2. 1.2 Scientific Method In science we make observations and look for patterns. Scientific law: Tells what always occurs Theory: mental picture, explains why the law happens.

3. Steel wool weighs more after its heated Wood gets lighter as it burns In the 17 th and 18 th centuries, scholars held the theory of phlogiston (“phlog” rhymes with “dodge”) ; a material which escaped when something burned, but could be given to metals when they were heated Think about this theory. Does it serve to explain the changes that we observe?

4. Steel wool weighs more after its heated Wood gets lighter as it burns The theory of the atom provides an alternative explanation for the same observations. Atoms are lost when wood burns. Atoms are gained when steel wool burns. Think about this theory. Does it serve to explain the changes that we observe?

5. Antoine LaVoisier (1743-1794) Mass increased Mass stayed the same Heated tin In a closed flask unstoppered Air rushes in In the 18 century, Lavoisier – the father of modern quantitative chemistry, disproved the phlogiston theory by heating metals in closed containers illustrating that mass was always conserved. Can you explain this? Lost their heads in the French revolution  How does this experiment provide evidence for the atomic theory?

6. Law of conservation of mass With the coming of the theory of the atom, it became simple to explain the conservation of mass. If all the atoms are conserved, mass will always remain the same. This is the law of conservation of mass.

7. Particle diagram Key: H =O = Water reacts according to this equation: 2H 2 + O 2  2 H 2 O Draw the products consistent with the law of conservation of mass Reactantsproducts Leftover oxygen molecule Question: If 4 grams of hydrogen combines with 32 grams of oxygen What mass of water is formed? 36 grams Mass must be conserved!

8. 3.1 Types of Observations and Measurements We make QUALITATIVE observations of reactions — changes in color and physical state.We make QUALITATIVE observations of reactions — changes in color and physical state. COLD!

9. We also make QUANTITATIVE MEASUREMENTS, which involve numbers. Use SI units — based on the metric system 5 0 C

10. Scientific Notation consists of two parts: Measurement digitsMeasurement digits Number between 1 and 10Number between 1 and 10 Decimal after first digitDecimal after first digit Factor of TensFactor of Tens Ten to a powerTen to a power Provides order of magnitudeProvides order of magnitude Example: Mass of the earth: 6592000000000000000000 tons 6.592 x 10 21 tons

11. Given: 289,800,000Given: 289,800,000 Use: 2.898 (moved 8 places)Use: 2.898 (moved 8 places) Answer:Answer: Given: 0.000567Given: 0.000567 Use: 5.67 (moved 4 places)Use: 5.67 (moved 4 places) Answer:Answer: 2.898 x 10 8 5.67 x 10 - 4 To change standard form to scientific notation… Decimal after first digit # of decimal places moves = exponent

12. Given: 5.093 x 10 6Given: 5.093 x 10 6 Answer:Answer: Given: 1.976 x 10 -4Given: 1.976 x 10 -4 Answer:Answer: 5,093,000 (moved 6 places to the right) 0.0001976 (moved 4 places to the left) To change scientific notation to standard form… Move decimal right (bigger) for positive exponent Move decimal left (smaller) for negative exponents

13. Learning Check Express these numbers in Scientific Notation: 1) 4057 2) 0.00387 3) 30000 4) 2 5) 0.4760 4.057 x 10 3 3.87 x 10 -3 3 x 10 4 4.760 x 10 -1 2 x 10 0

14. Multiplying with scientific notation Sample problems: (3.0)(6.0 x 10 3 ) (3.0)(6.0 x 10 -3 ) Rule: Multiply significant digits, add exponents = (3.0)(6.0) x 10 3 = 18 x 10 3 ÷10 x10 = 1.8 x 10 4 = 18 x 10 -3 = 1.8 x 10 -2

15. (3.0 x 10 3 )(6.0 x 10 3 ) Rule: Multiply significant digits, add exponents Multiplying with scientific notation = (3.0)(6.0) x 10 3 + 3 = 18 x 10 6 = 1.8 x 10 7 (3.0 x 10 2 )(6.0 x 10 -5 )= 18 x 10 -3 = 1.8 x 10 -2

16. (3.0) (6.0 x 10 3 ) (3.0) Dividing with scientific notation Rule: divide significant digits, subtract exponents = (6.0) x 10 3 (3.0) = 2.0 x 10 3 = (3.0) x 10 -3 (6.0) Switch the sign = 0.50 x 10 -3 = 5.0 x 10 -4

