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# Ch 3 Measurement And Density

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• ### Ch 3 Measurement And Density

1. 1. Ch 3 Measurement and Density
2. 2. Types of Observations and Measurements <ul><li>We make QUALITATIVE observations of reactions — changes in color and physical state. </li></ul><ul><li>We also make QUANTITATIVE MEASUREMENTS , which involve numbers . </li></ul><ul><ul><li>Use SI units — based on the metric system </li></ul></ul>
3. 3. What is Scientific Notation? <ul><li>Scientific notation is a way of expressing really big numbers or really small numbers. </li></ul><ul><li>It is most often used in “scientific” calculations where the analysis must be very precise. </li></ul><ul><li>For very large and very small numbers, scientific notation is more concise. </li></ul>
4. 4. Scientific notation consists of two parts: <ul><li>A number between 1 and 10 </li></ul><ul><li>A power of 10 </li></ul><ul><li>N x 10 x </li></ul>
5. 5. To change standard form to scientific notation… <ul><li>Place the decimal point so that there is one non-zero digit to the left of the decimal point. </li></ul><ul><li>Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. </li></ul><ul><li>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. </li></ul>
6. 6. Examples <ul><li>Given: 289,800,000 </li></ul><ul><li>Use: 2.898 (moved 8 places) </li></ul><ul><li>Answer: 2.898 x 10 8 </li></ul><ul><li>Given: 0.000567 </li></ul><ul><li>Use: 5.67 (moved 4 places) </li></ul><ul><li>Answer: 5.67 x 10 -4 </li></ul>
7. 7. To change scientific notation to standard form… <ul><li>Simply move the decimal point to the right for positive exponent 10. </li></ul><ul><li>Move the decimal point to the left for negative exponent 10. </li></ul><ul><li>(Use zeros to fill in places.) </li></ul>
8. 8. Example <ul><li>Given: 5.093 x 10 6 </li></ul><ul><li>Answer: 5,093,000 (moved 6 places to the right) </li></ul><ul><li>Given: 1.976 x 10 -4 </li></ul><ul><li>Answer: 0.0001976 (moved 4 places to the left) </li></ul>
9. 9. Learning Check <ul><li>Express these numbers in Scientific Notation: </li></ul><ul><li>405789 </li></ul><ul><li>0.003872 </li></ul><ul><li>3000000000 </li></ul><ul><li>2 </li></ul><ul><li>0.478260 </li></ul>4.05789 X 10 5 3.872 X 10 -3 3 X 10 9 2 X 10 0 4.78260 X 10 -1
10. 10. Accuracy Vs. Precision <ul><li>What do you think the differences are? </li></ul><ul><li>Ideas anyone??? </li></ul>
11. 11. 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?
12. 12. Let’s use a golf anaolgy
13. 13. Accurate? No Precise? Yes 10
14. 14. Accurate? Yes Precise? Yes 12
15. 15. Precise? No Accurate? Maybe? 13
16. 16. Accurate? Yes Precise? We cant say! 18
17. 17. Accurate? Yes Precise? We cant say! 18
18. 18. Accurate? Yes Precise? We cant say! 18
19. 19. Accuracy Precision Resolution subsequent samples time offset [arbitrary units] not accurate, not precise accurate, not precise not accurate, precise accurate and precise accurate, low resolution -2 -3 -1 0 1 2 3
20. 20. In terms of measurement <ul><li>Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. </li></ul><ul><li>Were they precise? </li></ul><ul><li>Were they accurate? </li></ul>
21. 21. Significant Figures <ul><li>The numbers reported in a measurement are limited by the measuring tool </li></ul><ul><li>Significant figures in a measurement include the known digits plus one estimated digit </li></ul>
