1. Chemistry 103 Chapter 2 $ ₤ ¥ L m kg ml mm μg + - * / y x

2. Chapter 2 – Slide 2 of 99 General Course structure Learning Tools Atoms ---> Compounds ---> Chemical Reactions

3. Chapter 2 – Slide 3 of 99 Outline Mathematics of Chemistry (Measurements) –Units –Significant Figures (Sig Figs) –Calculations & Sig Figs –Scientific Notation –Dimensional Analysis –Density

4. Chapter 2 – Slide 4 of 99 Importance of Units Job Offer: Annual Salary = 1,000,000. Do you Accept or Reject? A)Accept B)Reject $ Great Offer $1,000,000. ¥ (JPY) Not So Great 1,000,000 ¥ ≈ $9,100. P

5. Chapter 2 – Slide 5 of 99 Measured vs Exact numbers

6. Chapter 2 – Slide 6 of 99 Scientists make many kinds of measurements –The determination of the dimensions, capacity, quantity or extent of something –Length, Mass, Volume, Density All measurements are made relative to a standard All measurements have uncertainty Units and Measurements

7. Chapter 2 – Slide 7 of 99 Systems of Measurement English System –Common measurements –Pints, quarts, gallons, miles, etc. Metric System –Units in the metric system consist of a base unit plus a prefix.

8. Chapter 2 – Slide 8 of 99 Everyday Measurements You make a measurement every time you Measure your height. Read your watch. Take your temperature. Weigh a cantaloupe.

9. Chapter 2 – Slide 9 of 99 Measurement in Chemistry In chemistry we Measure quantities. Do experiments. Calculate results. Use numbers to report measurements. Compare results to standards. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

10. Chapter 2 – Slide 10 of 99 Length Measurement Length Is measured using a meter stick. Has the unit of meter (m) in the metric (SI) system. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

11. Chapter 2 – Slide 11 of 99 Inches and Centimeters The unit of an inch is equal to exactly 2.54 centimeters in the metric (SI) system. 1 in. = 2.54 cm Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

12. Chapter 2 – Slide 12 of 99 Volume Measurement Volume Is the space occupied by a substance. Has the unit liter (L) in metric system. 1 L = 1.057 qt Uses the unit m 3 (cubic meter) in the SI system. Is measured using a graduated cylinder. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

13. Chapter 2 – Slide 13 of 99 Mass Measurement The mass of an object Is the quantity of material it contains. Is measured on a balance. Has the unit gram(g) in the metric system. Has the unit kilogram(kg) in the SI system. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

14. Chapter 2 – Slide 14 of 99 Temperature Measurement The temperature of a substance Indicates how hot or cold it is. Is measured on the Celsius (  C) scale in the metric system. On this thermometer is 18ºC or 64ºF. In the SI system uses the Kelvin(K) scale. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

15. Chapter 2 – Slide 15 of 99 Units in the Metric System In the metric (SI) system, one unit is used for each type of measurement: Measurement MetricSI lengthmeter (m)meter (m) volumeliter (L)cubic meter (m 3 ) massgram (g)kilogram (kg) timesecond (s)second (s) temperatureCelsius (  C)Kelvin (K)

16. Chapter 2 – Slide 16 of 99 Metric Base Units

17. Chapter 2 – Slide 17 of 99 For each of the following, indicate whether the unit describes A) length, B) mass, or C) volume. ____ 1. A 2.6 kg bag of onions. ____ 2. A person is 2.0 m tall. ____ 3. A medication contains 0.50 g aspirin. ____ 4. A bottle contains 1.5 L of water. Learning Check

18. Chapter 2 – Slide 18 of 99 Learning Check Identify the measurement with an SI unit. 1. John’s height is A) 1.5 ydB) 6 ft C) 2.1 m 2. The race was won in A) 19.6 sB) 14.2 minC) 3.5 hr 3. The mass of a lemon is A) 12 ozB) 0.145 kgC) 0.6 lb 4. The temperature is A) 85  CB) 255 KC) 45  F P

19. Chapter 2 – Slide 19 of 99 Exact (Defined) and Inexact (Measured) Numbers Exact numbers –Have no uncertainty associated with them –They are known exactly because they are defined or counted –Example: 12 inches = 1 foot Measured numbers –Have some uncertainty associated with them –Example: all measurements

20. Chapter 2 – Slide 20 of 99 Accuracy vs. Precision Accuracy How closely a measurement comes to the true, accepted value Precision How closely measurements of the same quantities come to each other

21. Chapter 2 – Slide 21 of 99 Have you learned about Significant Figures in another course; i.e., here at UNLV, at another college or university, or in high school? A)Yes B)No P

22. Chapter 2 – Slide 22 of 99 Significant Figures Digits in any measurement are known with certainty, plus one digit that is uncertain. Measured numbers convey *Magnitude *Uncertainty *Units

23. Chapter 2 – Slide 23 of 99 The Calculator Problem 7.8 3.8 Calculator Answer: 2.05263…… Is this a realistic answer? Is it 2, 2.0, 2.1, 2.05, 2.06, 2.052, 2.053, 2.0526, etc.? Answer must reflect uncertainty expressed in original measurements.