17. (3.0 x 10 2 ) (6.0 x 10 3 ) (3.0 x 10 2 ) Dividing with scientific notation Rule: divide significant digits, subtract exponents = (6.0) x 10 3-2 (3.0) = 2.0 x 10 1 = (3.0) x 10 2-3 (6.0) = 0.50 x 10 -1 = 5.0 x 10 -2

18. (6.0 x 10 3 ) + (3.0 x 10 2 ) Add or subtract with scientific notation Rule: convert to like exponents, add or subtract significant digits = (6.0 + 0.3) x 10 3 (6.0 x 10 3 ) + (0.3 x 10 3 ) ÷10 x10 = 6.3 x 10 3

19. Learning check 1.(2.0)(6.3 x 10 4 ) 2. (6.4 x 10 4 ) (2.0) 3.(2.0 x 10 -2 )(6.3 x 10 4 ) 4. (6.4 x 10 4 ) (2.0 x 10 -2 ) 5. (6.3 x 10 4 ) - (2.0 x 10 3 ) = 1.26 x 10 5 = 1.3 x 10 5 = 3.2 x 10 4 = 1.3 x 10 3 = 3.2 x 10 6 0.2 x 10 4 = 6.1 x 10 4

20. Three targets with three arrows each to shoot. Can you hit the bull's-eye? Both accurate and precise Precise but not accurate Neither accurate nor precise How do they compare? Can you define accuracy and precision? Accuracy – how close are you to the target Precision – how repeatable are your shots.

21. A student calculates the density of mercury to be 13.2 g/cm 3. If the accepted value is 13.6 g/cm 3, what is the percentage error? % error = measured value – accepted value x 100 Accepted value % error = 13.2 - 13.6 x 100 13.6 = - 2.94 PERCENT NEGATIVE ERROR = MEASURED VALUE BELOW ACCEPTED! 3.2 Accuracy and percent error

22. Try One: At a track meet, you time a friend running 100 m in 11.00 seconds. The electronic clock records 10.67 seconds. Calculate your percentage error. Show work: 3.1%

23. Significant Figures (digits) and precision The numbers reported in a measurement are limited by the precision of the measuring tool The numbers reported in a measurement are limited by the precision of the measuring tool Significant figures in a measurement include the known digits plus one estimated digit Significant figures in a measurement include the known digits plus one estimated digit 36.5 mL

24. Taking a measurement. l 2.... I.... I 3....I.... I 4.. cm First digit (known)= 2 2.?? cm Second digit (known)= 0.7 2.7? cm Third digit (estimated) between 0.04- 0.06 Length reported=2.75 cm or2.74 cm or2.74 cm or2.76 cm

25. Known + Estimated Digits In 2.75 cm… Known digitsandare 100% certain Known digits 2 and 7 are 100% certain The third digit 5 is estimated (uncertain) The third digit 5 is estimated (uncertain) In the reported length, all three digits (2.76 cm) are significant including the estimated one In the reported length, all three digits (2.76 cm) are significant including the estimated one

26. Zero as a Measured Number. l 3.... I.... I 4.... I.... I 5.. cm What is the length of the line? First digit 4.?? cm Second digit 4.7? cm Last (estimated) digit is 4.70 cm If the last digit is “on the line” we write a zero

27. Zeros as placeholders Mass of the earth: 6592000000000000000000 tons 6.592 x 10 21 tons 4 Significant digits 18 Placeholder zeros Notice the placeholders get wrapped up in the power to the base 10.

28. Zeros as placeholders Radius of a carbon atom: 77 picometers 77 x 10 -12 m 0.0000000000077 m 2 Sig digs 11 placeholder zeros Notice the placeholders again get wrapped up in the power to the base 10.

29. Zeros as placeholders Placeholders left after rounding: Ex:734567 Rounded to nearest thousand: 3 sig digs Note: the zeros left after rounding are only placeholders They drop out when not needed – as in scientific notation 3 placeholder zeros 7.35 x 10 5 735000

30. Counting Significant Figures RULE: All non-zero digits in a measured number are significant. (Only zeros can be used as placeholders.) Number of Significant Figures 38.15 cm4 5.6 ft2 65.6 lb___ 122.55 m 122.55 m___ 3 5

31. Sandwiched Zeros RULE : Zeros between nonzero numbers are significant. (They can not be rounded or dropped, unless they are on an end of a number.) Number of Significant Figures 50.8 mm3 2001 min4 0.702 lb____ 0.00405 m 0.00405 m ____ 3 3

