1. MEASUREMENT AND DATA PROCESSING REFERENCE: PGS.: 421-434 IB CHEMISTRY CH. 11

2. LEARNING TARGETS 11.1 Uncertainty and error in measurement Describe and give examples of random uncertainties and systematic errors. Distinguish between precision and accuracy Describe how the effects of random uncertainties may be reduced. State random uncertainty as an uncertainty range State the results of calculations to the appropriate number of significant figures

3. WHAT CONSTITUTES SCIENCE… Science is a communal activity that requires information sharing By necessity, information and how it is collected must be communicated to the broader public and must be open to scrutiny In science, this is often done through the peer-review process Journals and Conferences are two common examples of how scientific information is shared, and consensus is built

4. UNCERTAINTY Even though scientists strive to limit the uncertainty within their data by rigorously planning and thinking through the ways that they conduct scientific experiments, ALL measurements have uncertainties So, it is important that these uncertainties are communicated when scientific data is shared Chemistry provides us with a deep understanding of the material world, but does not, and cannot offer absolute uncertainty

5. HOW SCIENTIFIC DATA IS PRESENTED Graphical representation is a powerful way of visually presenting how one quantity is related to another A graph is also a useful tool to assess errors as it identifies data points which do not ‘fit’ the general trend, giving another measure of the reliability of data

6. PRECISION VS. ACCURACY Draw 4 Bulls-eyes… In the first, draw a representation of what it means to be both imprecise and innaccurate. In the second, draw a representation of what it means to be a PRECISE, but NOT AN ACCURATE dart thrower. In the third, draw a representation of what it means to be an ACCURATE but NOT A PRECISE dart- thrower. Finally, draw a representation of what it means to be BOTH PRECISE AND ACCURATE

7. PRECISION VS. ACCURACY

8. UNCERTAINTY IN ANALOGUE MEASUREMENTS The uncertainty of an analogue scale is (+-) ½ the smallest division.

9. UNCERTAINTY IN DIGITAL MEASUREMENTS The uncertainty in a digital scale is (+-) the smallest scale division.

10. OTHER SOURCES OF UNCERTAINTY Timing: Reaction time of the experimenter Judging: When an indicator changes color What is the temperature at a particular time in an exothermic reaction Even if these extra uncertainties cannot be quantified, they should be noted when data are collected in experimental work

11. SIGNIFICANT FIGURES Significant figures are critical when reporting scientific data because they give the reader an idea of how well you could actually measure/report your data. 1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. 2) ALL zeroes between non-zero numbers are ALWAYS significant.

12. SIGNIFICANT FIGURES CONTINUED… 3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant. 4) ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are ALWAYS significant. A helpful way to check rules 3 and 4 is to write the number in scientific notation. If you can/must get rid of the zeroes, then they are NOT significant.

13. EXPERIMENTAL ERRORS *THE DIFFERENCE BETWEEN THE RECORDED VALUE (EXPERIMENTALLY MEASURED) AND THE GENERALLY ACCEPTED OR LITERATURE VALUE R andom error source Reliability of the measuring instrument Effects of changes in the surroundings such as temperature variations or air currents Insufficient data Observer misinterpretation of the reading *Random errors can be reduced through repeated measurements! *If the same results are found by the same experimenter-the data is considered repeatable, if several experimenters duplicate the results, they are considered reproducible. Systematic error source Measuring the volume of water from the top of the meniscus rather than the bottom Overshooting the volume of a liquid delivered to reach a specific point (titrations) Heat losses in an exothermic reaction *Systematic errors can be reduced through careful experimental design

14. ACCURACY AND PRECISION RE-VISITED Accuracy The smaller the systematic error, the greater the accuracy. Precision The smaller the random uncertainties, the greater the precision.

15. 11.2 LEARNING TARGETS State uncertainties as absolute and percentage uncertainties Determine uncertainties in results

16. RULES OF SIGNIFICANT FIGURES IN CALCULATIONS Multiplication and Division The answer should be rounded to the same number of significant figures as the number with the least number of significant figures (the least precise). Addition and Subtraction The answer should be rounded to the least # of digits after the decimal.

17. PERCENTAGE UNCERTAINTIES AND ERRORS Which is less certain, a time measurement of 1s, 10 s, or 100s? Percentage Uncertainty= (Absolute Uncertainty/measured value)X 100% Percentage Error= ((Accepted value-experimental value)/Accepted value) X 100%

18. PERCENTAGE UNCERTAINTY Percentage Uncertainty Percentage uncertainty= (absolute uncertainty/measured value) x 100 Example: You are measuring the mass of a sample of Iron with a scale that measures to the nearest.01 grams. Calculate the percentage of uncertainty when the mass of Iron is.1 grams? 100.00 grams? Why does this relationship exist?

19. PROPAGATION OF UNCERTAINTIES ADDITION & SUBTRACTION Consider 2 Graduated Cylinder Readings Initial Reading: 15.05 +/- 0.05 mL Final Reading: 37.20 +/- 0.05 mL Vol(max)=22.25 mL Vol(min)=22.05 mL Uncertainties=.05 mL+.05 mL= Total=.1mL Reported value: 22.15 +/-.1mL Rule: Add. & Sub. When adding or subtracting measurements, the uncertainty is the sum of absolute uncertainties.

20. PROPAGATION OF UNCERTAINTIES MULTIPLICATION & DIVISION Example: Density Mass=24.0 g +/-.5g.5/24.0 x 100= 2% Volume=2.0 mL +/-.1g.1/2.0 X 100= 5% Value= 24.0/2.0, Max=24.5/1.9=12.89, Min=23.5/2.1=11.19 Absolute Uncertainty = 12.89-12.00= +/-.89 So, (.89/12.00)X 100= 7.4% Rule: Multiplication & Division The total percentage uncertainty is the sum of the individual percentage uncertainties. The absolute uncertainty can be calculated from the percentage uncertainty.

21. PERCENTAGE ERROR (Accepted Value- experimental Value)/Accepted Value x100 Example you are measuring a standardized weight with a mass of 200.0 grams. What percentage error exists for your scale measure, if you measure a mass of 198.9 grams?

22. 11.3 LEARNING TARGETS Sketch graphs to represent dependences and interpret graph behavior Construct graphs from experimental data Draw best-fit lines through data points on a graph Determine the values of physical quantities from graphs

23. GRAPHICAL TECHNIQUES Give the graph a title Label the axes with both quantities and units Use the available space as effectively as possible Use sensible linear scales-there should be no uneven jumps Plot all the points correctly A line of best fit should be drawn smoothly and clearly. It should show the overall trend. Think carefully about the inclusion of the origin. (0,0) can be the most accurate data point, or irrelevent.

24. REVIEW OF GRAPHS Linear data Y=mx + b X is the independent variable Y is the dependent variable M is the gradient (slope) B is the intercept (y axis) M=Change in Y/X ‘Best-fit’ Line

25. ERRORS AND GRAPHS Systematic-Random-