Presentation on theme: "Measurement 100 mL Graduated Cylinder Units of Measuring Volume"— Presentation transcript:
1Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a MeniscusUnits for Measuring MassQuantities of MassSI-English Conversion FactorsAccuracy vs. PrecisionAccuracy Precision ResolutionSI units for Measuring LengthComparison of English and SI UnitsReporting MeasurementsMeasuring a PinPractice Measuring
2Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a MeniscusUnits for Measuring MassQuantities of MassSI-English Conversion FactorsAccuracy vs. PrecisionAccuracy Precision ResolutionSI units for Measuring LengthComparison of English and SI UnitsReporting MeasurementsMeasuring a PinPractice Measuring
3100 mL Graduated CylinderZumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119
4Instruments for Measuring Volume GraduatedcylinderSyringeVolumetricflaskBuretPipet
5Units of Measuring Volume 1 L = mL1 qt = 946 mLUNITS OF MEASURING VOLUMEA measurement has two parts: a number and a unit.Note: NO NAKED NUMBERSTimberlake, Chemistry 7th Edition, page 3
6Reading a Meniscus line of sight too high reading too high 108610 mLline of sight too highreading too highproper line of sightreading correctline of sight too lowreading too lowgraduatedcylinder
7Units for Measuring Mass Mass – amount of substance present. Does not change when going to the moon.Mass is measured on a pan balance.Weight – related to gravity. Your weight is about 1/6 on the moon and 2.36X on Jupiter.As gravity increases your weight increases.Pull of gravity on jet fighter planes – make your arms and legs very heavy and g-forces increase.Weight is measured on a scale.1 kg = lbTimberlake, Chemistry 7th Edition, page 3
8Units for Measuring Mass 1 kg(1000 g)1 lb1 lb0.20 lbChristopherson ScalesMade in Normal, Illinois USA1 kg = lb
9Quantities of Mass Giga- Mega- Kilo- base milli- micro- nano- pico- Earth’s atmosphereto 2500 km1018 gQuantities of Mass1015 g1012 gOcean linerGiga-Mega-Kilo-basemilli-micro-nano-pico-femto-atomo-109 gIndian elephant106 gAverage human103 g1.0 liter of water100 g10-3 g10-6 gGrain of table salt10-9 g10-12 g10-15 g10-18 gTypical protein10-21 gUranium atom10-24 gWater moleculeKelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25
10Factor Name Symbol Factor Name Symbol decimeter dm decameter damcentimeter cm hectometer hmmillimeter mm kilometer kmmicrometer mm megameter Mmnanometer nm gigameter Gmpicometer pm terameter Tmfemtometer fm petameter Pmattometer am exameter Emzeptometer zm zettameter Zmyoctometer ym yottameter Ym
11Scientific Notation: Powers of Ten Rules 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 = 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!
12Multiples of bytes as defined by IEC 60027-2 SI prefixBinary prefixesNameSymbolMultiplekilobytekB103 (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 )
14SI-US Conversion Factors Relationship Conversion FactorsLength2.54 cm1 in1 in2.54 cm2.54 cm = 1 in.and39.4 in1 m1 m39.4 in.1 m = 39.4 in.andVolume946 mL1 qt1 qt946 mL946 mL = 1 qtand1.06 qt1 L1 L1.06 qtandDominoes Activity1 L = 1.06 qtMass454 g1 lb1 lb454 g454 g = 1 lband2.20 lb1 kg1 kg2.20 lb1 kg = 2.20 lband
15Accuracy vs. Precision Systematic errors: reduce accuracy Scientists repeat experiments many times to increase their accuracy.Good accuracyGood precisionPoor accuracyGood precisionPoor accuracyPoor precisionSystematic errors:reduce accuracyRandom errors:reduce precision(instrument)(person)
16Accuracy vs. Precision Random errors: reduce precision Scientists repeat experiments many times to increase their accuracy.Good accuracyGood precisionPoor accuracyGood precisionPoor accuracyPoor precisionRandom errors:reduce precisionSystematic errors:reduce accuracy
17 Precision Accuracy check by check by using a repeating PrecisionAccuracyreproducibilitycheck byrepeatingmeasurementspoor precisionresults from poortechniquecorrectnesscheck by using adifferent methodpoor accuracyresults fromprocedural orequipment flaws.
18Types of errors Systematic Random Instrument not ‘zeroed’ properly Reagents made at wrong concentrationRandomTemperature in room varies ‘wildly’Person running test is not properly trained
19Errors Systematic Random Errors in a single direction (high or low) Can be corrected by proper calibration or running controls and blanks.RandomErrors in any direction.Can’t be corrected. Can only be accountedfor by using statistics.Systematic error is when you get the same mistake every time you perform a measurement, and random error is when the mistake varies randomly. It’s much easier to compensate for systematic error than for random error.