24. Chapter 2 – Slide 24 of 99 Rules for Significant Figures It’s ALL about the ZEROs

25. Chapter 2 – Slide 25 of 99 Rules for Sig Figs All non-zero numbers in a measurement are significant. 4573 4573 has 4 sig figs

26. Chapter 2 – Slide 26 of 99 Rules for Sig Figs All zeros between sig figs are significant. 23007 23007 has 5 sig figs

27. Chapter 2 – Slide 27 of 99 Rules for Sig Figs In a number less than 1, zeros used to fix the position of the decimal are not significant. 0.00021 0.00021 has 2 sig figs

28. Chapter 2 – Slide 28 of 99 Rules for Sig Figs When a number has a decimal point, zeros to the right of the last nonzero digit are significant 0.0002100 0.0002100 has 4 sig figs

29. Chapter 2 – Slide 29 of 99 Rules for Sig Figs When a number without a decimal point explicitly shown ends in one or more zeros, we consider these zeros not to be significant. If some of the zeros are significant, bar notation is used. _ 820000 meters 3 sig figs 820000

30. Chapter 2 – Slide 30 of 99 Practice Identifying Sig Figs

31. Chapter 2 – Slide 31 of 99 Significant Figures How many assuming all numbers are measured? a). 75924 75924(5 sig figs) b). 30.002 30.002(5 sig figs) c). 0.004320 0.004320(4 sig figs) d). 0.000002 0.000002(1 sig fig) e). 46,000 46,000(2 sig figs)

32. Chapter 2 – Slide 32 of 99 Measured Numbers A measuring tool Is used to determine a quantity such as height or the mass of an object. Provides numbers for a measurement called measured numbers. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

33. Chapter 2 – Slide 33 of 99. l 2.... l.... l 3.... l.... l 4.. cm The markings on the meter stick at the end of the orange line are read as The first digit 2 plus the second digit 2.7 The last digit is obtained by estimating. The end of the line might be estimated between 2.7–2.8 as about half-way (0.5) which gives a reported length of 2.75 cm Reading a Meter Stick

34. Chapter 2 – Slide 34 of 99 Known + Estimated Digits In the length reported as 2.75 cm, The digits 2 and 7 are certain (known) The final digit 5 was estimated (uncertain) All three digits (2.75) are significant including the estimated digit

35. Chapter 2 – Slide 35 of 99 Learning Check. l 8.... l.... l 9.... l.... l 10.. cm What is the length of the red line? 1) 9.0 cm 2) 9.03 cm 3) 9.04 cm

36. Chapter 2 – Slide 36 of 99 Solution. l 8.... l.... l 9.... l.... l 10.. cm The length of the red line could be reported as 2) 9.03 cm or 3) 9.04 cm The estimated digit may be slightly different. Both readings are acceptable.

37. Chapter 2 – Slide 37 of 99. l 3.... l.... l 4.... l.... l 5.. cm For this measurement, the first and second known digits are 4.5. Because the line ends on a mark, the estimated digit in the hundredths place is 0. This measurement is reported as 4.50 cm. Zero as a Measured Number

38. Chapter 2 – Slide 38 of 99 Significant Figures in Measured Numbers Significant figures Obtained from a measurement include all of the known digits plus the estimated digit. Reported in a measurement depend on the measuring tool.

