Presentation on theme: "Topic 11: Measurement and Data Processing"— Presentation transcript:
1 Topic 11: Measurement and Data Processing Honors ChemistryMrs. PetersFall 2014
2 11.1 Uncertainty and Error in Measurement Measurement is important in chemistry.Many different measurement apparatus are used, some are more appropriate than others.Have out each of the different types of measurement devices, have students walk around and record what they notice about the increments and measurements of each item.
3 11.1 Uncertainty and Error in Measurement Example: You want to measure 25 cm3 (25 ml) of water, what can you use?Beaker, volumetric flask, graduated cylinder, pipette, buret, or a balanceAll of these can be used, but will have different levels of uncertainty. Which will be the best?Have out each of the different types of measurement devices, have students walk around and record what they notice about the increments and measurements of each item.
4 A & S 1. Systematic ErrorsSystematic Error: occur as a result of poor experimental design or procedure.Cannot be reduced by repeating experimentCan be reduced by careful experimental design
5 A & S 1. Systematic ErrorsSystematic Error Example: measuring the volume of water using the top of the meniscus rather than the bottomMeasurement will be off every time, repeated trials will not change the error
6 A & S 1. Random ErrorRandom Error: imprecision of measurements, leads to value being above or below the “true” value.Causes:Readability of measuring instrumentEffects of changes in surroundings (temperature, air currents)Insufficient dataObserver misinterpreting the readingCan be reduced by repeating measurements
7 A & S 1: Random and Systematic Error Systematic and Random Error ExampleRandom: estimating the mass of Magnesium ribbon rather than measuring it several times (then report average and uncertainty)g, g, g, g, g, gAvg Mass= g
8 A & S 1: Random and Systematic Error Systematic and Random Error ExampleSystematic: The balance was zeroed incorrectly with each measurement, all previous measurements are off by gg, g, g, g, g, gAvg Mass =
9 A & S 8. Distinguish between precision and accuracy in evaluating results Precision: how close several experimental measurements of the same quantity are to each otherhow many sig figs are in the measurement.Smaller random error = greater precision
10 Accuracy: how close a measured value is to the correct value A & S 8. Distinguish between precision and accuracy in evaluating resultsAccuracy: how close a measured value is to the correct valueSmaller systematic error = greater accuracyExample: masses of Mg had same precision, 1st set was more accurate.
11 U 5. Reduction of Random Error Random errors can be reduced byUse more precise measuring equipmentRepeat trials and measurements (at least 3, usually more)
12 A & S 2. Uncertainty Range (±) Random uncertainty can be estimated as half of the smallest division on a scaleAlways state uncertainty as a ± number
13 A & S 2. Uncertainty Range (±) Example:A graduated cylinder has increments of 1 mLThe uncertainty or random error is1mL / 2 = ± 0.5 mL
14 A & S 2. Uncertainty Range (±) Uncertainty of Electronic DevisesOn an electronic devices the last digit is rounded up or down by the instrument and will have a random error of ± the last digit.Example:Our balances measure ± 0.01 gDigital Thermometers measure ± 0.1 oC
15 State uncertainties as absolute and percentage uncertainties Absolute uncertaintyThe uncertainty of the apparatusMost instruments will provide the uncertaintyIf it is not given, the uncertainty is half of a measurementEx: a glass thermometer measures in 1oC increments, uncertainty is ±0.5oC; absolute uncertainty is 0.5oC
16 State uncertainties as absolute and percentage uncertainties Percentage uncertainty= (absolute uncertainty/measured value) x 100%
17 Determine the uncertainties in results Calculate uncertaintyUsing a 50cm3 (mL) pipette, measure 25.0cm3. The pipette uncertainty is ± 0.1cm3.What is the absolute uncertainty?0.1cm3What is the percent uncertainty?0.1/25.0 x 100= 0.4%
18 Determine the uncertainties in results Calculate uncertaintyUsing a 150 mL (cm3) beaker, measure 75.0 ml (cm3). The beaker uncertainty is ± 5 ml (cm3).What is the absolute uncertainty?5 ml (cm3)What is the percent uncertainty?5/75.0 x 100= 6.66% 7%
19 Determine the uncertainties in results Percent error = I error l x 100acceptedWhen…Percent error > UncertaintySystematic errors are the problemUncertainty > Percent errorRandom error is causing the inaccurate data
20 Determine the uncertainties in results Error Propagation: If the measurement is added or subtracted, then absolute uncertainty in multiple measurements is added together.
21 Determine the uncertainties in results Example:If you are trying to find the temperature of a reaction, find the uncertainty of the initial temperature and the uncertainty of the final temperature and add the absolute uncertainty values together.
22 Determine the uncertainties in results Example: Find the change in temperatureInitial Temp: 22.1 ± 0 .1oCFinal Temp: 43.0 ± 0.1oCChange in temp: = 20.9Uncertainty: = 0.2Final Answer: Change in Temp is 20.9 ± 0.2 oC
23 Determine the uncertainties in results Error Propagation: If the measurement requires multiplying or dividing: percent uncertainty in multiple measurements is added together.
24 Determine the uncertainties in results Example:If you are trying to find the density of an object, find the uncertainty of the mass, the uncertainty of the volume, you add the percent uncertainty for each to get the uncertainty of the density.
25 Determine the uncertainties in results Example: Find the Density given:Mass: ± 0.01 g and Volume: 10.3 ± 0.05 mLDensity: /10.3 = 2.47 g/mL% uncertainty Mass: (0.01/25.45) x 100 = 0.04%% uncertainty Volume: (0.05/10.3) x 100 = .5%= .54%Final Answer: Density is 2.47 ± .54%
26 Determine the uncertainty in results Uncertainty in Results (Error Propagation)1. Calculate the uncertaintya. From the smallest division (on a graduated cylinder or glassware)b. From the last significant figure in a measurement (a balance or digital thermometer)c. From data provided by the manufacturer (printed on the apparatus)2. Calculate the percent error3. Comment on the errora. Is the uncertainty greater or less than the % error?b. Is the error random or systematic? Explain.