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Errors and uncertainities net
- Random uncertainties arise from imprecision in measurements and can cause readings to be above or below the true value. They can be reduced by more precise instruments or repeating measurements. - Systematic uncertainties result in all readings being consistently too high or too low. They may be due to instrumentation errors or experimental technique and can sometimes be addressed through calibration. - Uncertainty is incorporated into measurements as a range rather than a single value, and it is important to propagate uncertainties through calculations.
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Errors and uncertainities net
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- 2. TOPICS: I. Types ofErrors: Systematic Random 11.1.1 http://www.youtube.com/watch?v=50iFTcCsG_Y&feature=relmfu http://chemwiki.ucdavis.edu/Analytical_Chemistry/Quantifying_Nature/Uncertainties_in_Measurements
- 3. Science, Measurement, Uncertaintyand Error 3 Measurements are rarely exactly the same. Measurements are always somewhat different from the “true value.” These deviations from the true value are called errors.
- 4. ERRORS: Two sourcesof error in a measurement are limitations in the sensitivity of the instruments imperfections in experimental design or measurement techniques Errors are often classified as: Systematic Random www.nabis.govt.nz
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- 7. SYSTEMATIC ERROR (RELATED TO ACCURACY) Systematic errors result in readings all being shifted too high, or too low. All the data is off in the same direction.They can be: a. Personal errors: This type of error can be greatly reduced if you are familiar with the experiment you are doing.(wrong choice of calorimeter) b. Instrumental Errors: Instrumental errors are attributed to imperfections in the tools with which the analyst works. For example, volumetric equipment such as burets, pipets, and volumetric flasks frequently deliver or contain volumes slightly different from those indicated by their graduations. Calibration can eliminate this type of error.
- 8. Systematic errorsresult in readings all being shifted too high, or too low. Systematic Error may be due to the apparatus itself, or to the way in which readings are taken. A systematic error, would include consistent errors that always arise. Example 1: Readings should always be volumes made to the bottom point of the meniscus.
- 9. Example 2:Calibration, when feasible, is the most reliable way to reduce systematic errors. adjust the scale to read zero when there is nothing on it.
- 10. DEMO: CALORIMETRY DissolvingNaOH in water.
- 12. SYSTEMATIC ACCURACY %ERROR , DECREASES AS THE SIZE OF THE MEASUREMENT INCREASES
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- 14. RANDOM( RELATED TOPRECISION) Random errors arise from the imprecision of measurements and can lead to readings being above or below the “true” value. Random errors can be reduced with the use of more precise measuring equipment or its effect minimized through repeating measurements so that the random errors cancel out. Random errors are the major source of uncertainty. (keep this thought)
- 15. EXAMPLES OF RANDOMERRORS You measure the mass of a ring three times using the same balance and get slightly different values: 17.46 g, 17.42 g, 17.44 g Volume measurements made with a 50-mL beaker are accurate to within ±5 mL. In other words, you would be as likely to obtain 20 mL of solution (5 mL too little) as 30 mL (5 mL too much). You could decrease the amount of error by using a graduated cylinder, which is capable of measurements to within ±1 mL. The error could be decreased even further by using a buret, which is capable of delivering a volume to within 1 drop, or ±0.05 mL.
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- 17. Show burette/titrationand give IB question Hodder Assignment page 324 # 10
- 19. LABEL THE FOLLOWINGAS SYSTEMATIC OR RANDOM
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- 21. Random Uncertainties Youtube 11.1.4 State random uncertainty as an uncertainty range (+/-) IB Chemistry http://www.youtube.com/watch?v=XcaYc9xr9- k&feature=related
- 22. WHAT IS “UNCERTAINTYOF MEASUREMENT”? The true value of the measure is never known A value is assigned based on an estimate, within a certain level of confidence This results in a range of possible values © CSIR 2006 www.csir.co.za
- 23. UNCERTAINTIES Remember that allmeasurements contain three parts: The measurement The uncertainty The unit
- 24. UNCERTAINTY IN MEASUREMENT A measurement always has some degree of uncertainty. How long is this nail?
- 25. UNCERTAINTY IN MEASUREMENT Different people estimate differently. • Record all certain numbers and one estimated number. • Whenever we measure in chemistry we always record one extra decimal place (estimated number) beyond the markings on the measurement device.
- 26. • The uncertaintyof this measure would be defined as 1/2 the smallest division, 1/2 of 1 mL = 0.5 mL. So, the true measure should lie either 0.5 mL above or 0.5 mL below our measurement. We would say then our measure is 43.5 ± 0.5 mL.
