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Unit 2 – MEASUREMENTS AND CALCULATIONS

Unit 2 – MEASUREMENTS AND CALCULATIONS. Mrs. Teates Newport High School. Lesson 1 - Measurement. Lesson Essential Questions What are the different systems of measurement? Why is it important to have the correct unit?. Number vs. Quantity. Quantity - number + unit. UNITS MATTER!!.

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Unit 2 – MEASUREMENTS AND CALCULATIONS

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  1. Unit 2 – MEASUREMENTS AND CALCULATIONS Mrs. Teates Newport High School

  2. Lesson 1 - Measurement • Lesson Essential Questions • What are the different systems of measurement? • Why is it important to have the correct unit?

  3. Number vs. Quantity • Quantity - number + unit UNITS MATTER!!

  4. A Common System for Trade English system of measurement originated in 1215 with the signing of the Magna Carta. It attempted to bring uniform measurements to world trade. In 1790, the French government appointed a committee of scientists to develop a universal measuring system. It took ~10 years, and they unveiled the Metric system. length meter m mass gram g volume liter L time second s

  5. 3 Systems of Measurement • English • What we typically use in our lives. • We will never use them in this class. • Metric • What the rest of the world uses. • SI • What the scientific community uses. Map of the world where red represents countries whichdo not use the metric system

  6. 1/10,000,000 Earth H2O H2O 1/10 m = 1 kilogram = 1 liter 1 kg = 1 meter 1/10 m 1/10 m Volume Mass Length The Original Metric Reference

  7. The Official Standard Meter

  8. The Official Standard Kilogram

  9. Units of Measurement Table

  10. mega- kilo- k M 106 103 BASE UNIT deci- --- d 100 10-1 centi- c 10-2 milli- m 10-3 micro-  10-6 nano- n 10-9 pico- p 10-12 SI Units Prefix Symbol Factor

  11. SI-US Conversion Factors Relationship 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 454 g 454 g 1 lb 454 g = 1 lb and 2.20 lb 1 kg 1 kg 2.20 lb 1 kg = 2.20 lb and

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

  13. M V D = Derived Units • Combination of base units form derived units. • Volume (m3 or cm3) • length  length  length 1 cm3 = 1 mL 1 dm3 = 1 L • Density (kg/m3 or g/cm3) • mass per volume • Area (m2) • Length x length

  14. 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

  15. Density Mass (g) Volume (cm3)

  16. Density • An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? WORK: M = DV M = (13.6 g/cm3)(825cm3) M = 11,200 g

  17. WORK: V = M D V = 25 g 0.87 g/mL Density • A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g V = 29 mL

  18. Instruments for Measuring Volume Graduated cylinder Syringe Volumetric flask Buret Pipet

  19. 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

  20. Factor Name Symbol Factor Name Symbol 10-1 decimeter dm 101 decameter dam 10-2centimeter cm 102 hectometer hm 10-3millimeter mm 103kilometer km 10-6micrometermm 106 megameter Mm 10-9nanometer nm 109 gigameter Gm 10-12 picometer pm 1012 terameter Tm 10-15 femtometer fm 1015 petameter Pm 10-18 attometer am 1018 exameter Em 10-21 zeptometer zm 1021 zettameter Zm 10-24 yoctometer ym 1024 yottameter Ym

  21. Lesson 2 – Conversion Factors and Dimensional Analysis • Lesson Essential Questions: • How are conversion factors used? • Why is dimensional analysis a helpful tool?

  22. Scientific Notation We often use very small and very large numbers in chemistry. Scientific notation is a method to express these numbers in a manageable fashion. Thus 0.000 000 1 cm can be written 1 x 10-7 cm. Lets see why… Scientific notation expresses a number as the product of two factors, the first falling between 1 and 10 and the second being a power of 10.

  23. 000000187000000 . . Change to standard form. 1.87 x 10–5 = 3.7 x 108 = 7.88 x 101 = 2.164 x 10–2 = 0.0000187 370,000,000 78.8 0.02164

  24. Change to 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

  25. 7. 2,400,000 g 8. 0.00256 kg 9. 7  10-5 km 10. 6.2  104 mm Scientific Notation Practice Problems 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

  26. Dimensional Analysis • The “Factor-Label” Method • Units, or “labels” are canceled, or “factored” out

  27. Dimensional Analysis • Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

  28. Dimensional Analysis • Lining up conversion factors: = 1 1 in = 2.54 cm 2.54 cm 2.54 cm 1 = 1 in = 2.54 cm 1 in 1 in

  29. qt mL  Dimensional Analysis • How many milliliters are in 1.00 quart of milk? 1 L 1.057 qt 1000 mL 1 L 1.00 qt = 946 mL