22. 22. Counting Significant Figures <ul><li> </li></ul><ul><li>RULE 1. All non-zero digits in a measured number are significant. Only a zero could indicate that rounding occurred. </li></ul><ul><ul><ul><ul><ul><li>Number of Significant Figures </li></ul></ul></ul></ul></ul><ul><li>38.15 cm 4 </li></ul><ul><li>5.6 ft 2 </li></ul><ul><li>65.6 lb ___ </li></ul><ul><li>122.55 m ___ </li></ul>3 5
23. 23. Leading Zeros <ul><li>RULE 2. Leading zeros in decimal numbers are NOT significant. </li></ul><ul><li>Number of Significant Figures </li></ul><ul><li>0.008 mm 1 </li></ul><ul><li>0.0156 oz 3 </li></ul><ul><li>0.0042 lb ____ </li></ul><ul><li>0.000262 mL ____ </li></ul>2 3
24. 24. Sandwiched Zeros <ul><li>RULE 3. Zeros between nonzero numbers are significant. (They can not be rounded unless they are on an end of a number.) </li></ul><ul><li>Number of Significant Figures </li></ul><ul><li>50.8 mm 3 </li></ul><ul><li>2001 min 4 </li></ul><ul><li>0.702 lb ____ </li></ul><ul><li>0.00405 m ____ </li></ul>3 3
25. 25. Trailing Zeros <ul><li>RULE 4. Trailing zeros in numbers without decimals are NOT significant. They are only serving as place holders. </li></ul><ul><li> Number of Significant Figures </li></ul><ul><li>25,000 in. 2 </li></ul><ul><li>200. yr 3 </li></ul><ul><li>48,600 gal ____ </li></ul><ul><li>25,005,000 g ____ </li></ul>3 5
26. 26. Learning Check <ul><li>A. Which answers contain 3 significant figures? </li></ul><ul><li>0.4760 2) 0.00476 3) 4760 </li></ul><ul><li>B. All the zeros are significant in </li></ul><ul><li>1) 0.00307 2) 25.300 3) 2.050 x 10 3 </li></ul><ul><li>C. 534,675 rounded to 3 significant figures is </li></ul><ul><ul><li>1) 535 2) 535,000 3) 5.35 x 10 5 </li></ul></ul>
27. 27. Solution <ul><li>A. Which answers contain 3 significant figures? </li></ul><ul><ul><li>1) 0.4760 2) 0.00476 3) 4760 </li></ul></ul><ul><li>B. All the zeros are significant in </li></ul><ul><li>1) 0.00307 2) 25.300 3) 2.050 x 10 3 </li></ul><ul><li>C. 534,675 rounded to 3 significant figures is </li></ul><ul><ul><li>1) 535 2) 535,000 3) 5.35 x 10 5 </li></ul></ul>
28. 28. Learning Check <ul><li>In which set(s) do both numbers contain the same number of significant figures? </li></ul><ul><li> 1) 22.0 and 22.00 </li></ul><ul><ul><li>2) 400.0 and 40 </li></ul></ul><ul><ul><li>3) 0.000015 and 150,000 </li></ul></ul>
29. 29. Solution <ul><li>In which set(s) do both numbers contain the same number of significant figures? </li></ul><ul><li> </li></ul><ul><ul><li>3) 0.000015 and 150,000 </li></ul></ul>
30. 30. <ul><li>State the number of significant figures in each of the following: </li></ul><ul><li>A. 0.030 m 1 2 3 </li></ul><ul><li>B. 4.050 L 2 3 4 </li></ul><ul><li>C. 0.0008 g 1 2 4 </li></ul><ul><li>D. 3.00 m 1 2 3 </li></ul><ul><li>E. 2,080,000 bees 3 5 7 </li></ul>Learning Check
31. 31. <ul><li>State the number of significant figures in each of the following: </li></ul><ul><li>A. 0.030 m 1 2 3 </li></ul><ul><li>B. 4.050 L 2 3 4 </li></ul><ul><li>C. 0.0008 g 1 2 4 </li></ul><ul><li>D. 3.00 m 1 2 3 </li></ul><ul><li>E. 2,080,000 bees 3 5 7 </li></ul>Learning Check
32. 32. UNITS OF MEASUREMENT <ul><li>Use SI units — based on the metric system </li></ul><ul><li>Length </li></ul><ul><li>Mass </li></ul><ul><li>Volume </li></ul><ul><li>Time </li></ul><ul><li>Temperature </li></ul>Meter, m Kilogram, kg Seconds, s Celsius degrees, ˚C kelvins, K Liter, L
33. 33. Mass vs. Weight <ul><li>Mass: Amount of Matter (grams, measured with a BALANCE) </li></ul><ul><li>Weight: Force exerted by the mass, only present with gravity (pounds, measured with a SCALE) </li></ul>Can you hear me now?
