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Unit 1: Measurement and Conversions

Unit 1: Measurement and Conversions. http://old.unit5.org/roller. Scientific Notation Review. Often used to express very large or very small numbers. Also used to maintain correct number of significant figures. Form: (# from 1 to 9.999) x 10 exponent 800 2531 0.0014.

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Unit 1: Measurement and Conversions

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  1. Unit 1: Measurement and Conversions http://old.unit5.org/roller

  2. Scientific Notation Review Often used to express very large or very small numbers. Also used to maintain correct number of significant figures. Form: (# from 1 to 9.999) x 10exponent 800 2531 0.0014 = 8 x 10 x 10 = 8 x 102 = 2.531 x 10 x 10 x 10 = 2.531 x 103 = 1.4 x 10-3 = 1.4 / 10 / 10 / 10

  3. Scientific Notation Practice Change the given number to standard form. 1.87 x 10–5 = 3.7 x 108 = 7.88 x 101 = 2.164 x 10–2 = 000000187000000 0.0000187 370,000,000 78.8 0.02164 (+) exponent = number > 1 (-) exponent = number < 1

  4. Scientific Notation Practice Change the given number into scientific notation. 12,340 = 0.369 = 0.008 = 1,000,000,000 = 1.234 x 104 3.69 x 10–1 8 x 10–3 1 x 109

  5. Significant Figures about… A student is combining separate water samples, all of differing volumes, into one large bucket. Samples A, B and C are 25.5 mL, 16.37 mL and 51 mL, respectively. Once combined, what is the total volume of all the samples? NO! 92.87 mL Because the samples were each measured with a different level of precision, we must factor that into our calculations by identifying what are called significant figures.

  6. Measurement and Accuracy • The last digit of any measured number is assumed to be an estimate (uncertain) • The second to last digit is assumed to be known with certainty (based on a line) A (25.5 mL) B (16.37 mL) C (51 mL) 60 26 50 16.4 25 16.3

  7. Identifying Significant Figures Counting SF’s in a number Non-zero numbers:ALWAYScount as SF Zeroes Left: NEVER count as SF (0.000345) Middle: ALWAYS count as SF (5001) Right: sometimes… w/ decimal point: count as SF (25.10) w/o decimal point: DO NOT count as SF (8200) Exact Numbers: IGNORE SF Counts (28 students in this class) Constants (1 mol = 6.022 x 1023) Conversions (1 in = 2.54 cm) Relative to the non-zero numbers.

  8. How many Sig Figs? Measurement Number of SF Measurement Number of SF 0.12 kg 1240560. cm 6000000 kg 6.00 x 106 kg 409 cm 29.200 dm 0.02500 g 2 2 7 1 5 4 4 25 g 0.030 kg 1.240560 x 106 mg 6 x 104 sec 246.31 g 20.06 cm 1.050 m 2 7 1 3 3 5 4

  9. Sig Figs with Calculations Note: For any calculations, always perform the entire calculation without rounding, and then round the final answer. Addition/Subtraction • Round the answer to the LEAST number of decimal places found (least precise) 11.31 + 33.264 + 4.1 = 48.674 Multiplication/Division • Round the answer to the smallest number of SF found 5.282 x 3.42 = 18.06444 → rounded to 48.7 → rounded to 18.1 (3.42 only has 3 SF)

  10. Back to the original question… A student is combining separate water samples, all of differing volumes, into one large bucket. Samples A, B and C are 25.5 mL, 16.37 mL and 51 mL, respectively. Once combined, what is the total volume of all the samples? 25.5 mL + 16.37 mL + 51 mL = 92.87 mL 93 mL Could I write that as 93.0? NO!

