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1 A. Yes B. No Is your clicker set to Channel 41? 0% A. 0% B. 2 SUSB-003 AVERAGE = M1 + M2 + …. + Mn n Introduction to Laboratory Measurement SUSB-003 3 ? QUESTIONS ? What are the uses and limitations of devices we use in the laboratory? What is involved in making and reporting a measurement? What contributes to the accuracy and precision of measurements? How do we measure and report accuracy and precision? What contributes to uncertainties in quantities computed from measurements? Questions 4 Concepts: Measurement Mass/Weight Deliver/Contain Accuracy Average Percent Error Uncertainty Volume Meniscus Linear Density Homogeneity Precision Average Deviation Error Propagation Significant Figures (see web page) Techniques: Weighing Buret Use Pipet & Syringe Error Analysis Preparing Solutions of given concentration Concepts/Techniques 5 Apparatus: Ruler Analytical Balance Buret Transfer Pipet/Syringe Top loading balance Volumetric Flask Apparatus 6 But first, a brief digression. Concept Maps – A handy study aid A 4-step process for enhancing and verifying understanding 7 Concept Maps 1. Formulate a Focus Question 2. List Concepts and write them on “Post-its” [ Road Map] 3. Arrange the “Post-its” on a Map 4. Connect them with Linking Phrases to form Propositions Use a “flow-chart” type of program to arrange and connect the concepts 8 How are Isotopes related to the Structure of Matter? Atoms Focus Question Atomic Number Atomic Mass Electrons Element Isotope Roadmap Matter Molecules Nucleus Number of Neutrons Number of Protons 9 Resulting in a tentative Map 10 Map with linking phrases For more information, see the Web page: Why Concept Maps? 11 Concept Map for CHE 133 Activities and Grading 12 Back to the Exercise For latecomers: Make sure your clickers are set to Channel 41 Set clickers to Channel 41 13 Background - Measurement Measuring devices have intrinsic uncertainties i.e., limitations due to their design/construction bathroom scale 1 lb ( 454 g) measuring cup 1 fl oz ( 28 mL) balance 0.0002 g buret 0.02 mL Measurement process itself may introduce additional uncertainty e.g., try to measure temperature of five drops of a warm solution with a cold laboratory thermometer Uncertainty 14 Background (cont’d) Measurer/quantities Measurer often plays a role in the measurement process reading a scale or liquid level, or dial determining a quantity from a graph, describing the color of a solution In the physical sciences, certain Mauvefundamental: quantities are considered Amethyst Orchid length Cerise (area, volume), mass Periwinkle Fuchsia time (intervals), Plum Lilac ElectricHeliotrope Currrent; Purple Temperature Thistle Lavender Many more can be described in terms of m, l, t. Violet 2vacuum 2 1e.g. m1 is the length ofas path traveled light in sec is defined asby 9,129,631,770 kgVelocity is Lilac defined mass of a prototype made of Energy m l / t =1the lthe /t; during the time interval of kept 1/299 792 458 a second oscillations ofatthe Cs of atom. Wisteria platinum-iridium and the133 International Magenta 2 s-215 Bureau of Weights and Measures. (Paris) 1 joule = 1 kg m Some cannot, and require other fundamental quantities Most measuring devices are LINEAR e.g. RULER: markings at same interval everywhere ANALOG CLOCK: 1 minute = 6o around entire dial RULE OF THUMB: On a LINEAR SCALE, human eye is capable of estimating Wikipedia: a principle with location of a mark lying between broad two smallest divisions application not to the nearest 1/5 th of a division intended to be strictly accurate or reliable for every situation. Linea r/Rul 16 e Rule - Demo 11.66 virtual The eye “squeezes” additional digit out of the ruler! 