39. Chapter 2 – Slide 39 of 99 Rounding off Numbers The number of significant figures in measurements affects any calculations done with these measurements –Your calculated answer can only be as certain as the numbers used in the calculation

40. Chapter 2 – Slide 40 of 99 Calculator: Friend or Foe? Sometimes, the calculator will show more (or fewer) significant digits than it should –If the first digit to be deleted is 4 or less, simply drop it and all the following digits –If the first digit to be deleted is 5 or greater, that digit and all that follow are dropped and the last retained digit is increased by one

41. Chapter 2 – Slide 41 of 99 Sig Fig Rounding Example: Round the following measured number to 4 sig figs: 82.56702

42. Chapter 2 – Slide 42 of 99 Sig Fig Rounding Example Round the following measured number to 4 sig figs:  82.56702

43. Chapter 2 – Slide 43 of 99 Sig Fig Rounding Example Round the following measured number to 4 sig figs:  82.56702ANSWER: 82.57

44. Chapter 2 – Slide 44 of 99 Adding Significant Zeros Sometimes a calculated answer requires more significant digits. Then one or more zeros are added. Calculated AnswerZeros Added to Give 3 Significant Figures 44.00 1.51.50 0.20.200 12 12.0

45. Chapter 2 – Slide 45 of 99 Practice Rounding Numbers

46. Chapter 2 – Slide 46 of 99 a). 28.394 b). 0.000230600 c). 2568 d). 2562 e). 8 ANSWER: 28.4 ANSWER: 0.000231 ANSWER: 2570 ANSWER: 2560 ANSWER: 8.00 Significant Figures Round each to 3 sig figs

47. Chapter 2 – Slide 47 of 99 When multiplying or dividing, use The same number of significant figures in your final answer as the measurement with the fewest significant figures. Rounding rules to obtain the correct number of significant figures. Example: 110.5 x 0.048 = 5.304 = 5.3 (rounded) 4 SF 2 SF calculator 2 SF Multiplication and Division

48. Chapter 2 – Slide 48 of 99 When adding or subtracting, use The same number of decimal places in your final answer as the measurement with the fewest decimal places. Use rounding rules to adjust the number of digits in the answer. 25.2 one decimal place + 1.34 two decimal places 26.54calculated answer 26.5 answer with one decimal place Addition and Subtraction

49. Chapter 2 – Slide 49 of 99 Math operations with Sig Figs

50. Chapter 2 – Slide 50 of 99 Report Answer with Correct Number of Sig Figs A) 124.54 x 2.2 = 273.98800 B) 3420. + 2400. + 1095 = 6915.0000 C) 3420 + 2400 + 1095 = 6915.0000 D) 98.5564 = 2.1575394 45.68

51. Chapter 2 – Slide 51 of 99 When Math Operations Are Mixed If you have both addition/subtraction and multiplication/division in a formula, -carry out the operations in parenthesis first, and round according to the rules for that type of operation. -complete the calculation by rounding according to the rules for the final type of operation.

52. Chapter 2 – Slide 52 of 99 When Math Operations Are Mixed _____5.681g_____ = (52.15ml - 32.4ml) -carry out the operations in parenthesis first, and round according to the rules for that type of operation.

53. Chapter 2 – Slide 53 of 99 When Math Operations Are Mixed _____5.681g_____ = 5.681g (52.15ml - 32.4ml) 19.8ml -carry out the operations in parenthesis first, and round according to the rules for that type of operation.

54. Chapter 2 – Slide 54 of 99 When Math Operations Are Mixed _____5.681g_____ = 5.681g (4 sig figs) (52.15ml - 32.4ml)19.8ml (3 sig figs) -complete the calculation by rounding according to the rules for the final type of operation.

55. Chapter 2 – Slide 55 of 99 When Math Operations Are Mixed _____5.681g_____ = 5.681g (4 sig figs) (52.15ml - 32.4ml)19.8ml (3 sig figs) ANSWER: 0.287g/ml -complete the calculation by rounding according to the rules for the final type of operation.

56. Chapter 2 – Slide 56 of 99 Mixed Operations and Significant Figures What is the result (to the correct number of significant figures) of the following calculations? Assume all numbers are measured. (23 - 21) x (24.4 - 23.1) 2 x 1.3= 3 (1 sig fig) (2 sig figs) (298 - 270) x (322) 30 x 322= 10,000 (1 sig fig) (3 sig fig)

57. Chapter 2 – Slide 57 of 99 The Calculator Problem 7.8 3.8 Calculator Answer: 2.05263…… Is this a realistic answer? Is it 2, 2.0, 2.1, 2.05, 2.06, 2.052, 2.053, 2.0526, etc.? Answer must reflect uncertainty expressed in original measurements.

58. Chapter 2 – Slide 58 of 99 The Calculator Problem 7.8 3.8 Calculator Answer: 2.05263…… Is this a realistic answer? Is it 2, 2.0, 2.1, 2.05, 2.06, 2.052, 2.053, 2.0526, etc.? Answer must reflect uncertainty expressed in original measurements.

