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1. Pre-lab for Experiment 1 is due (5 pts) 2. Experiment 1. "Are the Densities of Coke and Diet Coke Different?" have a write-up in your notebook Next week
1. Report for Experiment 1 is due (40 pts) 2. Post-lab for Experiment 1 is due (10 pts) 3. Pre-lab for Experiment 2 is due (5 pts) 4. Experiment 2. Separation and Recovery of the Components of the Mixture have a write-up in your notebook 5. Be prepared to take a QUIZ on the material of Experiment 1 Spring 2007 Evaluation of Experimental Data
Everything is vague to a degree ... you do not realize it `till you have tried to make it precise. Bertrand Russell Every physical measurement has some uncertainty, which is called experimental error It is not possible to measure the absolute "true value" of a physical quantity We can only estimate the reliability of a measured quantity based on the limitations of equipment and methodology used Placing bounds on lack of reliability is basis for PROBABILITY and STATISTICS Spring 2007 Types of Experimental Error
Systematic error associated with a method or equipment flaw. All errors are same magnitude and direction. In principle these errors can be discovered and corrected. Example: miscalibrated meter Random error due to the limitations of the measuring process itself. Can be positive or negative. Cannot be eliminated. Can only be treated with statistics. Example: random electrical noise in an instrument Gross error errors caused by committing a personal faux pas or fault. AKA: blooper, bungle, foul-up, flub, sin, boob, goof, botch, fumble, botch up, muff, blow, flub, screw up, spoil, muck up, fluff, bollix, bollocks, bobble, mishandle, louse up, foul up, mess up, slip up, trip up, hosed up, etc. Example: many come to mind Best to redo the measurement! Spring 2007 Accuracy
Accuracy closeness of measurement or set of measurements to the "true" value. Requires knowledge of the "true" value (best estimate). Expressed in terms of error Absolute error: E =| x i - x t |
Er = Er = | xi - x t | xt | xi - x t | 100% xt Relative error: % relative error: x t = "true" value (best estimate) x i = current measurement Spring 2007 Precision
Precision agreement between two or more measurements that have been carried out in exactly the same fashion. Expressed in terms of standard deviation (accounts for random errors ONLY):
( x i - X ) 2 s= n -1 where xi = x1, x2, ..., xn repeated individual measurements n number of measurements X average value X= x 1 + x 2 + ... + x n n Standard deviation is a measure of precision of an experiment but provides no information about its accuracy. Spring 2007 Significant Figures
Minimum number of digits required to express a value in scientific notation without loss of accuracy (used to express accuracy and precision)
Rules: Leading zeros are not significant Captive zeros are significant Trailing zeros are significant (on the right-hand side of a decimal point) Trailing zeros can be significant 0.0234 3 sig figs 1230243 7 sig figs 23.040 5 sig figs 3000 ! Know how to convert to scientific notation ! Compare 7,000,000,000,000 to 7 1012 Spring 2007 Significant Figures and Calculations
Addition and subtraction: the number of significant figures in the answer is determined by the least certain quantity Example: 5.68 + 4.7542 10.4342 round to 10.43 Multiplication and division: the answer is rounded to the same number of significant figures as the quantity with the least number of significant figures Example: 5.68 4.7542 = 27.003856 round to 27.0
2 Example: .434 0 =1 Mixed operations: apply above rules in each portion of the calculation , BUT do not round off intermediate results (5.68 + 4.7542) 0.020 = 0.208684 round to 0.21
Spring 2007 Significant Figures and Experimental Results
Experimental Result Experimental Error
OR Average Standard Deviation
1. Rule for Stating Experimental Errors (St. Deviations) Experimental errors are always rounded to ONE significant figure.
Example: Avg. value 0.02785 g Should report: Avg. value 0.03 g 2. Rule for Stating Experimental Results (Average Values) The last significant figure in any stated result should usually be of the same order of magnitude (in the decimal position) as the experimental error.
Example: 92.8178 0.03 g Should report: 92.82 0.03 g Spring 2007 Follow... Simple Rules to Follow...
Reports (more than one trial)
DO NOT follow the rules for math operations Carry more significant figures throughout the calculation than you think you will need at the end; DO NOT round off intermediate results Use St. Deviation as an evaluation of your experimental error, i.e. round it to ONE significant figure Your experimental error will determine the number of significant figures that you need to keep in the final reported value (Average) PostReports (one trial) & Post-lab calculations
Follow the rules for math operations Spring 2007 Experiment 1. "Are the Densities of Different?" Coke and Diet Coke Different?"
PURPOSE AND LEARNING OBJECTIVES To learn how to use an analytical balance To learn to perform volume measurements using different pieces of glassware To evaluate precision of these measurements To measure and compare densities of Coke and Diet Coke To verify experimentally that density is an intensive property Spring 2007 What is the difference between Coke? Coke and Diet Coke? Spring 2007 Density m d= V
Density d density of a substance (kg/m3 or g/ml) m mass of a sample (kg or g) V volume of a sample (m3 or ml) physical property intensive property (independent of the amount of material examined). To determine density of a substance, need to measure mass and volume for the same sample Spring 2007 Measuring mass
Analytical Balances sensitivity is 0.0001 g Measuring volume
Graduated glassware Example: beaker, volumetric pipette, volumetric flask, graduated cylinder, burette, etc. sensitivity varies Spring 2007 Glassware tolerance 0.1 ml Graduated Cylinder tolerance 0.01 ml Volumetric Pipette tolerance 0.05 ml Spring 2007 Burette Tolerance allowable deviation How to Read Your Glassware
incorrect eye position (high reading) correct eye position (~ 2.75 ml) incorrect eye position (low reading) How to Clean Your Glassware
Tap Water & Soap Wash DI Water Wash Solution Wash (Priming)
Spring 2007 Last Minute Miscellaneous Tips
Take your time and learn how to properly use your glassware Beakers are NOT volumetric! Type and double check Remember to rinse your burette and put it away Have your data signed by your TA before you leave for the day At the end of the day, you will have to attach three print-outs to your report (one from Part 1 and two from Part 2) Any time you report your result as AVERAGE ST. DEV., use the correct number of significant figures Spring 2007 ...
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- Spring '08
- Experimental Error