34. 34. Some Tools for Measurement Which tool(s) would you use to measure: A. temperature B. volume C. time D. weight
35. 35. Solution <ul><li>A . temperature thermometer </li></ul><ul><li>B. volume measuring cup , graduated cylinder </li></ul><ul><li>C. time watch </li></ul><ul><li>D . weight scale </li></ul>
36. 36. Learning Check <ul><li>Match L) length M) mass V) volume </li></ul><ul><li>____ A. A bag of tomatoes is 4.6 kg. </li></ul><ul><li>____ B. A person is 2.0 m tall. </li></ul><ul><li>____ C. A medication contains 0.50 g Aspirin. </li></ul><ul><li>____ D. A bottle contains 1.5 L of water. </li></ul>M L M V
37. 37. Learning Check <ul><li>What are some U.S. units that are used to measure each of the following? </li></ul><ul><li>A. length </li></ul><ul><li>B. volume </li></ul><ul><li>C. weight </li></ul><ul><li>D. temperature </li></ul>
38. 38. Solution <ul><li>Some possible answers are </li></ul><ul><li>A. length inch, foot, yard, mile </li></ul><ul><li>B. volume cup, teaspoon, gallon, pint, quart </li></ul><ul><li>C. weight ounce, pound (lb), ton </li></ul><ul><li>D. temperature  F </li></ul>
39. 39. Metric Prefixes <ul><li>Kilo- means 1000 of that unit </li></ul><ul><ul><li>1 kilometer (km) = 1000 meters (m) </li></ul></ul><ul><li>Centi- means 1/100 of that unit </li></ul><ul><ul><li>1 meter (m) = 100 centimeters (cm) </li></ul></ul><ul><ul><li>1 dollar = 100 cents </li></ul></ul><ul><li>Milli- means 1/1000 of that unit </li></ul><ul><ul><li>1 Liter (L) = 1000 milliliters (mL) </li></ul></ul>
40. 40. Metric Prefixes
41. 41. Metric Prefixes
42. 42. Units of Length <ul><li>? kilometer (km) = 500 meters (m) </li></ul><ul><li>2.5 meter (m) = ? centimeters (cm) </li></ul><ul><li>1 centimeter (cm) = ? millimeter (mm) </li></ul><ul><li>1 nanometer (nm) = 1.0 x 10 -9 meter </li></ul>O—H distance = 9.4 x 10 -11 m 9.4 x 10 -9 cm 0.094 nm
43. 43. Learning Check <ul><li>Select the unit you would use to measure </li></ul><ul><li>1. Your height </li></ul><ul><li>a) millimeters b) meters c) kilometers </li></ul><ul><li>2. Your mass </li></ul><ul><li>a) milligrams b) grams c) kilograms </li></ul><ul><li>3. The distance between two cities </li></ul><ul><li>a) millimeters b) meters c) kilometers </li></ul><ul><li>4. The width of an artery </li></ul><ul><li>a) millimeters b) meters c) kilometers </li></ul>
44. 44. Solution <ul><li>1. Your height </li></ul><ul><li>b) meters </li></ul><ul><li>2. Your mass </li></ul><ul><li>c) kilograms </li></ul><ul><li>3. The distance between two cities </li></ul><ul><li>c) kilometers </li></ul><ul><li>4. The width of an artery </li></ul><ul><li>a) millimeters </li></ul>
45. 45. Equalities <ul><li>State the same measurement in two different units </li></ul>length 10.0 in. 25.4 cm
46. 46. <ul><li>1. 1000 m = 1 ___ a) mm b) km c) dm </li></ul><ul><li>2. 0.001 g = 1 ___ a) mg b) kg c) dg </li></ul><ul><li>3. 0.1 L = 1 ___ a) mL b) cL c) dL </li></ul><ul><li>4. 0.01 m = 1 ___ a) mm b) cm c) dm </li></ul>Learning Check
