Presentation on theme: "Topic 11: Measurement and Data Processing"— Presentation transcript:
1 Topic 11: Measurement and Data Processing Honors ChemistryMrs. PetersFall 2014
2 What is Chemistry?Chemistry is the study of the composition of matter and the changes that matter undergoes.What is matter?Anything that takes up space and has massWhat is change?To make into a different form
3 Scientific Process Steps to Scientific Process: Observations: Use your senses to obtain information directlyProblem: propose a question based on your observationsHypothesis: Propose an explanation of your problem (If…, then… statement)
4 Scientific Process Steps to Scientific Process: 4. Experiment: Materials list and procedure to test your hypothesis5. Results: Collection of experiment’s data and analysis of data6. Conclusion: statements about what your experiment found based on the data collected
5 Measurement in Chemistry Use the International System of Units (SI)Aka: the metric systemQuantityUnitSymbolLengthmetermVolumeliterLMassgramgTemperatureDegree CelciusoCDensityGrams per cubic cm or grams per milliliterg/cm3 or g/mL
6 Metrics for Honors Chemistry Scientific Units and DevicesDeviceUnitMeasurementBalanceGrammassGraduated cylinderLitervolumeMeter StickMeterLength or distanceThermometerCelsiustemperatureClockSecondTime
7 Measurement in Chemistry Devices to use for taking measurements:Balance – mass, usually in gramsRuler – length, usually in cm or mmThermometer: temperature, usually in oCGraduated cylinder: volume, usually in mL
8 11.1 Uncertainty and errors in measurements EI: All measurement has a limit of precision and accuracy, and this must be taken into account when evaluating experimental results.NOS: Making quantitative measurements with replicated to ensure reliability – precision, accuracy, systematic, and random errors must be interpreted through replication
9 U1 & U2. Types of Data Qualitative Data Non-numerical data Usually observations made during an experimentUse your senses, with exception to tasteEX: color, texture, smell, luster, temperatureQuantitative DataNumerical dataMeasurements collected during the experimentEX: 5.64 g, 9.25mm
10 A & S 8. Distinguish between precision and accuracy Precision: how close several experimental measurements of the same quantity are to each otherAccuracy: how close a measured value is to the actual value
11 A & S 8. Precision and Accuracy Low accuracy, low precisionLow accuracy, high precisionHigh accuracy, low precisionHigh accuracy, high precision
12 A & S 7. Calculating ErrorError: the difference between the accepted value and the experimental valueAccepted value: the correct value based on reliable resourcesExperimental value: value measured in the labError = experimental value - accepted value
13 A & S 7. Calculating Percent Error Percent Error: the relative error, shows the magnitude of the errorPercent Error = I error I x 100accepted value
14 Metrics for Honors Chemistry Metric Prefixes M K H D _ d c m_ _ mMega (M) 106Kilo (K) 103Hecta (H) 102Deca (D) 101ORIGIN: meter, liter, gramdeci (d) 10-1centi (c) 10-2milli (m) 10-3micro (m) 10-6
15 Ex: 62 cm3 = 2 sig figs; 100.00 g = 5 sig figs U 2. Sig FigsSignificant Figures (sig figs): the digits in a measurement up to and including the first uncertain digitEx: 62 cm3 = 2 sig figs; g = 5 sig figs
16 Rules for Counting Sig Figs U 2. Sig FigsRules for Counting Sig FigsEvery nonzero digit represented in a measurement is significant.24.7 m has 3 sig figshas 4 sig figshas ? sig figshas ? sig figs
17 Rules for Counting Sig Figs U 2. Sig FigsRules for Counting Sig FigsZeros appearing between non zero digits are significant.70.03 has 4 sig figshas 5 sig figshas ? sig figshas ? sig figs
18 Rules for Counting Sig Figs U 2. Sig FigsRules for Counting Sig Figs3. Zeros ending a number to the right of the decimal point are significant23.80 has 4 sig figshas 6 sig figs1, has ? sig figshas ? sig figs
19 U 2. Sig FigsRules for Counting Sig Figs 4. Zeros starting a number or ending the number to the left of the decimal point are not counted as significant has 2 sig figs has 4 sig figs 870,600 has ? sig figs has ? sig figs
20 U 2. Sig FigsGeneral Rule for Counting Sig Figs Start on the left with the first nonzero digit. End with the last nonzero digit OR with the last zero that ends the number to the right of the decimal point
21 U 2. Sig Figs Sig Fig Practice In your notes: copy the problem and write the number of sig figs for each number34.6 g56.78 gggg
22 U 2. Sig Figs Sig Fig Calculations Adding/Subtracting: the number of decimal places is important, answer should have same number of decimal places as the smallest number of decimal places7.10 g g = g22.36 g – g = 7.20 g
23 U 2. Sig Figs Sig Fig Calculations Adding/Subtracting: 3.45 g g =g – 5.46 g =
24 U 2. Sig Figs Sig Fig Calculations 2. Multiplying/Dividing: the number of sig figs is important, the number with the least number of sig figs determines sig figs in the answer.0.125kg x 7.2 oC x 4.18kJ kg-1 oC-1= kJ round to 3.8 kJ7.55 m x 0.34 m =
25 Sig Fig Calculations Practice U 2. Sig FigsSig Fig Calculations PracticeIn your notes: copy the problems and solve.4.67 g g =59.74 ml – ml =34.57 g x 23.4 g =256.8 g / 5.36 g =
26 U 2. Scientific NotationScientific Notation is useful for very small and very large numbers.is written as 4.50 x 10-6is written as 7.7 x 108
27 U 2. Scientific Notation To Convert into Scientific Notation: move the decimal point so only 1 non-zero digit is to the left of the decimal point.if you move the decimal point to the left, the power of 10 will be positive (the number is the number of spaces moved)if you move the decimal point to the right, the power of 10 will be negative.----- Meeting Notes (9/29/14 14:17) -----need to have new seats in h chem
28 U 2. Scientific Notation Scientific Notation Practice 3,600 = 3.6 x 103= 7.52 x 10-55,732, = ?= ?
29 U 2. Scientific Notation To Convert out of Scientific Notation: if the power of 10 is positive move the decimal point to the right the power number of placesif the power of 10 is negative move the decimal point to the left the power number of places.
