Measurements and their uncertainty

1. Measurements and their uncertainty

2. Objectives Convert measurements to scientific notation Distinguish among accuracy, precision and error of measurement Determine the number of significant figures in a measurement and in a calculated answer

3. Measurements • Definition – quantity that has both a number and a unit • Measurements are made every day: • Buying products • Sports activities • Cooking

4. Measurement types • 2 types of measurements • Qualitative – measurements are words, not numbers – hot, heavy • Quantitative – measurements involve numbers and depends on: • Reliability of measuring instrument • The care with which it is read

5. Scientific Notation • Number is written as the product of two numbers: • A coefficient • 10 raise to a power • Example: • 602,000,000,000,0000,0000,000,000 • 6.02 x 1023

6. Accuracy, Precision, and Error • Accuracy – how close measurement is to true value • Measured value must be compared to correct value • Precision – how close the measurements are to each other • Compare values of two or more repeated measurements (reproducible)

7. Precision vs. Accuracy

9. Determining Error • Accepted value – correct value based on reliable references • Example: Density table pg 90 • Experimental value – value measure in the lab

10. Determining Error • Error – difference between experimental value and accepted value • Error = exp. value – accepted value • Error can be either positive or negative

11. Percent Error Percent error – absolute value of error divided by the accepted value multiplied by 100 Percent error = |error| accepted value x 100

12. Sample Problem For a boiling point measurement of water in the lab you read 99.1 oC. What is the percent error?

13. Sample Problem • For a boiling point measurement of water in the lab you read 99.1 oC. What is the percent error? • Answer: 0.9%

14. Why Is There Uncertainty? • Measurements are performed with instruments • No instrument can be read to an infinite number of decimal places

15. Why Is There Uncertainty? Which of these has the greatest uncertainty?

16. Significant Figures Significant digits – in a measurement it includes all of the digits that are unknown plus a last digit that is estimated Measurements are reported in correct sig figs b/c calculated answers depend on number of sig figs in the values used in the calculations

17. Figure 3.5 Significant Figures - Page 67 Which measurement is the best?

18. Sig Fig Rules Non – zeros always count as significant figures: 3456 4 sig figs

19. Sig Fig Rules • Zeros • Leading zeros do not count as significant figures 0.0486 3 sig figs

20. Sig Fig Rules • Zeros • Captive zeros always count as significant figures 16.07 4 sig figs

21. Sig Fig Rules • Zeros • Trailing zeros are significant only if the number contains a decimal point 9.300 9300 4 sig figs 2 sig figs

22. Sig Fig Rules • Two special situations – have unlimited number of sig figs • Counted items • 23 people, 435 thumbtacks • Exactly defined quantities • 60 minutes = 1 hour

24. Sig Fig Practice • How many sig figs in the following? • 1.0070 m • 17.10 kg • 100890 L • 3.29 x 103 s • 0.0054 cm • 3,200,000 mL • 5 dogs

25. Sig Figs in Calculations • A calculated answer cannot be more precise than the least precise measurement from which it was calculated • The chain is only as strong as its weakest link • Calculated values need to be rounded

26. Rounding • Decide how many sig figs are needed • Round to that many digits counting from the left! • Is the next digit <5? Drop it • Is the next digit >5? Increase by 1

27. Problems • Round off each measurement to the number of sig figs shown in ( ). Write the answers in scientific notation. • 314.721 (four) • 0.001755 (two) • 8792 (two)

28. Rounding – Addition and Subtraction • Answer should be rounded to same number of decimal places as the LEAST number of decimal places in problem • Problem: • Calculate the sum: • 12.52 m + 349.0 m + 8.24 m

29. Rounding – Addition and Subtraction • Answer should be rounded to same number of decimal places as the LEAST number of decimal places in problem • Problem: • Calculate the sum: • 12.52 m + 349.0 m + 8.24 m • 369.8 m

30. Rounding – Multiplication and Division • Round the answer to the same number of significant figures as the LEAST number of sig figs in the problem • How many sig figs for the following operations: • 7.55 x 0.34 meters • 2.10 x 0.70 meters • 2.4526/8.4

31. Rounding – Multiplication and Division • Round the answer to the same number of significant figures as the LEAST number of sig figs in the problem • How many sig figs for the following operations: • 7.55 x 0.34 meters  2 sig figs • 2.10 x 0.70 meters  2 sig figs • 2.4526/8.40  3 sig figs

32. Section Assessment A technician experimentally determined the boiling point of octane to be 124.1 oC. The actual BP is 125.7 oC. Calculate the error and percent error.

33. Section Assessment • Determine the number of sig figs in the following: • 11 soccer players • 10,800 meters • 0.070020 meters • 5.00 cubic meters

34. The International System of Units

35. Objectives List SI units of measurement and common SI prefixes Distinguish between the mass and weight of an object Convert between Celsius and Kelvin temperature scales

36. International System of Units SI – from French name Measurements depend on units that are used as reference standards In chemistry we use metric system

37. 5 SI Base Units • SI units normally used in chemistry:

38. Nature of Measurements • Measurement – quantitative observation consisting of 2 parts: • Number • Unit • Example: 20 grams or 20 g

39. SI • Non-SI units are used in chemistry as well: • Liter – volume • Celsius – temperature • Calorie - heat

40. Common SI Prefixes

41. Units of Length • SI unit – meter • Measured using rulers • Most common metric units of length are: • Centimeter – cm • Meter – m • Kilometer - km

42. Volume • Space occupied by sample of matter • Calculated from a solid by multiplying length x width x height • Thus, SI is cubic meter or cm3 • We normally use liters for volume • 1 mL = 1 cm3

43. Measuring Volume Graduated cylinder Pipets Burets Volumetric flask Syringes

44. Volume Changes • With an increase in temperature, the volume also increases • Seen most in gases • Instruments are calibrated for 20 oC which is room temperature

45. Units of Mass • Mass – measure of the quantity of matter present • Weight – force that measures the pull by gravity – changes with location

46. Measuring Mass SI unit for mass is kg – we commonly use grams in the laboratory Mass is measured using a triple beam balance (or electric balance)

47. Temperature • Measure of how hot or cold something is • Heat moves from object of higher temperature to object of lower temp • 2 units used: • Kelvin • Celsius

48. Temperature • Celsius scale defined by two readily determined temperatures: • Freezing point of water = 0 oC • Boiling point of water = 100 oC • Kelvin scale does not use the degree sign, but is just represented by K • absolute zero = 0 K (thus no negative values) • formula to convert: K = oC + 273

49. Sample Problem Normal human body temperature is 37 oC. What is the temperature in Kelvin?

50. Energy • Energy is the capacity to do work or produce heat • Energy can be measured using: • Joule (J) – the SI unit for energy • Calorie (cal) – the heat needed to raise 1 gram of water by 1 oC