- 27. HTTP://WWW.WELLESLEY.EDU/CHEMISTRY/CHEM105MANUAL/APPEND ICES/UNCERTAINTY_VOLUMETRIC.HTML Instrument Typical Uncertainty TypicalDigital Balance 0.01 g Analytical balance 0.002 g -10 ˚C to 110˚ C thermometer 0.2 ˚C 10 mL graduated cylinder 0.05 mL 100 mL graduated cylinder 0.5 mL 50 mL buret 0.05 mL 1 mL pipet 0.01 mL 10 mL pipet 0.02 or 0.05 mL 25 mL pipet 0.03 mL 100 mL flask 5 125 mL flask 10 mL
- 28. – This isthe simple uncertainty in the value itself. The absolute uncertainty has the same units as the value. 3.8 cm ± 0.1 cm ( 3.8 ± 0.1) cm Usually reported with one significant figure http://scidiv.bellevuecollege.edu/Physics/Measure%26sigfigs/F-Uncert-Percent.html www.chemactive.com
- 29. PERCENT UNCERTAINTY – Thisis the simple ratio of uncertainty to the value multiplied by 100. As a ratio of similar quantities, the relative uncertainty has no units. For example the percentage uncertainty of 28.50 ± 0.05g is %u = ( 0.05/28.50) x 100 = 0.18% You report as 28.50g ± 0.18% Note that it is acceptable to report percent uncertainties to two significant figures.
- 30. • The uncertaintiesin individual measurements can be combined to calculate the uncertainty in the final value of the quantity being determined. – In addition and subtraction: Add absolute uncertainties – In multiplication, division and powers: Add percentage uncertainties – If one uncertainty is much larger than the others, ignore the other uncertainties and estimate the uncertainty based on the larger one using the rules above. www.chemactive.com
- 31. EXAMPLE 1: Find thedifference in temperature. Initial temp. = 34.50 ± 0.05oC Final Temp. = 45.21oC ± 0.05oC
- 32. EXAMPLE 1: ΔT= 45.21-34.5 =10.71oC u = ± 0.05 + 0.05 = ± 0.10oC ΔT = 10.71 ± 0.10oC = 10.7 ± 0.1 oC Absolute Uncertainties usually have one significant figure.
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- 34. If youmultiply the variable, of course the uncertainty also increases appropriately. Suppose you had x = 4.5 ±0.1, that is, the uncertainty = 0.2, since the measurement could be anywhere between 4.4 and 4.6 If you now look at 5x, then the result could be anywhere between 5(4.4) = 22.0, and 5(4.6) = 23.0. So the uncertainty in 5x is 1.0, or 5 times the uncertainty in x. That is, 5x = 22.5 ±0.5.
- 35. TRY THIS ONE:FIND THE HEAT.
- 39. PERCENT ERROR If the% Error is greater than the % uncertainty, systematics errors are more significant than random errors.
- 40. A student performsan experiment to determine the heat of a reaction, ΔH. A certain mass of a metal at (95.5 +- 0.5) °C was placed into (150.25 +- 0.05)g of water in the calorimeter. The temperature went down to 37.5 ˚C. What is the heat of reaction in kJ ? Literature value:48 kJ
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- 42. IMPORTANT!!!!!!!!!!! Average Values When several trials are performed in an investigation, each set of data obtained should be used to make a separate calculation of the desired quantity. If the raw data from one trial varies greatly from other trial data then this should NOT be included but an explanation should be given as to why it was not included. Once calculations have been made for each trial separately, then you should determine the average value, with appropriate uncertainty. You can disregard trials 1 and 5. If it not the case, consider the highest percent uncertainty of all trials.
- 46. Justify theirconclusion by discussing whether systematic errors or further random errors were encountered. The direction of any systematic errors should be appreciated. The percentage error should be compared with the total estimated random error as derived from the propagation of uncertainties (conclusion and evaluation: aspect 1). comment about the precision and accuracy of the measurements when evaluating their procedure (conclusion and evaluation: aspect 2) suggest how the effects of random uncertainties may be reduced and systematic errors be eliminated. Students should be aware that random, but not systematic, errors are reduced by repeating readings (conclusion and evaluation: aspect 3)
- 47. IB EXAMPLE!!!!! Assignment: Percent Uncertainty Example
- 48. GRAPHS Determine fromgraphs physical quantities (with units) by measuring and interpreting a slope (gradient) or intercept. When constructing graphs from experimental data, students should make an appropriate choice of axes and scale, and the plotting of points should be clear and accurate. (Millimeter square graph paper or software is appropriate. Quantitative measurements should not be made from sketch graphs.) The uncertainty requirement can be satisfied by drawing best-fit curves or straight lines through data points on the graph (data collection and processing: aspect 3). (Note: Chemistry students at SL and HL are not expected to construct uncertainty bars on their graphs and may achieve “complete” for aspect 3 of data collection and processing without them. However, students, probably those who also study IB physics, often construct error bars and there is no requirement to discourage them from doing so.)
- 49. HTTP://WWW2.NIDO.CL/~HLOVEJOY/PRACTICALS/ERROR_AND_UNCERTAINITIES.HTML Figure 1is a graph of the gas law data showing the significant uncertainty. The computer drew the uncertainty bars based on the student entering the correct information, which in this case was 0.5 mm for each value. Figure 2 does not show the uncertainty bars. In chemistry, students are not expected to construct uncertainty bars. In both graphs the title is given (although it should be more explicit), and the student has labelled the axes and included units. The level of achievement for aspect 3 of data collection and processing for both graphs is complete = 2.