1Introduction to Introduction to Laboratory MeasurementLaboratory MeasurementSUSBSUSB--003003SUSB-0031Last Update: 8/30/2012 5:27 PMWhat is involved in makingand reportinga measurement? What contributes to the accuracyand What are the uses and limitations of deviceswe use in the laboratory?? QUESTIONS ?? QUESTIONS ?What contributes to the accuracyand precisionof measurements?What contributes to uncertaintiesin quantities computedfrom measurements?2QuestionsHow do we measure and report accuracy and precision?Concepts:Concepts:Measurement Uncertainty Linear Mass/Weight Volume Density Deliver/Contain Meniscus HomogeneityAccuracy PrecisionAverage Average DeviationPercent Error Error Propagation Significant Figures Significant Figures (see web page)TechniquesTechniques::3Concepts/TechniquesSignificant Figures Significant Figures (see web page)WeighingPipet & SyringeBuret UseError AnalysisPreparing Solutions of given concentrationhttp://www.ic.sunysb.edu/Class/che133/lectures/sigfigs.htmlApparatus:RulerAnalytical BalanceTop loading balanceTransfer Pipet/SyringeBuretVolumetric Flask4ApparatusConcept Maps Concept Maps –– A handy study A handy study aidaidare described at:are described at:http://www.ic.sunysb.edu/Class/che133/conceptmaps/Example/MapOverview.htmlhttp://www.ic.sunysb.edu/Class/che133/conceptmaps/Example/MapOverview.html5Measuring deviceshave intrinsic uncertaintiesi.e., limitations due to their design/constructionBackground Background --Measurement Measurement bathroom scale 1 lb ( 454 g)balance 0.0002 gmeasuring cupburet002 L6UncertaintyMeasurement processitself may introduce additional uncertainty1 fl oz (28 mL)0.02 mLe.g., try to measure temperature of five drops of a warm solution with a cold laboratory thermometer2MeasurerMeasureroften plays a role in the measurement processreading a scale or liquid level, or dialdetermining a quantity from a graph, describing the color of a solutionBackground (cont’d)Background (cont’d)In the physical sciences, certain qu ntiti s nsid d fund m nt l:Measurer/quantitiesquantities are considered fundamental:llength massttime(intervals),(area, volume), Many more can be described in terms of mm, ll, tt. e.g.TemperatureEnergy  ml2/ t2Velocity = l /t;7Electric Currrent;Some cannot, and require other fundamental quantitiesMost measuring devices are LINEARe.g. RULER: markings at same interval everywhereRULE OF THUMBANALOG CLOCK: 1 minute = 6oaround entire dialRULE OF THUMB:On a LINEAR SCALELINEAR SCALE, human eye is capable of estimating location of a mark lying between two smallest divisionsto the nearest 1/5 1/5 thth of a divisionof a division8Linear/Rule11.66Rule - Demo9The eye “squeezes” additional digit out of the ruler!virtualvirtualEstimating measurements between values is called INTERPOLATIONApparatus designers expend major effortto make a user interface linear, through mechanical (cams, gears) or electronic means. When scales are not linearlinear, visual interpolation becomes difficult We occasionally encounter non-linear scales!10Interpol/non-linearRule of thumb does not apply!e.g., some auto fuel gaugesconical measuring cupse.g., logarithmic scale10 units100 unitsRULE OF THUMB DOES NOT APPLY TO NON-LINEAR SCALES11log scaleUnits & DimensionsUnits & DimensionsWhat distinguishes scientific computationfrom arithmeticprimarily is that most scientific numbers include unitsunits. Bad news:Bad news:calculators don’t keep track of unitscalculators don t keep track of units. Good news:Good news:Proper attention to units by usersby usersoften shows whether or not a calculation makes sense12units31.Measure Diameterof Plastic Sphere2. WeighPlastic Sphere on two types of balance3. ComputeDensity usingDiameter & Weight4. Exploreuncertainty in calculationSUSBSUSB--003 Procedures003 ProceduresNote that while this is the order in which the manual describes procedures, you may do them in any order you wish.5.Make Direct Measurement of Liquid Volumes using Pipet & Buret6.Prepare a solution of known concentraation13Procedure1. Measure DIAMETER, dFrom that, computecomputeAREA and VOLUME of a sphere from their mathematical relationships to its diameter.A =  d2V =  d3/ 6PurposePurpose:: To explore To explore error propagationerror propagationininquantities derived from diameterquantities derived from diameterCubeI.e., suppose we make a small error in measuring d. How large an error will that produce in A and V?Note that “” , “2”, “3” and “6” in the geometric formulas have no associated uncertainty. The uncertainty in Aand Vwill be solely due toThe uncertainty in d!As an illustration, let’s look at a cube of side 14L = 10L = 9.00 L = 10.0 L = 11.0VOLUME = L3729 1000 1331*Diff from L=10 (cm) 271 0 3311 cm uncertainty in the edge( 1 /10 = 10% ) 15Cube Table 2yg()produces an uncertainty of ~ 300 cm3in the volume ( 300 / 1000 = 30% )In the exercise, you perform analogous calculationfor computed area and volume of a plastic sphere.Your ruler has its smallest markingsat 1 mm intervals.By our rule of thumb, you should be able to read ruler to nearest 0.2 mm ( = 0.02 cm) h d d 1/5 mmAssuming you have measured diameter as accurately as you are able:You are asked to calculate the effect of an uncertainty of + & - 0.02 cm in the diameter. area and volume. 162. 2. Weight of a Plastic SphereWeight of a Plastic SphereLabs are equipped with 2 types of balances:1.Single pan electronic Analytical Balanceused in exercises that require highly quantitative (  0.0002 g ) results. Capacity < 100gBalances2. Top loading balanceappropriate for weighing in exercisesrequiring less quantitative (  0.01 g )results17You weigh the sphere whose diameter you measure with bothbalances.The weights you measure should be consistent, but will differ in one critical aspectSIGNIFICANT FIGURESSIGNIFICANT FIGURESPRECISIONPRECISIONFor devices with digital output, our rule of thumb does not applyAll we can do is to record alldigits that the device provides and rely on the manufacturer’s specifications of the intrinsic precision of the device.For the analytical balance, this always includes 4 4 decimalsdecimals. Include all zeros (0).Include all zeros (0).18Sig Figs Transition4SIGNIFICANT FIGURESSIGNIFICANT FIGURES Bad news:calculators don’t keep track of significant figures Good news:There is no good news!Sig Figs NewsYou simply must learn to handle significant figures. g19CHE 133