1. Chapter 2 Data Analysis

2. Objectives: Define SI base units for time, length, mass and temperature Use prefixes with units Compare the derived units for volume and density Use scientific notation Use dimensional analysis to convert between units and ………

3. Objectives (cont’d) Define and compare accuracy and precision Use significant figures and rounding to reflect the certainty of data Use % error to describe the accuracy of experimental data Correctly create, read and interpret graphs AL COS Objectives 4, 7, 9, 10, and 16

4. Terms to know…. Base unit kilogram Derived unit density Metersecond Length accuracy Liter precision Kelvinconversion factor

5. Terms to know…. (Cont’d) Random error Systematic error Independent variable Dependent variable

6. Units of Measurement SI QuantityBase unitsymbol TimeSeconds LengthMeterm MassKilogramkg TemperatureKelvinK Amt of a substance Molemol

7. You can change any base unit with a prefix Some prefixes are for large numbers: giga (G) 10 9 gigameter mega (M) 10 6 megameter kilo (k) 1000 kilometer

8. And some for smaller ones… deci0.110 -1 centi0.0110 -2 milli0.00110 -3 micro0.000 00110 -6 nano0.000 000 00110 -9 pico0.000 000 000 001 10 -12

10. So, how much is…. A milliliter? ________ A centigram? ________ A kilowatt? ________ A nanometer? ________ A picosecond? ________

11. Base vs derived units A base unit is a single unit and is measured directly--- Example: - time in seconds with a stopwatch - mass in grams with a balance - length in cm with a ruler

12. A derived unit is a combination of two or more base units Example: speed meters/sec km/hr densityg/mL or g/cm 3 and …….

13. Volume is a derived unit = L x w x h 1 liter = 10 cm x 10 cm x 10 cm = 1000 cm 3 or = 1 dm* x 1 dm x 1 dm = 1 dm 3 * 10 cm = 1 decimeter

14. Density is the amount of mass packed in to a same volume Low density High density

15. Density = mass volume Example #1: A 121.5 g sample of aluminum has a volume of 45 cm 3. What is the density of Al?

16. Solution: D= m/v = 121.5g 45 cm 3 = 2.7 g/cm 3

17. Another density problem: Example #2: What would be the mass of 1000 mL of liquid mercury, density 13.5 g/mL?

18. Solution: D = m v 13.5 g/mL = m 1000 mL (13.5g/mL) (1000 mL) = 13 500 g = 13.5 kg

19. Scientific notation Used to simplify reading numbers that are very large or very small In normal scientific notation there is one number to the left of the decimal Ex.: 5.66 x 10 13

20. Another version of scientific notation is called Engineering mode In Engineering mode two numbers are left in front of the decimal Ex: 56.6 x 10 12

21. You will see both in your Scientific calculator Chemists typically use normal scientific notation Ex: 1.66 x 10 -19 6.022 x 10 23

22. -is a way of solving problems that focuses on the units rather than the numbers to solve the problem -solves problems by using a conversion factor Dimensional analysis

23. A conversion factor is --- -a ratio of equivalent values expressed in different units -a conversion factor is like multiplying a number by 1 such as……

24. 12 inches 1 foot 1 hour 3600 seconds = a conversion factor = a conversion factor Same thing = 1

25. Ex. #1: How many seconds are in 9 weeks? 9 wks x 7 days x 24hrs x 60min x 60 sec 1 1 wk 1 day 1 hr 1 min Answer 

26. Notice how the units canceled out: 9 wks x 7 days x 24hrs x 60min x 60 sec 1 1 wk 1 day 1 hr 1 min = 5 443 200 sec Answer:

27. In Europe, the posted speed limit is 90 km/hr – what would that be in miles/hr? Ex.#2: 1 km = 0.62 miles

28. Ex. #2 90 km x 0.62 miles = 55.8 miles 1 hr 1 km hr

29. Ex. #3: If a baseball player hit 70 home runs in a single season, and it’s 90 feet between each of the four bases, how many miles did he run that year in just home runs? Try this on your own paper. 1 mile = 5280 feet Answer

30. 70 home runs x 360 ft x 1 mile 1season 1 homerun 5280 ft = 4.77 miles/season Answer #3

31. How reliable are measurements? Scientists are concerned with the accuracy of a measurement the precision of a measurement

32. Accuracy = how close your answer comes to the “real answer,” the accepted value Poor accuracy Good accuracy

33. Precision Precision refers to how close a series of measurements are to each other Precision is the “repeatability” of a measurement

34. …accuracy is typically determined by the equipment you use Did you use a good analytical balance or a old triple-beam balance? Remember…

35. … determined by how good YOU are with the equipment provided. Can you do over and over and get similar answers? While precision is

36. Poor precision Poor accuracy Good precision Poor accuracy

37. Good precision Good accuracy

38. Reporting measurements Every measurement has some reported error or uncertainty Uncertainty is assumed to be ± one unit in the last reported place

39. Example: You record 1.24g as the mass of a sample. This is automatically assumed to be between 1.23 and 1.25 or ± 0.01 grams.