59. Chapter 2 – Slide 59 of 99 Scientific Notation Scientific notation Is used to write very large or very small numbers The width of a human hair, 0.000 008 m is written as: 8 x 10 -6 m A large number such as 2 500 000 s is written as: 2.5 x 10 6 s Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

60. Chapter 2 – Slide 60 of 99 Scientific Notation A number in scientific notation contains a coefficient (1 or greater, less than 10) and a power of 10. 150 0.000735 coefficient power of ten coefficient power of ten 1.5 x 10 2 7.35 x 10 -4 To write a number in scientific notation, the decimal point is moved after the first non zero digit. The spaces moved are shown as a power of ten. 52 000 = 5.2 x 10 4 0.00378 = 3.78 x 10 -3 4 spaces left 3 spaces right

61. Chapter 2 – Slide 61 of 99 Some Powers of Ten

62. Chapter 2 – Slide 62 of 99 Comparing Numbers in Standard and Scientific Notation Standard Format Scientific Notation Diameter of Earth 12 800 000 m1.28 x 10 7 m Mass of a human 68 kg 6.8 x 10 1 kg Length of a pox virus 0.000 03 cm3 x 10 -5 cm

63. Chapter 2 – Slide 63 of 99 Comparing Numbers in Standard and Scientific Notation Standard Format Scientific Notation Diameter of Earth 12 800 000 m1.28 x 10 7 m (3 sig figs) Mass of a human 68 kg 6.8 x 10 1 kg (2 sig figs) Length of a pox virus 0.000 03 cm3 x 10 -5 cm (1 sig fig) NOTE: The Coefficient is used to identify the number of significant figures in the measurement.

64. Dimensional Analysis Defining Conversion Factors

65. Chapter 2 – Slide 65 of 99 Conversion Factors Conversion factors A ratio that specifies how one unit of measurement is related to another Creating conversion factors from equalities 12 in.= 1 ft 1 L = 1000 mL

66. Chapter 2 – Slide 66 of 99 Dimensional Analysis How many seconds are in 2 minutes? ? seconds = 2 minutes ? seconds = 2 minutes x 60 seconds = 1 minute 120 seconds (exactly)

67. Chapter 2 – Slide 67 of 99 Dimensional Analysis If we assume there are exactly 365 days in a year, how many seconds are in one year? ? seconds = 1 year

68. Chapter 2 – Slide 68 of 99 Dimensional Analysis A problem solving method in which the units (associated with numbers) are used as a guide in setting up the calculations. Conversion Factor

69. Chapter 2 – Slide 69 of 99 Exact vs Measured Relationships Metric to Metric – exact English to English – exact Metric to English – typically measured (must consider sig figs)

70. Chapter 2 – Slide 70 of 99 English to Metric Conversion Factors

71. Chapter 2 – Slide 71 of 99 Dimensional Analysis What is 165 lb in kg? STEP 1 Given: 165 lb Need: kg STEP 2 Plan STEP 3 Equalities/Factors 1 kg = 2.205 lb 2.205 lb and 1 kg 1 kg 2.205 lb STEP 4 Set Up Problem ? kg = 165 lb

72. Chapter 2 – Slide 72 of 99 Learning Check If a ski pole is 3.0 feet in length, how long is the ski pole in mm? (1000mm = 1m, 12 inches=1ft, 1m=39.37inches)

73. Chapter 2 – Slide 73 of 99 Learning Check If a ski pole is 3.0 feet in length, how long is the ski pole in mm? (1000mm = 1m, 12 inches=1ft, 1m=39.37inches) 3.0 feetmm? Plan

74. Chapter 2 – Slide 74 of 99 Learning Check If a bucket contains 4.65L of water. How many gallons of water is this? (1 gallon = 4qts, 1L = 1.057qt)

75. Chapter 2 – Slide 75 of 99 Dimensional Analysis If Jules Vern expressed the title of his famous book, “Twenty Thousand Leagues Under the Sea” in feet, what would the title be? (1mile = 5280ft, 1 League = 3.450miles)

76. Chapter 2 – Slide 76 of 99 A rattlesnake is 2.44 m long. How many centimeters long is the snake? A) 24.4 cm B)244 cm C)2440 cm D) 2440. cm Quiz Question 2 pts

77. Chapter 2 – Slide 77 of 99 Quiz Question 2 pts If a particular fad diet claims a weight loss of 3.0 pounds per week, how many grams per day would this be? (1lb = 453.6g) A)1360 g/day B)190 g/day C)194 g/day D)194.4 g/day E)200 g/day

78. Chapter 2 – Slide 78 of 99 What is the symbol for the element hydrogen? A) He B)Hg C)H D) Ho Quiz Question 2 pts

79. Chapter 2 – Slide 79 of 99 What is the symbol for the element chlorine? A) Ce B)C C)Ch D) Cl Quiz Question 2 pts

80. Chapter 2 – Slide 80 of 99 What is the symbol for the element Iron? A) I B)Fr C)Fe D) Ir Quiz Question 2 pts

81. Chapter 2 – Slide 81 of 99 Converting from squared units to squared units or cubed units to cubed units Warning: This type of conversions give many students difficulties!!!!! The one thing you have to remember: –What does it mean to say that a unit is squared or cubed? –m 2 = m x m; s 3 = s x s x s When there are squared or cubed units, you have multiple units to cancel out!