47. 47. <ul><li>1. 1000 m = 1 ___ a) mm b) km c) dm </li></ul><ul><li>2. 0.001 g = 1 ___ a) mg b) kg c) dg </li></ul><ul><li>3. 0.1 L = 1 ___ a) mL b) cL c) dL </li></ul><ul><li>4. 0.01 m = 1 ___ a) mm b) cm c) dm </li></ul>Learning Check
48. 48. Instruments for Measuring Volume Graduated cylinder Syringe Volumetric flask Buret Pipet
49. 49. Units of Measuring Volume 1 L = 1000 mL 1 qt = 946 mL Timberlake, Chemistry 7 th Edition, page 3
51. 51. Units for Measuring Mass 1 kg = 2.20 lb Timberlake, Chemistry 7 th Edition, page 3
52. 52. Quantities of Mass Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25 Earth’s atmosphere to 2500 km Ocean liner Indian elephant Average human 1.0 liter of water Grain of table salt Typical protein Uranium atom Water molecule 10 24 g 10 21 g 10 18 g 10 15 g 10 12 g 10 9 g 10 6 g 10 3 g 10 0 g 10 -3 g 10 -6 g 10 -9 g 10 -12 g 10 -15 g 10 -18 g 10 -21 g 10 -24 g Giga- Mega- Kilo- base milli- micro- nano- pico- femto- atomo-
53. 53. DENSITY - an important and useful physical property 13.6 g/cm 3 21.5 g/cm 3 2.7 g/cm 3 Mercury Aluminum Platinum
54. 54. <ul><li>Problem A piece of copper has a mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. Calculate density (g/cm 3 ). </li></ul>
55. 55. <ul><li>Strategy </li></ul><ul><li>1. Get dimensions in common units. </li></ul><ul><li>2. Calculate volume in cubic centimeters. </li></ul><ul><li>3. Calculate the density. </li></ul>
56. 56. DENSITY <ul><li>Density is an INTENSIVE property of matter. </li></ul><ul><ul><li>does NOT depend on quantity of matter. </li></ul></ul><ul><ul><li>temperature </li></ul></ul><ul><li>Contrast with EXTENSIVE </li></ul><ul><ul><li>depends on quantity of matter. </li></ul></ul><ul><ul><li>mass and volume. </li></ul></ul>Styrofoam Brick
57. 57. PROBLEM: Mercury (Hg) has a density of 13.6 g/cm 3 . What is the mass of 95 mL of Hg in grams? In pounds? Solve the problem using DIMENSIONAL ANALYSIS.
58. 58. <ul><li>Strategy </li></ul><ul><li>1. Use density to calc. mass (g) from volume. </li></ul><ul><li>2. Convert mass (g) to mass (lb) </li></ul><ul><li>Need to know conversion factor </li></ul><ul><li>= 454 g / 1 lb </li></ul>PROBLEM: Mercury (Hg) has a density of 13.6 g/cm 3 . What is the mass of 95 mL of Hg? First, note that 1 cm 3 = 1 mL
59. 59. <ul><li>1. Convert volume to mass </li></ul>PROBLEM: Mercury (Hg) has a density of 13.6 g/cm 3 . What is the mass of 95 mL of Hg? 2. Convert mass (g) to mass (lb)
60. 60. Learning Check <ul><li>Osmium is a very dense metal. What is its </li></ul><ul><li>density in g/cm 3 if 50.00 g of the metal occupies </li></ul><ul><li>a volume of 2.22cm 3 ? </li></ul><ul><li>1) 2.25 g/cm 3 </li></ul><ul><li>2) 22.5 g/cm 3 </li></ul><ul><li>3) 111 g/cm 3 </li></ul>
61. 61. Volume Displacement <ul><li>A solid displaces a matching volume of water when the solid is placed in water. </li></ul><ul><li> 33 mL </li></ul><ul><li>25 mL </li></ul>
62. 62. Learning Check <ul><li>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? </li></ul><ul><li>1) 0.2 g/ cm 3 2) 6 g/m 3 3) 252 g/cm 3 </li></ul><ul><li> 33 mL </li></ul><ul><li>25 mL </li></ul>