  11. More practice with SF If you made measurements of three samples of water (128.7 mL, 18 mL and 23.45 mL), and then poured all of the water together in one, unmarked container, what total volume of water should you report? Support your answer. 128.7 mL + 18 mL + 23.45 mL = 170.15 mL 170. mL or 1.70 x 102 mL

  12. Practice with Sig Fig Calculations A A A A A = -6.118 x 10-9 report -6 x 10-9 (1 SF) = 3.63 x 109 report 3.6 x 109 (2 SF) = 15.563 report 15.6 (tenths place) = 16.27 report 20(tens place) = 1.7225 x 10-5 report 1.7 x 10-5 (2 SF) Complete calculation, and then follow order of operations to determine how many SF would be carried for each step

  13. The Metric System from Industry Week, 1981 November 30

  14. SI System • The International System of Units • abbreviated SI from the French Le Système international d'unités • Based on the metric system (with small variations) • Based on powers of ten • Uses prefixes to differentiate between powers • Used in nearly country except U.S. (Liberia and Myanmar are some others…)

  15. The International System of Units Quantity Name Symbol Volume liter L Length meter m Mass kilogram kg Time second s Amount of substance mole mol Thermodynamic temperature Kelvin K Electric current amperes amps Luminous intensity candela cd Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 16

  16. Area and Volume: Derived Units Area = length x width = 5.0 m x 3.0 m = 15 ( m x m) = 15 m2 Volume = length x width x height = 5.0 m x 3.0 m x 4.0 m = 60. ( m x m x m) = 60. m3

  17. Derived Units Commonly Used in Chemistry Quantity Name Symbol Area square meter m2 Volume cubic meter m3 Force newton N Pressure pascal Pa Energy joule J Power watt W Voltage volt V Frequency hertz Hz Electric charge coulomb C

  18. Prefixes in the SI System The Commonly Used Prefixes in the SI System Power of 10 for Prefix Symbol Meaning Scientific Notation _______________________________________________________________________ mega- M 1,000,000 106 kilo- k 1,000 103 deci- d 0.1 10-1 centi- c 0.01 10-2 milli- m 0.001 10-3 micro- m 0.000001 10-6 nano- n 0.000000001 10-9 Zumdahl, Zumdahl, DeCoste, World of Chemistry2002, page 118

  19. Giga- Mega- Kilo- base milli- micro- nano- pico- femto- atomo- 1024 g 1021 g Earth’s atmosphere to 2500 km Quantities of Mass 1018 g 1015 g 1012 g Ocean liner 109 g Indian elephant 106 g Average human 103 g 1.0 liter of water 100 g 10-3 g 10-6 g Grain of table salt 10-9 g 10-12 g 10-15 g 10-18 g Typical protein 10-21 g Uranium atom 10-24 g Water molecule Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25

  20. Reporting Measurements • Must use significant figures • Report what is known with certainty Using dashes • Add ONE digit of uncertainty beyond that Using estimation The implication is that for any measurement, the last digit is an estimate and uncertain, and the next to last is known with certainty Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

  21. 1 2 3 4 5 0 cm 1 2 3 4 5 0 cm 1 2 3 4 5 0 cm Practice Measuring 4.5 cm 4.54 cm 3.0 cm Timberlake, Chemistry 7th Edition, page 7

  22. Measurement/Sig Fig Practice Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water and explain your answers (the numbers given are as precise as possible): a. 128.7 mL b. 18 mL c. 23.45 mL Mark every 1 mL Mark every 10 mL Mark every 0.1 mL

  23. 5 4 40 60 6 30 3 50 Implied range of uncertainty in a measurement reported as 50. cm (±5) Implied range of uncertainty in a measurement reported as 5.0 cm (±0.5) 4 6 3 5 Implied range of uncertainty in a measurement reported as 5.00 cm (±0.05) Implied Range of Uncertainty Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32

  24. 10 8 6 Reading a Meniscus 10 mL reading too high line of sight too high proper line of sight reading correct line of sight too low reading too low graduated cylinder

  25. ? 20 15 mL ? 1.50 x 101 mL 15.0 mL 10

  26. 100 cm ______ 1 m 100 cm ______ 1 m 1 m 100 cm 132 cm Conversion Factors equality: 1 m = 100 cm (or 0.01 m = 1 cm) How many cm are in 1.32 meters? applicable conversion factors: or 1.32 m = We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose.

