Measurement

Instruments for Measuring Volume

GraduatedcylinderSyringeVolumetric flaskBuretPipet3Units of Measuring Volume

1 L = 1000 mL1 qt = 946 mLTimberlake, Chemistry 7th Edition, page 34UNITS OF MEASURING VOLUME

A measurement has two parts: a number and a unit.

Note: NO NAKED NUMBERSReading a Meniscus1086line of sight too highreading too lowreading too highline of sight too lowproper line of sightreading correctgraduatedcylinder10 mL5Christopherson ScalesMade in Normal, Illinois USAUnits for Measuring Mass1 kg = 2.20 lb1 kg(1000 g)1 lb1 lb0.20 lb6Quantities of MassKelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25Earths atmosphere to 2500 kmOcean linerIndian elephantAverage human1.0 liter of waterGrain of table saltTypical proteinUranium atomWater molecule

1024 g1021 g1018 g1015 g1012 g109 g106 g103 g100 g10-3 g10-6 g10-9 g10-12 g10-15 g10-18 g10-21 g10-24 gGiga- Mega-Kilo-basemilli-micro-nano-pico-femto-atomo-7 Factor Name Symbol Factor Name Symbol10-1 decimeter dm 101 decameter dam

10-2 centimeter cm 102 hectometer hm

10-3 millimeter mm 103 kilometer km

10-6 micrometer mm 106 megameter Mm

10-9 nanometer nm 109 gigameter Gm

10-12 picometer pm 1012 terameter Tm

10-15 femtometer fm 1015 petameter Pm

10-18 attometer am 1018 exameter Em

10-21 zeptometer zm 1021 zettameter Zm

10-24 yoctometer ym 1024 yottameter Ym

8Multiples of bytesas defined by IEC 60027-2SI prefixBinary prefixesNameSymbolMultipleNameSymbolMultiplekilobytekB103 (or 210)kibibyteKiB210megabyteMB106 (or 220)mebibyteMiB220gigabyteGB109 (or 230)gibibyteGiB230terabyteTB1012 (or 240)tebibyteTiB240petabytePB1015 (or 250)pebibytePiB250exabyteEB1018 (or 260)exbibyteEiB260zettabyteZB1021 (or 270)yottabyteYB1024 (or 280)A yottabyte (derived from the SI prefix )9SI-US Conversion FactorsRelationshipConversion FactorsLengthVolumeMass2.54 cm = 1 in.1 m = 39.4 in.946 mL = 1 qt1 L = 1.06 qt454 g = 1 lb1 kg = 2.20 lb 1 in2.54 cm 39.4 in 1 m 1 m 39.4 in.946 mL 1 qt 1 qt 946 mL 1.06 qt 1 L 1 L 1.06 qt 454 g 1 lb 1 lb 454 g 2.20 lb 1 kg 1 kg 2.20 lb2.54 cm 1 inandandandandandand10Dominoes ActivityAccuracy vs. PrecisionRandom errors: reduce precisionGood accuracyGood precisionPoor accuracyGood precisionPoor accuracyPoor precisionSystematic errors: reduce accuracy

(person)(instrument)11Scientists repeat experiments many times to increase their accuracy.

Accuracy vs. Precision

Random errors: reduce precision

Good accuracyGood precisionPoor accuracyGood precisionPoor accuracyPoor precisionSystematic errors: reduce accuracy

12Scientists repeat experiments many times to increase their accuracy.

PrecisionAccuracy reproducibility

check by repeating measurements

poor precision results from poor technique correctness

check by using a different method

poor accuracy results from procedural or equipment flaws.13http://antoine.frostburg.edu/chem/senese/101/measurement/slides/sld016.htmSI Prefixeskilo-1000centi-1/100milli-1/1000nano-1/1 000 000 000Also know1 mL = 1 cm3 = 1 cc14SI System for Measuring Length Unit Symbol Meter Equivalent _______________________________________________________________________

kilometerkm 1,000 m or 103 m

meter m 1 m or 100 m

decimeterdm 0.1 m or 10-1 m

centimetercm 0.01 m or 10-2 m

millimetermm 0.001 m or 10-3 m

micrometermm 0.000001 m or 10-6 m

nanometernm 0.000000001 m or 10-9 m

The SI Units for Measuring Length

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 11815Comparison of English and SI Units

1 inch2.54 cm1 inch = 2.54 cmZumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 11916Reporting MeasurementsUsing significant figures

Report what is known with certainty

Add ONE digit of uncertainty (estimation)

Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

17By adding additional numbers to a measurement you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement.Measuring a Pin

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 12218Practice Measuring4.5 cm4.54 cm3.0 cmTimberlake, Chemistry 7th Edition, page 7cm012345cm012345cm012345

19PRACTICE MEASURING

Estimate one digit of uncertainty.

a) 4.5 cmb) * 4.55 cmc) 3.0 cm

*4.550 cm is INCORRECT while 4.52 cm or 4.58 cm are CORRECT (although the estimate is poor)

By adding additional numbers to a measurement you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement.

In applying the rules for significant figures, many students lose sight of the fact that the concept of significant figures comes from estimations in measurement. The last digit in a measurement is an estimation.

