1. Data Analysis for General Chemistry Introduction

2. Contact Information Dr. Randa Roland UCSC:459-5486Thimann 317 e-mail:roland@chemistry.ucsc.edu website:chemistry.ucsc.edu course homepage syllabus, powerpoints, etc.

3. General Procedures Come to lab on time and prepared Complete prelab Appropriate attire Lab writeups due the following lab session Late lab penalty 25% off for each day late All writeups must be turned in no matter what Makeup labs Same week or following week only See me and your TA

4. Prelab includes: Title and date Definitions Answers to prelab questions Procedure* Data tables Prelabs are done PRIOR to lab in your notebook TA must sign off at start of lab session

5. Summary includes: Title and date Results (tables, graphs, values, errors, etc.) Primary souces of errors Sample calculations Summaries are due one week after lab completion Templates/guides are available (manual and web)

6. Lab Reports Includes: Abstract Results/sample calculations Discussion/conclusions Answers to postlab questions Write-ups must be neat Your TA decides whether your work is acceptable Grading rubric is a guideline for you

7. Equation/Concept List At the end of lab notebook, divide page(s) in half vertically For each lab: Left side:List primary equation(s) used Define symbols Right side:Indicate linked concept Example: M  V = molFinding moles of reactant M: molarity (mol/L)or product in solutions V: volume (L)Reactants and products are mol: molesrelated through mole ratio

8. Data Measurement How do we record data? What is the best value to report? What is uncertainty (precision)?

9. Precision, Accuracy, Error Precision:reproducibility Accuracy:trueness Error:standard deviation (uncertainty)

10. Accuracy vs. Precision Precise Not Accurate Better Accuracy Not Precise Precise Accurate

11. Types of Error 1 Systematic:Accuracy

12. Types of Error 2 Random:Reproducibility / precision

13. Reporting Data Average: Standard deviation:

14. Examples of Precision  100150200  140150160  149150.151  149.5150.0150.5  149.9150.0150.1 and so on… Average: “150” Precision: very different

15. Examples of Precision/Standard Deviation  100150200 ± 50  140150160 ± 10  149150.151 ± 1  149.5150.0150.5 ± 0.5  149.9150.0150.1 ± 0.1 and so on… Average: “150” Standard deviation: reflects measuring device

16. Reporting Data Example

17. Example continued

18. Report: 10.01 ± 0.02 g

19. Significant Figures Which numbers are meaningful? 1.Mathematical 2.Standard Deviation

20. Mathematical Sig. Figs. Multiplication/Division: Round answer to fewest sig. figs. Addition/Subtraction: Round answer to fewest decimal places. Standard deviation takes precedence over these rules.

21. Example 3 sig. figs./2 decimal places 4 sig. figs./2 decimal places Standard deviation takes precedence Report:10.01 ± 0.02 mL

22. Direct vs. Derived Values Direct: Measured /no calculations required Derived: Must be calculated from data How do we account for our uncertainty?

23. Uncertainty in Measuring Devices Ruler 1.38 cm ± 0.01 cm

24. Uncertainty in Measuring Devices Graduated cylinders 0.364 ± 0.001 mL 3.60 ± 0.01 mL 0.3 0.4 3 4

25. Error Propagation / Calculated Values Addition: Subtraction: Standard deviations are additive

26. Error Propagation Multiplication Division Relative errors are used

27. Addition 12.5 g    = 0.1 g + 2.05 g   = 0.01g 12.55 g  = 0.11 g Report:12.6 ± 0.1 g

28. Subtraction 12.5 g    = 0.1 g – 2.05 g   = 0.01g 10.45 g  = 0.11 g Report:10.4 ± 0.1 g

29. Multiplication 12.5 cm    = 0.1 cm  2.05 cm   = 0.01cm 25.625 cm 2  = ? Report:25.6 ± 0.3 cm 2  = 25.625 cm 2 0.1 cm 12.5 cm 0.01 cm 2.05 cm + = 0.33 cm 2

30. Division 12.5 g    = 0.1 g 2.05 cm 3   = 0.01cm 3 6.09756 g  = ? cm 3 Report:6.10 ± 0.08 g/cm 3  = 6.09756 g cm 3 0.1 g 12.5 g 0.01 cm 2.05 cm + = 0.0785g/cm 3

31. Example diameter, d length, l Measured:diameter length

32. ExampleDensity = mass/Volume diameter, d length, l Measured:mass diameter length

33. Density Calculation A 218.44 ± 0.01 g metal cylinder has diameter of 2.50 ± 0.01 cm and is 5.00 ± 0.01 cm long. What is the density of the metal? Mass:218.44 ± 0.01 g Diameter: 2.50 ± 0.01 cm Length: 5.00 ± 0.01 cm Volume = ¼  d 2 lDensity = m/V

34. Density of a Cylinder Formula: Density:

35. Density continued Standard deviation: Report:D = 8.90 ± 0.02 g/cm 3 Final answer:

36. Density of a cylinder, take 2 Volume: 24.5 ±0.2 cm 3 Standard deviation: Volume:

37. Density continued Note difference:D = 8.90 ± 0.07 g/cm 3 Volume: 24.5 ±0.2 cm 3 Mass: 218.44±0.01 g Standard deviation: Density:

38. Summary Multiple measurements required Average Standard deviation Direct uncertainty:device dependent Calculated uncertainty:error propagation Review sig. fig. rules

39. Graphing / Visualizing Data

40. Graphing For a plot of mass vs. volume y-axis:massin g x-axis:volumeinmL Density:linear relationship of mass to volume

41. Densities SubstanceDensity (g/mL) wood0.35 water1.00 quartz2.65 diamond3.51 Ti4.5 Ag10.5 Au19.3 Os22.4 Increasing density = Increasing “heaviness”