  27. 1 km 1 km 1,000 m 1,000 m ( ) ______ ( ) ____ 1 m 1 m 10 dm 10 dm 1.5 km Both ways are equally good! 1. How many kilometers is 15,000 decimeters? 15,000 dm = OR… 15,000 dm

  28. ( ) _____ 60 min 1 h 378,432 s ( ) ( ) ____ 60 s 3.78 x 105 s ____ 24 h 1 min 1 d 2. How many seconds is 4.38 days? 4.38 d = If we are accounting for significant figures, we would change this to…

  29. ( ( ( ( ) ) ) ) ______ ______ ______ ________ 1 m 1 m 1 m 1 m2 100 cm 100 cm 100 cm (100)2 cm2 41.2 cm2 = 0.412 m2 WRONG! 3. Convert 41.2 cm2 to m2 = 0.412 cm.m Recall that… 41.2 cm2 = 41.2 cm.cm 41.2 cm.cm = 0.00412 m2 41.2 cm2 = 0.00412 m2

  30. 102 mm2 1 cm2 ( ) _____ ( )2 ( )2 4. Convert 41.2 cm2 to mm2 Recall that… 1 cm = 10 mm 41.2 cm2 = 4,120 mm2

  31. ( ( ( ( ) ) ) ) 1 m 1 m 1 m 1 m _____ _____ _____ _____ 100 cm 100 cm 100 cm 100 cm ( ) 3 1 m _________ 3 1000000 cm cm.cm.cm 2 3 480 cm 5. Convert to 480 cm3 to m3 = or 3 480 cm3 = 0.00048 m3 or 4.8 x 10-4 m3 480 cm3 =

  32. Comparison of English and SI Units 1 inch 2.54 cm 1 inch = 2.54 cm Zumdahl, Zumdahl, DeCoste, World of Chemistry2002, page 119

  33. SI-US Conversion Factors Equality Conversion Factors Length 2.54 cm 1 in 1 in 2.54 cm 2.54 cm = 1 in. and 39.4 in 1 m 1 m 39.4 in. 1 m = 39.4 in. and Volume 946 mL 1 qt 1 qt 946 mL 946 mL = 1 qt and 1.06 qt 1 L 1 L 1.06 qt and 1 L = 1.06 qt Mass 1 lb 453.6 g 453.6 g 1 lb 453.6 g = 1 lb and 2.20 lb 1 kg 1 kg 2.20 lb 1 kg = 2.20 lb and

  34. Practical Conversions Teachers get a lot of grief from normal workers because they only work 36 weeks a year. How many extra hours, per day, would a teacher have to put in to match the typical worker, assuming a teacher works 8 hrs per day for those 36 weeks? What assumptions must we make?

  35. m D V liquids and gases Glass: liquid or solid? Density Review how tightly packed the particles are Density = Typical units: g/cm3 for solids g/mL for fluids

  36. Monty Python’s take on analytical science and density with regard to witches…

  37. m D V V Density Review 1. A sample of lead (Pb) has mass 22.7 g and volume 2.0 cm3. Find sample’s density. = 11 2. Another sample of lead occupies 16.2 cm3 of space. Find sample’s mass. m = D V = 180 g

  38. More Density Review Problems… 3. A 119.5 g solid cylinder has radius 1.8 cm and height 1.5 cm. Find sample’s density. 4. A 153 g rectangular solid has edge lengths 8.2 cm, 5.1 cm, and 4.7 cm. Will this object sink in water?

  39. m m D V 1.8 cm 1.5 cm 3. A 119.5 g solid cylinder has radius 1.8 cm and height 1.5 cm. Find sample’s density. 2 SF V = p r2 h = p (1.8 cm)2(1.5 cm) = 15.2681 cm3 = 7.8

  40. m D V 8.2 cm 5.1 cm 4.7 cm 4. A 153 g rectangular solid has edge lengths 8.2 cm, 5.1 cm, and 4.7 cm. Will this object sink in water? (Find object’s density and compare it to water’s density.) 2 SF V = l w h = 8.2 cm (5.1 cm)(4.7 cm) = 196.554 cm3 No; it floats. = 0.78 < 1

  41. m D V Will bowling balls sink or float in H2O? If DBB < 1, it will float If DBB > 1, it will sink 21.6 cm in diameter Vsphere = 4/3 p r3 V = 4/3p (10.8 cm)3 V = 5,276.7 cm3 m = D V m = (1.0 g/cm3)(5276.7 cm3) m = 5276.7 g Since the mass of a BB varies, let’s figure out at what mass it will sink v. float …or 11.6 lbs

  42. Measurements Metric (SI) units Prefixes Uncertainty Length Mass Volume Conversion factors Significant figures Density Problem solving with conversion factors Timberlake, Chemistry 7th Edition, page 40

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