Chemistry 1 – McGill Chapter 3 Scientific Measurement

1. Chemistry 1 – McGillChapter 3Scientific Measurement WARNING: Learn it now...it will be used all year in Chemistry!!!

2. 3.1 Qualitative measurements • measurements that give results in a descriptive, non-numerical form. Examples: He is tall Electrons are tiny

3. Quantitative measurements • measurement that gives results in a definite form, usually as numbers and units. Examples: He is 2.2 m tall Electrons are 1/1840 times the mass of a proton

4. What is Scientific Notation? • Scientific notation is a way of expressing really big numbers or really small numbers. • It is most often used in “scientific” calculations where the analysis must be very precise. • For very large and very small numbers, scientific notation is more concise.

5. Scientific notation consists of two parts: • A number between 1 and 10 • A power of 10 N x 10x

6. To change standard form to scientific notation… • Place the decimal point so that there is one non-zero digit to the left of the decimal point. • Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. • If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

7. Scientific Notation • a number is written as the product of two numbers: a coefficient and 10 raised to a power. Examples: 567000 = 5.67 X 105 0.00231 = 2.31 X 10-3

8. Examples: Convert to or from Scientific Notation: 2.41 x 102 6.015 x 103 1.62 x 10-2 5.12 x 10-1 662 .0034 241 = 6015 = .0162 = .512 = 6.62 x 102 = 3.4 x 10-3 =

9. Learning Check • Express these numbers in Scientific Notation: • 405789 • 0.003872 • 3000000000 • 2 • 0.478260 4.05789 X 105 3.872 X 10-3 3 X 109 2 X 100 4.78260 X 10-1

10. FYI: “EE” button on calc= typing “X10^” Scientific Notation Cont. (This is important to master!!!) 6.25 x 103 - 2.01 x 102 = (2.15 x 103)(6.1 x 105)(5.0 x 10-6) = 3.25 x 108 = 3.6 x 107 6.05 x 103 6.6 x 103 9.03

11. Accuracy Vs. Precision What do you think the differences are? Ideas anyone???

12. 3.2 Accuracy • the measure of how close a measurement comes to the actual or true value of whatever is measured. • how close a measured value is to the accepted value. Precision • the measure of how close a series of measurements are to one another.

13. Can you hit the bull's-eye? Three targets with three arrows each to shoot. How do they compare? Both accurate and precise Precise but not accurate Neither accurate nor precise Can you define accuracy and precision?

14. Let’s use a golf analogy

15. Accurate? No Precise? Yes 10

16. Precise? Yes Accurate? Yes 12

17. Accurate? Maybe? Precise? No 13

18. Precise? We cant say! Accurate? Yes 18

19. In terms of measurement • Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. • Were they precise? • Were they accurate?

20. Percent Error Formula: % Error = accepted value- experimental value x 100 accepted value *always a positive number- indicated by the absolute value sign* You will use this formula when checking the accuracy of your experiment.

21. think about a TARGET

22. Significant Figures – includes all of the digits that are known plus a last digit that is estimated. ! FYI: These rules are not fun, but they will save you many points in the future if you learn them NOW!

23. Rules for determining Significant Figures1. All non-zero digits are significant. 1, 2, 3, 4, 5, 6, 7, 8, 9

24. 2. Zeros between non-zero digits are significant. (AKA captive zeros) 102 7002

25. 3. Leading zeros (zeros at the beginning of a measurement) are NEVER significant. 00542 0.0152

26. 4. Trailing zeros (zeros after last integer) are significant only if the number contains a decimal point. 210.0 0.860 210

27. 5. All digits are significant in scientific notation. 2.1 x 10-5 6.02 x 1023 Time to practice!!

28. Exact numbers have unlimited Significant Figures Do not use these when you are figuring out sig figs… Examples: 1 dozen = exactly 12 29 people in this room

29. Examples:How many significant digits do each of the following numbers contain: a) 1.2 d) 4600b) 2.0 e) 23.450c) 3.002 f) 6.02 x 1023 2 2 2 5 3 4

30. Learning Check A. Which answers contain 3 significant figures? • 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 103 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 105

31. Solution A. Which answers contain 3 significant figures? 1) 0.47602) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.003072) 25.300 3) 2.050 x 103 C. 534,675 rounded to 3 significant figures is 1) 5352) 535,000 3) 5.35 x 105

32. Learning Check In which set(s) do both numbers contain the samenumber of significant figures? 1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150,000

33. Solution In which set(s) do both numbers contain the samenumber of significant figures? 3) 0.000015 and 150,000

34. Learning Check State the number of significant figures in each of the following: A. 0.030 m 1 2 3 B. 4.050 L 2 3 4 C. 0.0008 g 1 2 4 D. 3.00 m 1 2 3 E. 2,080,000 bees 3 5 7

35. Learning Check State the number of significant figures in each of the following: A. 0.030 m 1 2 3 B. 4.050 L 2 3 4 C. 0.0008 g 1 2 4 D. 3.00 m 1 2 3 E. 2,080,000 bees 3 5 7

36. Rounding Rules:  5 round up < 5 round down (don’t change) Examples: Round 42.63 to 1 significant digit = Round 61.57 to 3 sig. digs.= Round 0.01621 to 2 = Round 65,002 to 2 sig. digs. = 40 61.6 0.016 65,000

37. Addition and Subtraction The measurement with the fewest significant figures to the right of the decimal point determines the number of significant figures in the answer.

38. Examples: Solve using correct significant figures 45.756 m + 62.1 m = 75.263 m + 1123.93 m = 107.9 1199.19

39. Multiplying and Dividing Measurements The measurement with the fewest significant figures determines the number of significant figures in the answer.

40. Examples:Solve using correct significant figures: 3.43 m X 6.4253 m = 45.756 m X 1.2 m = 45.01 m / 2.2 m = 22.0 m2 55 m2 20. ***Why did the “m” unit go away on the last example?*** Noticethe decimal!

41. Uncertainty In lab, you record all numbers you know for sure plus the first uncertain digit. The last digit is estimated and is said to be uncertain but still considered significant. • Graduated cylinders have markings to the nearest mL (milliliter) and you will determine volume to the nearest 0.1 mL… because that is ONE DIGIT OF UNCERTAINTY.

42. International System of Units • revised version of the metric system • abbreviated SI All units, their meanings and values can be found on pgs. 63,64,65. Meter (m) – Liter (L) – Gram (g) – SI unit for length SI unit for volume SI unit for mass

43. Some Tools for Measurement Which tool(s) would you use to measure: A. temperature B. volume C. time D. weight

44. Solution A. temperature thermometer B.volume measuring cup, graduated cylinder C.time watch D. weightscale

45. Learning Check Match L) length M) mass V) volume ____ A. A bag of tomatoes is 4.6 kg. ____ B. A person is 2.0 m tall. ____ C. A medication contains 0.50 g Aspirin. ____ D. A bottle contains 1.5 L of water. M L M V

46. Learning Check What are some U.S. units that are used to measure each of the following? A. length B. volume C. weight D. temperature

47. Solution Some possible answers are A.length inch, foot, yard, mile B. volume cup, teaspoon, gallon, pint, quart C. weight ounce, pound (lb), ton D. temperature °F

48. Metric Prefixes • Kilo- means 1000 of that unit • 1 kilometer (km) = 1000 meters (m) • Centi- means 1/100 of that unit • 1 meter (m) = 100 centimeters (cm) • 1 dollar = 100 cents • Milli- means 1/1000 of that unit • 1 Liter (L) = 1000 milliliters (mL)

49. Metric Prefixes

50. Metric Prefixes