32. Leading Zeros RULE: Leading zeros in decimal numbers are NOT significant (they are only placeholders). Number of Significant Figures 0.008 mm1 0.0156 oz3 0.0042 lb____ 0.000262 mL 0.000262 mL ____ 2 3

33. Trailing Zeros RULE : Trailing zeros in numbers without decimals are NOT significant. (They are only serving as place holders - left after rounding). Number of Significant Figures 25,000 in. 2 25,000 in. 2 200. yr3 200. yr3 48,600 gal____ 48,600 gal____ 25,005,000 g ____ rounded to thousands decimal means not rounded 3 5

34. Trailing Zeros RULE : Trailing zeros in numbers with decimals are significant. (They represent greater precision – they’re not placeholders) Number of Significant Figures 25.10 in. 4 25.10 in. 4 20.0 yr3 20.0 yr3 48.600 gal____ 48.600 gal____ 25.0350 g ____ Nearest hundredth Nearest tenth 5 6

35. Learning Check A. Which answers contain 3 significant figures? 1) 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 10 3 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 10 5 1) 535 2) 535,000 3) 5.35 x 10 5 Rounded to nearest thousand

36. 0.000 75 Km = ? sf’s 6 92 000 grams = ? sf’s 5 090.030 = ? sf’s 0.003030 = ? sf’s 303,000. = ? sf’s Review A number larger than one, with a decimal. Everything is significant! Hint: which digits are required to express the measurement; which express the order of magnitude? Convert to meters and Kg to see

37. Significant Numbers in Calculations A calculated answer must match the least precise measurement used in the calculation. Significant figures are needed for final answers from Significant figures are needed for final answers from 1) adding or subtracting 1) adding or subtracting 2) multiplying or dividing

38. Adding and Subtracting The answer has the same number of “tens places” as the measurement with the fewest tens places. 25.2 nearest tenth + 1.35 nearest hundredth 26.55 26.55 answer 26.6 nearest tenth ?

39. Learning Check In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.83) 257 B. 58.925 - 18.2= 1) 40.725 2) 40.733) 40.7

40. Multiplying and Dividing Round (or add zeros to) the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures. Ex: 235.05 X 19.6 = 4606.98 5 sf’s vs. 3 sf’s rounds to 3 sf’s4607

41. Multiplying and Dividing Round (or add zeros to) the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures. Ex: 58.925 ÷ 0.023 =2561.9565 5 sf’svs. 2 sf’s round to 2 sf’s 2600 Notice that placeholder zeros substitute for the ones and tens place

42. Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.32) 11 3) 0.041

43. 3.3 UNITS OF MEASUREMENT Use SI units — based on the metric system LengthMassVolumeTimeTemperature Meter, m Kilogram, kg Seconds, s Celsius degrees, ˚C kelvins, K Liter, L or dm 3

44. Metric Prefixes Kilo- means 1000 of that unit ex: 1 kilometer (km) = 1000 meters (m) 1 kilo-unit = 1000 units 1 kilo-unit = 1000 units Ex: Air pressure is measured in pascals Normal air pressure is about 100 kilopascals How many pascals is 100 kilopascal? 1000 100 kilopascal = 100,000 pascals

45. Metric Prefixes 10 cm = 1 decimeter Centi- means 1/100 of that unit ex: 1 meter (m) = 100 centimeters (cm) 1 unit = 100 centi-units 1 unit = 100 centi-units but 10 cm = 1 decimeter ( ) 3 1000 cm 3 = 1 dm 3

46. Metric Prefixes A liter is the volume of a cube 10 cm x 10 cm x 10 cm = 1000 cm 3 If each cubic centimeter is 1/1000 th of the liter we can also call it a ________liter. milli So 1 cm 3 = 1mL Milli- means 1/1000 of that unit ex: 1 Liter (L) = 1000 milliliters (mL) 1 unit = 1000 milli-units

47. Metric Prefixes Reference table C is seldom used but may be useful to show the relationship between different units

48. Atomic dimensions A carbon atom has a radius of 91 picometers Since a pico = 10 -12 That’s 91 x 10 -12 meters OR 9 of a meter 1,000,000,000,000 That’s tiny!