20Accuracy Precision Resolution time offset [arbitrary units]not accurate, not preciseaccurate, not precisenot accurate, preciseaccurate and preciseaccurate, low resolution-2-3-1123subsequent samples
21Accuracy Precision Resolution not accurate, not preciseaccurate, not precisenot accurate, preciseaccurate and preciseaccurate, low resolution-2-3-1123time offset [arbitrary units]subsequent samples
22Standard DeviationThe standard deviation, SD, is a precision estimate basedon the area score: where xi is the i-th measurement x is the average measurement N is the number of measurements.One standard deviation away from the mean in either direction on the horizontal axis (the red area on the above graph) accounts for somewhere around 68 percent of the people in this group. Two standard deviations away from the mean (the red and green areas) account for roughly 95 percent of the people. And three standard deviations (the red, green and blue areas) account for about 99 percent of the people.The more practical way to compute it... In Microsoft Excel, type the following code into the cell where you want the Standard Deviation result, using the "unbiased," or "n-1" method:=STDEV(A1:Z99) (substitute the cell name of the first value in your dataset for A1, and the cell name of the last value for Z99.)yOne standard deviation away from the mean in eitherdirection on the horizontal axis (the red area on thegraph) accounts for around 68 percent of the peoplein this group.Two standard deviations away from the mean (thered and green areas) account for roughly 95 percentof the people.Three standard deviations (the red, green and blueareas) account for about 99 percent of the people.x
23SI Prefixes kilo- 1000 deci- 1/10 centi- 1/100 milli- 1/1000 Also know…1 mL = 1 cm3 and 1 L = 1 dm3
24SI System for Measuring Length The SI Units for Measuring LengthUnit Symbol Meter Equivalent _______________________________________________________________________kilometer km ,000 m or 103 mmeter m m or 100 mdecimeter dm m or 10-1 mcentimeter cm m or 10-2 mmillimeter mm m or 10-3 mmicrometer mm m or 10-6 mnanometer nm m or 10-9 mZumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118
25Comparison of English and SI Units 1 inch2.54 cm1 inch = 2.54 cmZumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119
26Reporting Measurements Using significant figuresReport what is known with certaintyAdd ONE digit of uncertainty (estimation)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.Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46
27Measuring a PinZumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 122
28Practice Measuring cm 1 2 3 4 5 4.5 cm cm 1 2 3 4 5 4.54 cm cm 1 2 3 4 123454.5 cmcm123454.54 cmPRACTICE MEASURINGEstimate 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.)cm123453.0 cmTimberlake, Chemistry 7th Edition, page 7
29Implied Range of Uncertainty 5643Implied range of uncertainty in a measurement reported as 5 cm.5643Implied range of uncertainty in a measurement reported as 5.0 cm.When 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.5643Implied range of uncertainty in a measurement reported as 5.00 cm.Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32
3020?1.50 x 101 mL15 mL ?15.0 mLA student reads a graduated cylinder that is marked at mL, as shown in the illustration.Is this correct? NOExpress the correct reading using scientific notation mL or 1.50 x101 mL10
31Reading a Vernier A Vernier allows a precise reading of some value. In the figure to the left, the Vernier moves up anddown to measure a position on the scale.This could be part of a barometer which readsatmospheric pressure.The "pointer" is the line on the vernier labeled "0".Thus the measured position is almost exactly 756in whatever units the scale is calibrated in.If you look closely you will see that the distancebetween the divisions on the vernier are not thesame as the divisions on the scale. The 0 line onthe vernier lines up at 756 on the scale, but the10 line on the vernier lines up at 765 on the scale.Thus the distance between the divisions on thevernier are 90% of the distance between thedivisions on the scale.756
32Reading a Vernier Scale Vernier A Vernier allows a precise reading of some value.In the figure to the left, the Vernier moves up anddown to measure a position on the scale.This could be part of a barometer which readsatmospheric pressure.The "pointer" is the line on the vernier labeled "0".Thus the measured position is almost exactly 756in whatever units the scale is calibrated in.If you look closely you will see that the distancebetween the divisions on the vernier are not thesame as the divisions on the scale. The 0 line onthe vernier lines up at 756 on the scale, but the10 line on the vernier lines up at 765 on the scale.Thus the distance between the divisions on thevernier are 90% of the distance between thedivisions on the scale.770510Vernier760Scale756Image courtesy:750
33750740760If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately on the scale.If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is510741.9What is the reading now?