40. When reading normal laboratoryequipment, avoid parallax errors. Take measurements from the bottom of the meniscus when observing at eye Level.

41. Read the bottom of the meniscus in a graduated cylinder- while holding it at eye level.

42. What about errors? All experiments have some errors! - human error - mechanical error An error can be a random error (because it is equally likely to be high or low)

43. Error (cont’d) Random errors are sometimes called indeterminate errors, because it is largely due to the limitations of the lab equipment you use

44. You can also have systematic errors (determinate errors). These are often caused by faulty measurements or problems with your measuring device. Error (cont’d) (Did you zero your balance before using it?)

45. Finding a % error % error is the ratio of your error (How much you were off) divided by the actual accepted answer.

46. Ex. #1 Donna calculated the density of aluminum to be 2.52 g/mL. The accepted density of aluminum is 2.70 g/mL. What is her % error? Error x 100 = % error Accepted (2.70-2.52) x 100= 6.67% error 2.70

47. Ex. #2 Bill did the same lab as Donna, But he found the density of Al to be 2.95 g/mL. What is his % error? Error* x 100 = % error Accepted (2.95-2.70) x 100= 9.26% 2.70 * Error is always considered positive

48. Ex. #3: Your turn Juan calculated the density of Copper to be 9.34 g/mL. What was his % error? (Find density using the chart on pg 914 in your textbook.) Answer

49. Ex. #3 Answer Error x 100 = % error Accepted (9.34-8.92) x 100 = 4.71% 8.92

50. Significant figures When you measure using any scientific instrument, your answer’s precision depends upon the equipment you used.

51. The digits that are reported when reading a scientific instrument called significant figures. Significant figures include all KNOWN digits plus one ESTIMATED digit.

52. 2 34 This ruler would read 2.5_ cm We would probably say 2.56 cm or maybe even 2.57 cm. The 2.5 are certain digits the last digit is an estimate.

53. Rules for significant figures: 1.Non-zero numbers are always significant. Example: 957 = 3 SF 1893 = 4 SF

54. 2. Zeroes between non-zero numbers are always significant. Example: 209 = 3 SF 34007= 5 SF

55. 3. All final zeroes to the right of the decimal are significant. Example: 256.90 = 5 SF 6,220,000.780 = 10 SF 240.519000 = 9 SF

56. 4. Zeroes that act as placeholders are NOT significant. Example: 0.06= 1 SF 290= 2 SF 982 400 = 4 SF 0.0045100 = 5 SF

57. 5. Counting numbers and defined constants have an infinite number of significant figures.

58. Rounding off numbers… Suppose you have to find the density of a sample of Al with a mass of 382.15 g and a volume of 145 ml.Your calculator would give you an answer of 2.63551724....... Your answer can not have any more significant figures than the data with the least # of SF. So then

59. 382.15 = 5 SF 145 = 3 SF So our answer can only have 3 SF 2.63551724....... Must be reported as 2.64 g/mL

60. Addition and subtraction with SF When you add or subtract, your answer is based on the number that has the fewest number of digits to the right of the decimal

61. Ex. #1 14.63 + 9.009 +135.2 158.839  158.8

62. Ex. #2 195.336 + 46.7788 242.1148  242.115

63. Ex. #3: Your turn 1200.03 - 125.669 And the answer is….

64. Answer: 1074.361  1074.36 1200.03 - 125.669

65. Pg. 41, Prac. Problems 35.a.) 142.9 cm b.) 768 kg c.) 0.1119 mg 36.a.) 12.12 cm b.) 2.10 cm c.) 2.7 x 10 3 cm

66. Multiplying and dividing SF Remember that old rule about no chain is any stronger than it’s weakest link? When you multiply or divide numbers, your answer must have the same number of sig. figs as the measurement with the fewest sig. figs.!!!!!!

67. Ex. #1: 6.220 x 12 = 74.64 (4 SF x 2SF = 2 SF) So 74.64 (4 SF)  75 (2 SF)

68. Ex. #2: 9.67 x 12 000 x 0.9007= ? Answer 

69. Answer 9.67 x 12 000 x 0.9007= ? 3SF 2SF 4 SF = 2 SF 104 517.228 becomes 100 000* * Bar shows that the zero is significant and not just a place holder!

70. Ex. #3 1.46 x 10 6 x 14.566 x 0.0230 63.289 Answer 

71. Answer #3 1.46 x 10 6 x 14.566 x 0.0230 63.289 3SF x 5 SF x 3 SF/5 SF = 3SF = 7 728.4564............(etc) = 7 730

72. Pg. 42 37. a. 78 b. 12 c. 2.5 d. 81.1 38. a. 2.0c. 2.00 b. 3.00d. 2.9

73. Insignificant

74. End Chapter 2