49. Converting between units uses fractions in which the numerator and denominator are EQUAL quantities expressed in different units ex: 1 in. = 2.54 cm We can build two fractions: Factors: 1 in. OR 2.54 cm 2.54 cm 1 in. 4.2 Dimensional analysis

50. Learning Check Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 2. Hours and minutes 3. Meters and kilometers 1 L 1000 mL OR 1000 mL 1 L 1 hr 60 min 1 hr OR 1 Km 1000 m 1 Km OR 1 liter = 1000 milliliters 1 hour = 60 minutes 1000 meters = 1 kilometer

51. Setting up conversions 1) Identify the starting and ending units: hours to minutes 2) Recognize the equality between the unit: 1 hour = 60 minutes 3) Build conversion factor with ending unit over starting unit: 60 min 1 hour How many minutes are in 2.5 hours? Starting: 2.5 hours Ending: ? minutes

52. How many minutes are in 2.5 hours ? 2.5 hr x = 2.5 hr x = using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers! Set up to Cancel 150 min Conversion factor 60 min 1 hr

53. Sample Problem 4 quarters 1 dollar 1 dollar X = 29 quarters You have $7.25 in your pocket in quarters. How many quarters do you have? 7.25 dollars How many quarters = 1 dollar? How will we set up our conversion factor? 4 quarters 1 dollar (Ending over starting unit) 4 quarters = 1 dollars

54. A practical problem: Driving in Canada, the speed limit says 90 km per hour, how fast is that in miles per hour? (Don’t want to get a speeding ticket, do I?) Step 1: ID Starting and ending unit Step 2: Do I know an equality? Step 3: Write down starting value and unit Step 4: Write X conversion fraction Ending unit Starting unit Step 5: cancel units and calculate km to miles 10 km = 6.2 miles 90 kmx 6.2 miles 10 km = (90)(6.2) (10) = 55.8 miles

55. Calculating fractions review 3 x 4 = 2 3 4 x 4 = 2 8 x 1 = 2 12 6 = 2 16 2 = 8 8282 = 4 ____ 1 8 ÷ 2

56. DENSITY - an intensive physical property (specific to a substance) Mercury 13.6 g/cm 3 21.5 g/cm 3 0.18 g/dm 3 Platinum Compactness of its matter (mass) Mass per 1 unit of volume

57. Problem A piece of copper has a mass of 57.54 g. It displaces 6.4 cm 3. Calculate its density (g/cm 3 ). D = M V D = 57.54 grams 6.4 cm 3 6.4 cm 3 D = 8.9953125 D = 9.0 g/cm 3

58. A minimum proper math setup D = M V D = 57.54 grams 6.4 cm 3 6.4 cm 3 D = 9.0 g/cm 3

59. PROBLEM: Mercury (Hg) has a density of 13.6 g/cm 3. What is the volume of 130 g of Hg in grams? Solve the problem using DIMENSIONAL ANALYSIS. 129 g x 1 cm3 13.6 g = 9.485 mL= 9.49 g D = 13.6 g/cm 3 or 13.6 g = 1 cm 3

60. Learning Check Osmium has a density of 22.5 g/cm 3. What is the volume of a 50.00 g sample? 1) 0.45cm 3 2)2.22 cm 3 3)11.3 cm 3 50.00 g x 1 cm 3 22.5 g

61. Volume Displacement A solid displaces a matching volume of water when the solid is placed in water. 33 mL 25 mL

62. Learning Check What is the density (g/cm 3 ) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? 1) 0.2 g/ cm 3 2) 6 g/cm 3 3) 252 g/cm 3 33 mL 25 mL

63. Temperature Scales 1 0 C = 1 K Notice that a change of 1 0 C = 1 K Boiling point of water Freezing point of water Celsius 100 ˚C 0 ˚C 100˚C Kelvin 373 K 273 K 100 K Fahrenheit 32 ˚F 212 ˚F 180˚F But that 0 0 C = 273 K

64. Celsius is based on water Is a relative scale 0 0 C = normal melting point 100 0 C = normal boiling point Kelvin is based on molecular speed energy Is an absolute scale 0 K – absolute zero - molecules stop moving

65. Calculations Using Temperature: Using a formula K = ˚C + 273 Body temp = 37 ˚C + 273 = 310 KBody temp = 37 ˚C + 273 = 310 K Liquid nitrogen = -196 ˚C + 273 = 77Liquid nitrogen = -196 ˚C + 273 = 77 Or ˚C = K - 273 K = ˚C + 273 Body temp = 37 ˚C + 273 = 310 KBody temp = 37 ˚C + 273 = 310 K Liquid nitrogen = -196 ˚C + 273 = 77Liquid nitrogen = -196 ˚C + 273 = 77 Or ˚C = K - 273

66. Learning Check Room temperature is 298 Kelvins. What is this expressed in Celsius? ˚C = K - 273 ˚C = 298 - 273 ˚C = 25