17 How should the value at the arrow be recorded? A. B. C. D. E. 2.3 2.30 2.36 2.360 2.4 0% 0% 0% 0% 0% 18 A. B. C. D. E. 2.36 2.30 2.40 2.35 or 2.37 are also acceptable. C 2.36 2.3 or 2.4 are NOT! 19 Q1 Answer Estimating measurements between values is called INTERPOLATION Apparatus designers expend major effort to make a user interface linear, through mechanical (cams, gears) or electronic means. When scales are not linear, visual interpolation becomes difficult e.g., some auto fuel gauges conical measuring cups Rule of thumb does not apply! Interpol /nonlinear We occasionally encounter non-linear scales! 20 e.g., logarithmic scale 10 units log scale 100 units RULE OF THUMB DOES NOT APPLY TO NON-LINEAR SCALES 21 Units & Dimensions What distinguishes scientific computation from arithmetic primarily is that most scientific numbers include units. joule Bad news: calculators don’t keep track of units. Good news: Proper attention to units by users often shows whether or not a calculation makes sense 22 units Units & Dimensions E.g., you will measure a weight of water, W, and use its tabulated density, d, to calculate volume, V V, w, d example W = 34.78 g, d = 0.9953 g/mL From Table VMeasured =? V = 34.78 W gX X 0.9953 d g / mL = 34.62 g2/mL V = 34.78 g 0.9953 g / mL = 34.94 mL Suppose we have forgotten the definition of density Common sense suggests that the answer should be ~ 35 mL 23 SUSB-003 Procedures 1. Measure Diameter of Plastic Sphere 2. Weigh Plastic Sphere on two types of balance 3. Compute Density using Diameter & Weight 4. Explore uncertainty in calculation 5. Make Direct Measurement of Liquid Volumes using Pipet & Buret 6. Prepare a solution of known concentration using a volumetric flask X Note that while this is the order in which the manual describes procedures, you may do them in any order you wish. 24 Procedure 1. Measure DIAMETER, d Cube From that, compute AREA and VOLUME of a sphere from their mathematical relationships to its diameter. A = d2 V = d3 / 6 Purpose: To explore error propagation in quantities derived from diameter I.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 geometricL = 10 formulas have no associated uncertainty. The uncertainty in A and V will be solely due to The uncertainty in d!) As an illustration, let’s look at a cube of side L = 10 25 L = 9.00 L = 10.0 L = 11.0 VOLUME = L3 Diff from L=10 (cm) 729 271 1000* 0 1 cm uncertainty in the edge ( 1 /10 = 10% ) produces an uncertainty of ~ 300 cm3 in the volume ( 300 / 1000 = 30% ) 1331* 331 10.0 1.0 1000 300 Cube Table 2 We often use the symbol ~ to (10 ±“approximately”. e)3 ˜ 103 ∓ 300 e …… indicate * Significant Figures 26 In the exercise, you perform analogous calculation for computed area and volume of a plastic sphere. The cm scale of your ruler has its smallest markings at 1 mm intervals. 1 mm By our rule of thumb, you should be able to read ruler to nearest 0.2 1/5mm mm( = 0.02 cm) Assuming you have measured diameter as accurately as you are able: e.g., 3.5 7 cm You are asked to calculate the effect of an uncertainty of + & - 0.02 cm in the diameter, area and volume. i.e. 3.55 cm and 3.59 cm 27 The volume of an icosahedron with a side of length a is given exactly by: V = 5 (3 + √5) a3 12 If the percent error in the length of a side is 10%, approximately what percent error will that cause in the volume? A. B. C. D. 10% 20% 30% It depends on the error in the coefficient of a3 0% A. 0% 0% B. C. 0% D. 28 The volume of an icosahedron with a side of length a is given exactly by: V = 5 (3 + √5) a3 12 If the percent error in the length of a side is 10%, approximately what percent error will that cause in the volume? Analysis is identical to that done for cube. Coefficient of a3 is known with as much precision as desired. C 30% 29 2. Weight of a Plastic Sphere Labs are equipped with 2 types of balances: Balance s 1.Single pan electronic Analytical Balance used in exercises that require highly quantitative ( 0.0002 g ) results. Capacity < 220g 2. Top