How could the measurement be affected by the use of several different rulers to measure the red wire?(Different rulers could yield different readings depending on their precision.)

Why is it important to use the same measuring instrument throughout an experiment?(Using the same instrument reduces the discrepancies due to manufacturing defects.)

Implied Range of Uncertainty5643Implied range of uncertainty in a measurement reported as 5 cm.5643Implied range of uncertainty in a measurement reported as 5.0 cm.Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 325643Implied range of uncertainty in a measurement reported as 5.00 cm.20When the plus-or-minus notation is not used to describe the uncertainty in a measurement, a scientist assumes that the measurement has an implied range, as illustrated above.

The part of each scale between the arrows shows the range for each reported measurement.2010? 15 mL ?15.0 mL1.50 x 101 mL21A student reads a graduated cylinder that is marked at 15.00 mL, as shown in the illustration.Is this correct? NO Express the correct reading using scientific notation. 15.0 mL or 1.50 x101 mLHow to Read a Thermometer(Celcius)

10504.0 oC10508.3 oC

10050064 oC

503.5 oC22

0oC10oC20oC30oC40oC50oC60oC0oC1oC2oC3oC4oC5oC6oC0oC5oC10oC15oC20oC25oC

0oC20oC40oC60oC80oC100oC0oC20oC40oC60oC80oC100oCRecord the Temperature(Celcius)ABCDE30.0oC3.00oC19.0oC48oC60.oC23Accuracy vs. PrecisionAccuracy - how close a measurement is to the accepted valuePrecision - how close a series of measurements are to each otherACCURATE = CorrectPRECISE = ConsistentCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

24Percent ErrorIndicates accuracy of a measurement

your valueaccepted valueCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

25Percent ErrorA student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.

% error = 2.9 %Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

26Significant FiguresIndicate precision of a measurement.Recording Sig FigsSig figs in a measurement include the known digits plus a final estimated digit

2.35 cm

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

27Significant FiguresCounting Sig Figs (Table 2-5, p.47)Count all numbers EXCEPT:Leading zeros -- 0.0025Trailing zeros without a decimal point -- 2,500 Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

28 Rules for Counting Significant Figures1. Nonzero integers always count as significant figures.2. Zeros: There are three classes of zeroes.Leading zeroes precede all the nonzero digits and DO NOT count assignificant figures. Example: 0.0025 has ____ significant figures.

Captive zeroes are zeroes between nonzero numbers. These alwayscount as significant figures. Example: 1.008 has ____ significant figures.

Trailing zeroes are zeroes at the right end of the number.

Trailing zeroes are only significant if the number contains a decimal point.Example: 1.00 x 102 has ____ significant figures.

Trailing zeroes are not significant if the number does not contain a decimalpoint. Example: 100 has ____ significant figure.

Exact numbers, which can arise from counting or definitions such as 1 in = 2.54 cm, never limit the number of significant figures in a calculation.

2431Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination 2006, page 5329Significant figures: Rules for zerosLeading zeros are not significant.Captive zeros are significant.Trailing zeros are significant.Leading zeroCaptive zeroTrailing zero0.4214012114.20 three significant figures four significant figures five significant figures304. 0.0803. 5,2802. 4021. 23.50Significant FiguresCounting Sig Fig Examples1. 23.502. 4023. 5,2804. 0.0804 sig figs3 sig figs3 sig figs2 sig figsCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

31Significant FiguresCalculating with Sig FigsMultiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.(13.91g/cm3)(23.3cm3) = 324.103g324 g4 SF3 SF3 SFCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

32Significant FiguresCalculating with Sig Figs (cont)Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL+ 4.1 mL 7.85 mL 224 g+ 130 g 354 g 7.9 mL 350 g 3.75 mL+ 4.1 mL 7.85 mL 224 g+ 130 g 354 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

33Significant FiguresCalculating with Sig Figs (cont)Exact Numbers do not limit the # of sig figs in the answer.Counting numbers: 12 studentsExact conversions: 1 m = 100 cm1 in any conversion: 1 in = 2.54 cmCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

34Significant Figures5. (15.30 g) (6.4 mL)Practice Problems= 2.390625 g/mL 18.1 g6. 18.9g- 0.84 g18.06 g4 SF2 SF 2.4 g/mL2 SFCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

35Scientific Notation: Powers of TenRules for writing numbers in scientific notation:

Write all significant figures but only the significant figures.

Place the decimal point after the first digit, making the number have a value between 1 and 10. Use the correct power of ten to place the decimal point properly, as indicated below. a) Positive exponents push the decimal point to the right. The number becomes larger. It is multiplied by the power of 10. b) Negative exponents push the decimal point to the left. The number becomes smaller. It is divided by the power of 10. c) 10o = 1

Examples: 3400 = 3.20 x 103 0.0120 = 1.20 x 10-2Nice visual display of Powers of Ten (a view from outer space to the inside of an atom) viewed by powers of 10!36Scientific NotationConverting into scientific notation:Move decimal until theres 1 digit to its left. Places moved = exponent.Large # (>1) positive exponentSmall # (