how many yards?Problem: 13 inches is how many yards? Known: 36 inches = 1 yard.Known: 36 inches = 1 yard. 1 yard = 11 yard = 1 36 36

inchesinches 13 inches x 1 yard 13 inches x 1 yard == 0.36 yards0.36 yards

36 inches 36 inches

Dimensional AnalysisDimensional AnalysisMethod of analyzing & solving problems, by using units (dimensions) of measurement

Dimension = unit (g, L, cm)Analyze = solve

◦Using units to solve problemsIf units of answer correct, you probably did math correctly!

Dimensional AnalysisDimensional Analysisprovides alternative approach to

problem solving, instead of with equation or algebra.

ruler is 12.0 inches long. How long is it in cm? ( 1 inch = 2.54 cm)

How long is this in meters?A race is 10.0 km long. How far is

this in miles, if:◦ 1 mile = 1760 yards◦ 1 meter = 1.094 yards

p. 82 practice problem p. 82 practice problem #28 #28

How many minutes are there in exactly one week?

p. 83 practice problem # p. 83 practice problem # 3030

An experiment requires that each student use an 8.5-cm length of magnesium ribbon. How many students can do the experiment if there is a 570-cm length of magnesium ribbon available?

Converting Between UnitsConverting Between Unitsmeasurements with one unit converted to equivalent measurement with another unit easily solved using dimensional analysis

Sample: Express 750 dg in grams.Many complex problems are best solved by breaking the problem into manageable parts.

p. 84 practice problem p. 84 practice problem #32#32Using tables from this chapter,

convert these: a. 0.044 km to meters

b. 4.6 mg to grams

c. 0.107 g to centigrams

Converting Between UnitsConverting Between Units Let’s say you need to clean your car:

1) Start by vacuuming the interior2) Next, wash the exterior3) Dry the exterior4) Finally, put on a coat of wax

• What problem-solving methods can help you solve complex word problems?

Break the solution down into steps, and use more than one conversion factor if necessary

p. 85 practice problem # 34p. 85 practice problem # 34(p. 30 in workbook)(p. 30 in workbook)

The radius of a potassium atom is 0.227 nm. Express this radius in the unit centimeters.

Converting Complex Units?Converting Complex Units? Complex units are those that are

expressed as a ratio of two units:◦ Speed might be meters/hour

Sample: Change 15 meters/hour to units of centimeters/second

How do we work with units that are squared or cubed? (cm3 to m3, etc.)

BONUS: Crash of Flight 143 – see my webpage

- Page 86

Section 3.4 DensitySection 3.4 Density Which is heavier- a pound of steel or a pound of styrofoam?Most people answer “steel”, but the weight is exactly the same

They are normally thinking about equal volumes of the two

The relationship here between mass and volume is called DensityDensity

DensityDensity The formula for density is: mass volume•Common units are: g/mL, or g/cm3, (or g/L for gas)

•Density is a physical property, and does notdoes not depend upon sample size•A gold nugget has the same density as a gold bar

Density =

- Page 90Note temperature and density units

Density and TemperatureDensity and Temperature

What happens to the density as the temperature of an object increases?Mass remains the sameMost substances increase in volume as temperature increases

Thus, density generally decreases as the temperature increases

Density and WaterDensity and Water Water is an important exception to the previous statement.

Over certain temperatures, the volume of water increases as the temperature decreases (You don’t want your water pipes to freeze in the winter, right?)Why does ice float in liquid water?

- Page 91

- Page 92

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Chapter 3 Scientific Measurement. Measurements 2 types: Qualitative measurements (words) Heavy, hot, or long Quantitative measurements (#’s) &