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1 CH204 Experiment 1 Are the Densities of Coke and Diet Coke Different? d = m V Dr. Brian Anderson Spring 2008 Today • Error in experimental data – Random – Systematic – Gross • Accuracy and precision – Accuracy – how close your final answer is to the correct one – Precision – how close your data points are to each other More Today • Significant digits – Count ’em! – Add and subtract ’em! – Multiply and divide ’em! • Standard deviation – A statistical measure of random error • Quick look at Experiment 12 How much does a quarter weigh? Weigh a few more... 5.7128 5.6947 5.7085 5.6907 5.6106 5.6339 5.6009 5.7205 5.6466 5.7195 Now what does a quarter weigh? Average = 5.67387 grams There’s got to be a better way! There is. Calculate the average ± standard deviation Standard deviation is a measure of the scatter in the data – and it also tells us how many decimal places we should keep in our average.3 What is Standard Deviation? It’s a calculation based on a set of data points that tells us how widely the data points are scattered around the average. σ = 1 σ = 2 σ = 3 68% 99% 95% Calculating Standard Deviation This is 2008. Don’t calculate it by hand. Use a builtin calculator function or use Excel. Let’s head to Excel right now and see how EZ this is. So now what does a quarter weigh? 5.67287 ± 0.046377 g Report the final answer only up to the first uncertain digit – which is the same decimal place where the standard deviation falls. Variability occurs HERE4 This is really important, folks! 5.67287 ± 0.046377 g Round the standard deviation to ONE significant digit: 0.05 And report the average only up to that decimal place: 5.67 Variability (random error) limits your answer 5.67287 ± 0.046377 g should be reported as 5.67 ± 0.05 g And that’s what a quarter weighs! So what does a quarter weigh? 5.67 ± 0.05 g 68% of all quarters should weigh between 5.62 and 5.72 grams. 5.7128 5.6947 5.7085 5.6907 5.6106 5.6339 5.6009 5.7205 5.6466 5.71955 Variability limits significant digits There were five significant digits in the mass of each quarter, but only three significant digits in the final result. The last two digits are insignificant because they are less than the variability in the measurement. “Variability in the measurement” = random error. Ways of Determining Random Error For a single reading: Precision of the equipment Tolerance of the glassware For many readings: Statistics That’s what we’re gonna do in lab today. Std. Dev. = random error We’ll use this same procedure to determine random error and significant digits in Experiment 1. And speaking of Experiment 1...6 Graduated cylinder 0.1 ml Volumetric pipette 0.01 ml Burette 0.01 ml Analytical balance Equipment 0.0001 grams! TwoPart Lab Part One: • Calculate density. Total of six data points. • Enter your results into the spreadsheet on the computer nearest the printer, and use all the class data in your report. • Measure the mass of 5 mL of sample using the analytical balance and three different types of glassware (pipette, burette, and graduated cylinder). TwoPart Lab Part Two: • Do NOT calculate density. • Enter your mass and volume measurements into the spreadsheet on the computer nearest the door, and use all the class data in your report. • Dispense your assigned volume using a burette, and measure the mass of the sample on the analytical balance.7 Important! You will need all three graphs: Part One: 1  Density chart and graph comparing different methods (includes average and standard deviation for each method). Part Two: 2  Mass vs volume graph for Coke 3  Mass vs volume graph for Diet Coke Handling bad data If you know it’s bad – because you know something went wrong, or because the number is physically impossible  you can discard it. If you don’t like it because it’s widely scattered, you can’t just toss it, you have to apply the Qtest (see the appendix of the lab manual). Interpolation In order to calculate the density of water at the same temperature as your Coke or Diet Coke sample, you will have to interpolate between the density values in the table on page 8 of the lab manual.8 Final comments When entering data, type with your fingerds, not witjh youpr thumbds. Beakers are not volumetric! Remember to rinse your burette and put it away. Final final comments Next week: Final Exam, Part 1. There is a sample quiz on the web site Freebies page. Also play with the spreadsheet on the Freebies Page. Bring a


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