82. Chapter 2 – Slide 82 of 99 Examples Convert 127.4 cm 3 to m 3. (100cm = 1m) Convert.572 miles 2 to km 2. (1km =.621miles)

83. Chapter 2 – Slide 83 of 99 Displacement volume for a stock engine in a 1984 Corvette is specified at 350 in 3. What is the displacement in L?

84. Chapter 2 – Slide 84 of 99 Percent Factor in a Problem If the thickness of the skin fold at the waist indicates an 11% body fat, how much fat is in a person with a mass of 86 kg? percent factor 86 kg mass x 11 kg fat 100 kg mass = 9.5 kg fat Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

85. Chapter 2 – Slide 85 of 99 Even MORE Practice with Conversion Factors A lean hamburger is 22% fat by weight. How many grams of fat are in 0.25 lb of the hamburger? (1lb = 453.6g)

86. Chapter 2 – Slide 86 of 99 Density A ratio of the mass of an object divided by its volume Density = Mass/Volume Typical units = g/mL (NOTE: 1mL=1cm 3 ) We have an unknown metal with a mass of 59.24 g and a volume of 6.64 mL. What is its density?

87. Chapter 2 – Slide 87 of 99 Density A ratio of the mass of an object divided by its volume Density = Mass/Volume Typical units = g/mL (NOTE: 1mL=1cm 3 ) We have an unknown metal with a mass of 59.24 g and a volume of 6.64 mL. What is its density? Density = 59.24g= 8.92g/mL 6.64mL

88. Chapter 2 – Slide 88 of 99 Densities of Common Substances Is Density a Physical or a Chemical Property?

89. Chapter 2 – Slide 89 of 99 Measuring Density in Lab

90. Chapter 2 – Slide 90 of 99 What is the density (g/cm 3 ) of 48.0 g of a metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added? A) 0.17 g/cm 3 B) 6.0 g/cm 3 C) 380 g/cm 3 25.0 mL 33.0 mL object Learning Check

91. Chapter 2 – Slide 91 of 99 Sink or Float Ice floats in water because the density of ice is less than the density of water. Aluminum sinks because its density is greater than the density of water. Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

92. Chapter 2 – Slide 92 of 99 Which diagram correctly represents the liquid layers in the cylinder? Karo (K) syrup (1.4 g/mL), vegetable (V) oil (0.91 g/mL,) water (W) (1.0 g/mL) A B C K K W W W V V V K Learning Check

93. Chapter 2 – Slide 93 of 99 A) Vegetable oil 0.91 g/mL Water 1.0 g/mL Karo syrup 1.4 g/mL K W V Solution

94. Chapter 2 – Slide 94 of 99 Osmium is a very dense metal. What is its density in g/cm 3 if 50.0 g of osmium has a volume of 2.22 cm 3 ? a) 2.25 g/cm 3 b) 22.5 g/cm 3 c) 111 g/cm 3 Learning Check

95. Chapter 2 – Slide 95 of 99 Osmium is a very dense metal. What is its density in g/cm 3 if 50.0 g of osmium has a volume of 2.22 cm 3 ? a) 2.25 g/cm 3 b) 22.5 g/cm 3 c) 111 g/cm 3 50.0g = 22.5g/cm 3 2.22cm 3 Learning Check

96. Chapter 2 – Slide 96 of 99 Density can be written as an equality. For a substance with a density of 3.8 g/mL, the equality is: 3.8 g = 1 mL From this equality, two conversion factors can be written for density. Conversion 3.8 g and 1 mL factors1 mL 3.8 g Density as a Conversion Factor

97. Chapter 2 – Slide 97 of 99 Density Example You have been given 150.g of ethyl alcohol which has a density of 0.785g/mL. Will this quantity fit into a 150mL beaker?

98. Chapter 2 – Slide 98 of 99 DENSITY PRACTICE

99. Chapter 2 – Slide 99 of 99 The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane? A) 0.614 kg B) 614 kg C) 1.25 kg Learning Check