loading balance appropriate for weighing in exercises requiring less quantitative ( 0.01 g ) results 30 You weigh the sphere whose diameter you measure with both balances. The weights you measure should be consistent, but will differ in one critical aspect PRECISION SIGNIFICANT FIGURES 3.3660 For devices with digital output, our rule of thumb does not apply 3.37 All we can do is to record all digits 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 decimals. Include all zeros (0). Sig Figs Transition 31 SIGNIFICANT FIGURES Bad news: calculators don’t keep track of significant figures Sig Figs News Good news: There is no good news! You simply must learn to handle significant figures. CHE 133 Web Page Introduction to Significant Figures 32 3. DENSITY OF A PLASTIC SPHERE Density is a reproducible physical characteristic of pure materials. For a homogeneous substance (uniform composition throughout), density is: d = m / V In this part of the exercise, we use the measured mass & computed volume of the sphere to calculate its apparent density. (Is the sphere homogeneous? How could you tell?) In other parts of this exercise, you use the measured mass of a sample of water and the tabulated density of water to calculate the volume of the water. 33 How do uncertainties in the • measured DIAMETER ( 0.02 cm) and • measured MASS ( ?) affect the uncertainty in the density of the sphere. From the measured data, we calculate 2 values, Dmax, Dmin. The uncertainty in the result, Davg, is measured by: • the range of the values of the density (Dmax – Dmin) and • the percent deviation of the density Dmax – Dmin 100 X −−−−−−−−− % Davg Density - errors 34 4. MEASUREMENT OF LIQUID VOLUMES Liquids adopt the shapes of their containers. These are often irregular objects where using rulers and geometry would be complex and errorprone. Chemistry uses a wide variety of objects designed to measure volumes. 4. Measurement of Liquid volumes 35 These devices can be classified in a number of ways • Precision • Accuracy • Fixed or variable volume • Whether they Contain or Deliver a specified volume of liquid when filled to ONE or MORE APPROPRIATE MARKS Appropriate mark is determined by comparing position of a liquid’s surface, i.e, the tangent to its meniscus, with marks on a vertical scale. Contain/Deliver/Ma rks 36 Some devices have only a single mark: e.g., Volumetric Flasks are made to CONTAIN a specified volume of liquid when filled to the mark Transfer Pipets are used to DELIVER a specified volume of solution from one container to another most transfer pipets have only a single mark (e.g., 5 mL, 10mL, 25mL, etc.) Vol flask/pipet Pipets are to be filled ONLY by using a syringe Mark indicates volume DELIVERED when pipet is emptied under ONLY THE FORCE OF GRAVITY 37 The volume markings on beakers, cylinders or flasks are sufficiently inaccurate that Used only when approximate, arbitrary the designations “contain” and “deliver” do volumes of liquids must be delivered. not matter. BEAKERS, FLASKS Used only for approximate volume measurements. Cylinder/Beaker Cylinder is a somewhat more precise Should read & record volume consistent with the rule of thumb – e.g.,0.2 mL 38 Buret Pix THE BURET Buret Pix B14 Assigned number 14 39 BURET Device to measure arbitrary DELIVERED volume of liquid with high accuracy & precision Buret Init Final Reading Initial Reading 27.68 -4.34 Delivered Volume 23.34 Proper Use: Initial reading must not be 0.00 Final reading: often depends on some other observation (e.g., a color change in solution to which liquid is being added) READ / RECORD BOTH TO NEAREST 0.02 mL (1/5th OF SMALLEST DIVISION) 40 BURET Device to measure arbitrary DELIVERED volume of liquid with high accuracy & precision Buret Init Final Reading Initial Reading 27.68 -4.34 Delivered Volume 23.34 41 Read Buret Using our rule of thumb 18.7 