  30. lb cm3 Dimensional Analysis • You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. 1 cm3 19.3 g 1 kg 2.2 lb 1000 g 1 kg 1.5 lb = 35 cm3

  31. in3 L Dimensional Analysis • How many liters of water would fill a container that measures 75.0 in3? 1 L 1000 cm3 (2.54 cm)3 (1 in)3 75.0 in3 = 1.23 L

  32. cm in Dimensional Analysis 5) Your hairdresser wants to cut your hair 8.0 cm shorter. How many inches will they be cutting off? 8.0 cm 1 in 2.54 cm = 3.2 in

  33. cm yd Dimensional Analysis 6) Penn State needs 550 cm for a 1st down. How many yards is this? 1 ft 12 in 1 yd 3 ft 1 in 2.54 cm 550 cm = 6.0 yd

  34. cm pieces Dimensional Analysis 7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? 1 piece 1.5 cm 100 cm 1 m 1.3 m = 86 pieces

  35. Lesson 3 – Significant Figures • Lesson Essential Questions: • What is the purpose of significant figures? • How are they useful in the laboratory setting? • How are significant figures used in calculations?

  36. Reporting Measurements • Using significant figures • Report what is known with certainty • Add ONE digit of uncertainty (estimation) Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

  37. Measuring a Pin Zumdahl, Zumdahl, DeCoste, World of Chemistry2002, page 122

  38. 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

  39. 4 4 6 6 3 3 5 5 Implied range of uncertainty in a measurement reported as 5 cm. Implied range of uncertainty in a measurement reported as 5.0 cm. 4 6 3 5 Implied range of uncertainty in a measurement reported as 5.00 cm. Implied Range of Uncertainty Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32

  40. ? 20 15 mL ? 1.50 x 101 mL 15.0 mL 10

  41. Significant Figures • Indicate precision of a measurement. • Recording Sig Figs • Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

  42. Rules for Counting Significant Figures 1. Nonzero integers always count as significant figures. 2. Zeros: There are three classes of zeroes. • Leading zeroes precede all the nonzero digits and DO NOT count as • significant figures. Example: 0.0025 has ____ significant figures. • Captive zeroes are zeroes between nonzero numbers. These always • count as significant figures. Example: 1.008 has ____ significant figures. • Trailing zeroes are zeroes at the right end of the number. • Trailing zeroes are only significant if the number contains a decimal point. • Example: 1.00 x 102 has ____ significant figures. • Trailing zeroes are not significant if the number does not contain a decimal • point. Example: 100 has ____ significant figure. • Exact numbers, which can arise from counting or definitions such as 1 in • = 2.54 cm, never limit the number of significant figures in a calculation. 2 4 3 1 Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination2006, page 53

  43. Significant figures: Rules for zeros Leading zeros are not significant. Leading zero – three significant figures 0.421 Captive zeros are significant. Captive zero 4012 – four significant figures Trailing zeros are significant. Trailing zero 114.20 – five significant figures

  44. Significant Figures & Scientific Notation Measurement Number of significant figures it contains Measurement Number of significant figures it contains 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 0.12 kg 1240560. cm 6000000 kg 6.00 x 106 kg 409 cm 29.200 cm 0.02500 g 2 7 1 3 3 5 4

  45. Significant Figures Counting Sig Fig Examples 1. 23.50 1. 23.50 4 sig figs 3 sig figs 2. 402 2. 402 3. 5,280 3. 5,280 3 sig figs 2 sig figs 4. 0.080 4. 0.080

  46. 3 SF Significant Figures • Calculating with Sig Figs • Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 324g

  47. Significant Figures • Calculating with Sig Figs (con’t) • Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 224 g + 130 g 354 g 224 g + 130 g 354 g 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL  350 g  7.9 mL

  48. Significant Figures • Calculating with Sig Figs (con’t) • Exact Numbers do not limit the # of sig figs in the answer. • Counting numbers: 12 students • Exact conversions: 1 m = 100 cm • “1” in any conversion: 1 in = 2.54 cm

  49. 5. (15.30 g) ÷ (6.4 mL)  2.4 g/mL 2 SF Significant Figures Practice Problems 4 SF 2 SF = 2.390625 g/mL 6. 18.9 g - 0.84 g  18.1 g 18.06 g

  50. Rounding Rules

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