63. 63. Learning Check <ul><li>Which diagram represents the liquid layers in the cylinder? </li></ul><ul><li>(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) </li></ul><ul><li>1) 2) 3) </li></ul>K K W W W V V V K
64. 64. Solution <ul><li>(K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) </li></ul><ul><li>1) </li></ul>K W V
65. 65. Learning Check <ul><li>The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane? </li></ul><ul><li>1) 0.614 kg </li></ul><ul><li>2) 614 kg </li></ul><ul><li>3) 1.25 kg </li></ul>
66. 66. Learning Check <ul><li>If blood has a density of 1.05 g/mL, how many liters of blood are donated if 575 g of blood are given? </li></ul><ul><li>1) 0.548 L </li></ul><ul><li>2) 1.25 L </li></ul><ul><li>3) 1.83 L </li></ul>
67. 67. Learning Check <ul><li>A group of students collected 125 empty aluminum cans to take to the recycling center. If 21 cans make 1.0 pound of aluminum, how many liters of aluminum (D=2.70 g/cm 3 ) are obtained from the cans? </li></ul><ul><li>1) 1.0 L 2) 2.0 L 3) 4.0 L </li></ul>
68. 68. Temperature Scales <ul><li>Fahrenheit </li></ul><ul><li>Celsius </li></ul><ul><li>Kelvin </li></ul>Anders Celsius 1701-1744 Lord Kelvin (William Thomson) 1824-1907
69. 69. Temperature Scales Notice that 1 kelvin = 1 degree Celsius Boiling point of water Freezing point of water Celsius Kelvin Fahrenheit 100 ˚C 0 ˚C 100˚C 373 K 273 K 100 K 32 ˚F 212 ˚F 180˚F
70. 70. Calculations Using Temperature <ul><li>Generally require temp’s in kelvins </li></ul><ul><li>T (K) = t (˚C) + 273.15 </li></ul><ul><li>Body temp = 37 ˚C + 273 = 310 K </li></ul><ul><li>Liquid nitrogen = -196 ˚C + 273 = 77 K </li></ul>
71. 71. Fahrenheit Formula – Honors Only <ul><li>180°F = 9°F = 1.8°F 100°C 5°C 1°C </li></ul><ul><li>Zero point: 0°C = 32°F </li></ul><ul><li>°F = 9/5 °C + 32 </li></ul>
72. 72. Celsius Formula – Honors Only <ul><li>Rearrange to find T°C </li></ul><ul><li>°F = 9/5 °C + 32 </li></ul><ul><li>°F - 32 = 9/5 °C ( +32 - 32) </li></ul><ul><li>°F - 32 = 9/5 °C </li></ul><ul><li>9/5 9/5 </li></ul><ul><li>(°F - 32) * 5/9 = °C </li></ul>
73. 73. Temperature Conversions – Honors Only <ul><li>A person with hypothermia has a body temperature of 29.1°C. What is the body temperature in °F? </li></ul><ul><li>°F = 9/5 (29.1°C) + 32 </li></ul><ul><li>= 52.4 + 32 </li></ul><ul><li>= 84.4°F </li></ul>
74. 74. Learning Check – Honors Only <ul><li>The normal temperature of a chickadee is 105.8°F. What is that temperature in °C? </li></ul><ul><li>1) 73.8 °C </li></ul><ul><li>2) 58.8 °C </li></ul><ul><li>3) 41.0 °C </li></ul>
75. 75. Solution <ul><li>3) 41.0 °C </li></ul><ul><li>Solution: </li></ul><ul><li>°C = 5/9 (°F - 32) </li></ul><ul><li>= 5/9 (105.8 - 32) </li></ul><ul><li> </li></ul><ul><li>= 5/9 * 73.8°F </li></ul><ul><li>= 41.0°C </li></ul>
76. 76. Learning Check – Honors Only <ul><li>Pizza is baked at 455°F. What is that in °C? </li></ul><ul><li>1) 437 °C </li></ul><ul><li>2) 235°C </li></ul><ul><li>3) 221°C </li></ul>
77. 77. Solution <ul><li>Pizza is baked at 455°F. What is that in °C? </li></ul><ul><li>2) 235°C </li></ul><ul><li>5/9 (455 - 32) = 235°C </li></ul>