18.78 18.8 42 This buret reads A. 16.2 mL B. 16.18 mL C. 15.98 mL D. 15.82 mL E. 16. mL 0% 0% 0% A. B. C. 0% D. 0% 43 E. Q2 Answer 15.80 mL D 15.82 mL 15.90 mL 44 Weighing by Difference Most errors in weighing are due to loss of material in the transfer from one container to another! How do we minimize this problem? Minimize the number of transfers Don’t use intermediate containers or devices X X 45 Weighing by Difference (cont’d) • Process: • weigh sample container, • transfer sample directly into final container by tapping • reweigh original sample container •Repeat until •Difference between initial and final weights of container is the desired sample weight You are NOT “weighing by difference” if you: • bring a spatula to the balance • place heavy flask or beaker on balance pan • use a watch glass or piece of paper • record only weight of sample 46 5. PREPARING ACCURATE SOLUTIONS Preparing solutions of accurately known concentration is central to experimental chemistry. It requires two coordinated measurement techniques: Accurate amount of substance Generally by weighing (by difference)* Accurate volume of solution Generally by adding solvent to a mark * If specified amount is in mol, also need precise molar mass to convert mass to moles 47 Preparing a solution Suppose you are asked to make a solution of potassium bromide (KBr) with an accurately known concentration of 5 g/L 20% - using a 500.0 mL volumetric flask. How much KBr should you weigh? To make 1 L (= 1000.0 mL), you would need 5 20% = 5 1 g To make 500.0 mL, you would need (500.0 / 1000.0) (5 1) = 2.5 0.5 g i.e., between 2.0 and 3.0 g * Suppose you actually weigh 2.7845 g. After bringing the volume to 500.0 mL, the concentration is: 2.7845 g / 0.5000 L = 5.5690 g/L * Any amount within that range is acceptable. 48 6. MEASURES OF ACCURACY AND PRECISION (SUPL-001) Lab provides opportunity to use some simple concepts in error analysis OPERATIONAL CONCEPTS: Accuracy/Precision SigFigs 2 ACCURACY: measured deviation from "true“ value. PRECISION: measures reproducibility of results when compared with one another Exercises involve small numbers of repetitions. We use simple statistical measures: Accuracy/Precision SigFigs Accuracy and precision are central to laboratory science and, therefore, to the grading of exercises. 49 AVERAGE (mean): M1 + M2 + …. + Mn n The average of the deviations from the AVERAGE DEVIATION: mean. |M1 – AVG| + |M2 – AVG| + … + |Mn – AVG| n PERCENT DEVIATION: The average deviation is what % of the mean? 100 X AVG DEV AVG Avg/A.D./Pct Dev Def 50 NEXT LECTURE SPECTROSCOPY OF FOOD DYES Read SUSB – 037 Do Pre-Lab for SUSB – 037 Also, READ SUPL-004 – Graphing (Pre-lab questions NOT assigned) & SUPL-005 – Spectroscopy 51 ANY ? QUESTIONS 52 53 The rest of the slides are bonus. If time permits. 54 AVERAGE, AVERAGE DEVIATION AND PERCENT ERROR Suppose a measurement is reproduced three times WEIGHT OF DEVIATION FROM AVG STEEL BALL | - 0.12| SAMPLE 1 75.63 g | +0.30| SAMPLE 2 76.05 g | - 0.18| SAMPLE 3 75.57 g AVG 75.75 g SUM = 0.60 0.00 where: AVG = ( 75.63 + 76.05 + 75.58 ) / 3 So, instead, we define Avg/Avg Dev 2 AVG DEV = ( 0.12 + 0.30 0.18) / 3 = 0.20 Result should be reported as WEIGHT = 75.75 0.20 g 55 WEIGHT = 75.75 0.20 g Suppose in weighing a plastic ball, we get the same average deviation (0.20 g) but the weight is only 7.57 g. WEIGHT = 7.57 0.20 g Percent Error Intuitively, the deviation is much “larger” in the second case. We can distinguish the precision by employing the measure: PERCENT ERROR, which we calculate as follows: PERCENT ERROR = 100 X 0.20 / 7.57 = 2.6% or, in the first case PERCENT ERROR = 100 X 0.20 / 75.75 = 0.26% 56 Or, visually: Avg/A.D./Pct Dev Avg/A.D./Pct Dev Fig d2 d1 0 M1 M2 d3 M3 Avg Dev Mavg Mavg is the average length of the three blue lines Avg Dev is the average length of the three green lines 57