34750740760If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately on the scale.If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is510756.0What is the reading now?
35750740760510Here is a final example, with the vernier at yet another position. The pointer points to a value that is obviously greater than and also less than Looking for divisions on the vernier that match a division on the scale, the 8 line matches fairly closely. So the reading is aboutIn fact, the 8 line on the vernier appears to be a little bit above the corresponding line on the scale. The 8 line on the vernier is clearly somewhat below the corresponding line of the scale. So with sharp eyes one might report this reading as ± 0.02.This "reading error" of ± 0.02 is probably the correct error of precision to specify for all measurements done with this apparatus.
36How to Read a Thermometer (Celcius) 1010100555504.0 oC8.3 oC64 oC3.5 oC
37Record the Temperature (Celcius) 60oC6oC50oC5oC25oC100oC100oC40oC4oC20oC80oC80oC30oC3oC15oC60oC60oC20oC2oC10oC40oC40oC10oC1oC5oC20oC20oC0oC0oC0oC0oC0oCA30.0oCB3.00oCC19.0oCD48oCE60.oC
39MEASUREMENT Using Measurements Courtesy Christy Johannesson
40Accuracy vs. Precision ACCURATE = Correct PRECISE = Consistent Accuracy - how close a measurement is to the accepted valuePrecision - how close a series of measurements are to each otherACCURATE = CorrectPRECISE = ConsistentCourtesy Christy Johannesson
41Percent Error Indicates accuracy of a measurement your value accepted valueCourtesy Christy Johannesson
42Percent Error % error = 2.9 % A 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
43Significant Figures Indicate precision of a measurement. Recording Sig FigsSig figs in a measurement include the known digits plus a final estimated digit2.35 cmCourtesy Christy Johannesson
44Significant Figures Counting Sig Figs (Table 2-5, p.47) Count all numbers EXCEPT:Leading zerosTrailing zeros without a decimal point -- 2,500Courtesy Christy Johannesson
45Counting Sig Fig Examples Significant FiguresCounting Sig Fig Examples4 sig figs3 sig figs3. 5,2803. 5,2803 sig figs2 sig figsCourtesy Christy Johannesson
46Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g Calculating with Sig FigsMultiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.(13.91g/cm3)(23.3cm3) = g4 SF3 SF3 SF324 gCourtesy Christy Johannesson
47Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL Calculating with Sig Figs (con’t)Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.3.75 mLmL7.85 mL3.75 mLmL7.85 mL224 g+ 130 g354 g224 g+ 130 g354 g 7.9 mL 350 gCourtesy Christy Johannesson
48Significant Figures Calculating with Sig Figs (con’t) Exact Numbers do not limit the # of sig figs in the answer.Counting numbers: 12 studentsExact conversions: 1 m = 100 cm“1” in any conversion: 1 in = 2.54 cmCourtesy Christy Johannesson
50Scientific Notation 65,000 kg 6.5 × 104 kg Converting into scientific notation:Move decimal until there’s 1 digit to its left. Places moved = exponent.Large # (>1) positive exponent Small # (<1) negative exponentOnly include sig. figs.Courtesy Christy Johannesson
52Scientific Notation Calculating with scientific notation (5.44 × 107 g) ÷ (8.1 × 104 mol) =Type on your calculator:EXPEEEXPEEENTEREXE5.4478.1÷4== 670 g/mol= 6.7 × 102 g/molCourtesy Christy Johannesson
53Proportions Direct Proportion Inverse Proportion y x y x Courtesy Christy Johannesson
54Reviewing Concepts Measurement Why do scientists use scientific notation?What system of units do scientists use for measurements?How does the precision of measurements affect the precision of scientific calculations?List the SI units for mass, length, and temperature.Prentice Hall Physical Science Concepts in Action (Wysession, Frank, Yancopoulos) 2004 pg 20Why do scientists use scientific notation? Scientific notation makes very large or very small numbers easier to work with.What system of units do scientists use for measurements? Scientists use a set of measuring units called SI.How does the precision of measurements affect the precision of scientific calculations? The precision of a calculation is limited by the least precise measurement used in the calculation.
55Rules for Counting Significant Figures 1. 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: has ____ significant figures.Captive zeroes are zeroes between nonzero numbers. These alwayscount as significant figures. Example: 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: 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 53
56Significant figures: Rules for zeros Leading zeros are not significant.Leading zero0.421– three significant figuresCaptive zeros are significant.Captive zero4012– four significant figuresTrailing zeros are significant.Trailing zero114.20– five significant figures