30 U 2. Scientific Notation Scientific Notation: 8.1 x 10-5 = 0.000081
31 Scientific Notation Calculations U 2. Scientific NotationScientific Notation CalculationsAddition/ Subtraction: exponents must be the same, adjust each number to the same exponent, then add or subtract as usual.
32 Scientific Notation Calculations U 2. Scientific NotationScientific Notation CalculationsEx: 5.40 x x 102 =convert 6.0x 102 to 0.60 x 1035.40x x 103 = 6.00x 103
33 Scientific Notation Calculations U 2. Scientific NotationScientific Notation CalculationsMultiplication: multiply the coefficients, then add the exponents.(3.0x 104) x (2.0 x 102) = 6.0 x 106
34 Scientific Notation Calculations U 2. Scientific NotationScientific Notation CalculationsDivision: divide the coefficients, then subtract the exponents.(3.0 x 104) / (2.0 x 102) = 1.5 x 102
35 U 2. Density Density: The ratio of the mass of an object to its volume Density = MassVolumeunits = g/cm3 (solid & liquid) or g/L (gases)
36 U 2. DensityEx: a piece of lead has a volume of 10.0 cm3 and a mass of 114 g, what is it’s density?114g/ 10.0cm3 = 11.4 g/cm3
37 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.
38 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.
39 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
40 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
41 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
42 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
43 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 =
44 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
45 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.
46 U 5. Reduction of Random Error Random errors can be reduced byUse more precise measuring equipmentRepeat trials and measurements (at least 3, usually more)
47 A & S 2. Uncertainty Range (±) Random uncertainty can be estimated as half of the smallest division on a scaleAlways state uncertainty as a ± number
48 A & S 2. Uncertainty Range (±) Example:A graduated cylinder has increments of 1 mLThe uncertainty or random error is1mL / 2 = ± 0.5 mL
49 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
50 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
51 State uncertainties as absolute and percentage uncertainties Percentage uncertainty= (absolute uncertainty/measured value) x 100%
52 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%
53 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%
54 Determine the uncertainties in results Percent error = I error l x 100acceptedIf percent error is greater than uncertainty, then systematic errors are a problemRandom error is estimated by uncertainty, if smaller than percent error, then systematic errors are causing inaccurate data.
55 Determine the uncertainties in results Error Propagation: If the measurement is added or subtracted, then absolute uncertainty in multiple measurements is added together.
56 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.
57 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
58 Determine the uncertainties in results Error Propagation: If the measurement requires multiplying or dividing: percent uncertainty in multiple measurements is added together.
59 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.
60 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%
61 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.
62 11.2 GraphingEI: Graphs are a visual representation of trends in data. NOS: The idea of correlation – can be tested in experiments whose results can be displayed graphically.
63 U 1. Graphical Techniques Why do are graphs used?Graphs are an effective means of communicating the effect of the independent variable on a dependent variable, and can lead to determination of physical quantities.
64 U1. Graphical Techniques Example GraphGraphs are used to present and analyze data.show the relationship between the independent variable and the dependent variableDependentIndependent
65 U2. Sketched graphs Sketched graphs: Have labeled, but unscaled axes Example GraphSketched graphs:Have labeled, but unscaled axesUsed to show qualitative trendsVariables that are proportional or inversely proportionalDependentIndependent
66 U3. Drawn Graphs Graphs MUST have: A title Candle Mass After BurningGraphs MUST have:A titleLabel axes with quantities and unitsMass (g)Time (min.)
67 U3, A &S 1. Drawn Graphs Graphs MUST have: Candle Mass After BurningGraphs MUST have:Use available space as effectively as possibleUse sensible linear scales- NO uneven jumpsPlot ALL points correctlyMass (g)Time (min.)
68 A&S 3. Best Fit Lines Best Fit Lines should be drawn smoothly and clearlyDo not have to go through all the points, but do show the overall trendTemperature (oC)Time (sec)
69 A & S 4 Physical quantities from graphs Find the gradient (slope) and the interceptUse y = m x + b for a straight liney= dependent variablex = independent variablem= the gradient (slope)b = the intercept on the vertical (y) axis
70 A & S 4 Physical quantities from graphs Ex: to find the slope (m), find 2 data points (2,5) and (4, 10)m= (y2-y1) = (10-5) = 5 = 2.5(x2-x1) (4-2) 2
71 A & S 2. Interpretation of Graphs Example GraphVariables: Independent- the cause, plotted on the horizontal axis (x-axis) AKA: ManipulatedDependentIndependent
72 A & S 2 Interpretation of Graphs Example GraphVariables: Dependent- the effect, plotted on the the vertical axis (y-axis) AKA: RespondingDependentIndependent
73 A & S 2. Interpretation of Graphs Interpolation: determining an unknown value using data points within the values already measured
74 A & S 2. Interpretation of Graphs Extrapolation: when a line has to be extended beyond the range of the measurements of the graph to determine other valuesAbsolute zero can be found by extrapolating the line to lower temperatures.