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CHEM 10: CHAPTER TWO

CHEM 10: CHAPTER TWO. MEASUREMENT & PROBLEM SOLVING. Scientific Notation. Very large and very small numbers are often encountered in science. Large: 602210000000000000000000 And small: 0.00000000000000000000625

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CHEM 10: CHAPTER TWO

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  1. CHEM 10: CHAPTER TWO MEASUREMENT & PROBLEM SOLVING

  2. Scientific Notation Very large and very small numbers are often encountered in science. Large: 602210000000000000000000 And small: 0.00000000000000000000625 Very large and very small numbers like these are awkward and difficult to work with. A method for representing these numbers in a simpler form is called scientific notation. Large: 6.022 x 1023 And small: 6.25 x 10-21

  3. Scientific Notation To write a number as a power of 10 - Move the decimal point in the original number so that it is located after the first nonzero digit. - Follow the new number by a multiplication sign and 10 with an exponent (power). - The exponent is equal to the number of places that the decimal point was shifted.

  4. Write 6419 in scientific notation. decimal after first nonzero digit power of 10 6.419 x 103 64.19x102 641.9x101 6419. 6419

  5. Write 0.000654 in scientific notation. decimal after first nonzero digit power of 10 6.54 x 10-4 0.000654 0.00654 x 10-1 0.0654 x 10-2 0.654 x 10-3

  6. Scientific Notation Adding and subtracting in exponential or scientific notation: - must be in same power of ten Try adding: 3.47x102 + 5.93267x105 0.00347x105 + 5.93267x105 = 5.93614x105

  7. Scientific Notation Multiplying and dividing: 10a * 10b = 10a+b 10a/10b = 10a-b Your calculator will do all this for you, if you enter the numbers correctly! Group practice: A. 3.47 x 102 * 1.20 x 10-3 = B. 0.0012 + 1.3 x 10-2 = C. 3.47 x 102 / 1.20 x 10-3 = A. 4.16 x 10-1 B. 1.4 x 10-2 C. 2.89 x 105

  8. Measurements Experiments are performed. Numerical values or data are obtained from these measurements. The values are recorded to the most significant digits provided by the measuring device. The units (labels) are recorded with the values.

  9. numerical value 70.0 kilograms = 154 pounds unit Form of a Measurement

  10. known estimated Significant Figures The number of digits that are known plus one estimated digit are considered significant in a measured quantity 5.16143

  11. known estimated Significant Figures The number of digits that are known plus one estimated digit are considered significant in a measured quantity 6.06320

  12. The temperature 21.2oC is expressed to 3 significant figures. Temperature is estimated to be 21.2oC. The last 2 is uncertain.

  13. The temperature 22.0oC is expressed to 3 significant figures. Temperature is estimated to be 22.0oC. The last 0 is uncertain.

  14. The temperature 22.11oC is expressed to 4 significant figures. Temperature is estimated to be 22.11oC. The last 1 is uncertain.

  15. Exact Numbers Exact numbers have an infinite number of significant figures. Exact numbers occur in simple counting operations 1 2 3 4 5 • Defined numbers are exact. 12 inches = 1 foot 100 centimeters = 1 meter

  16. Significant Figures All nonzero numbers are significant. 461

  17. Significant Figures All nonzero numbers are significant. 461

  18. Significant Figures All nonzero numbers are significant. 461

  19. Significant Figures All nonzero numbers are significant. 3 Significant Figures 461

  20. Significant Figures A zero is significant when it is between nonzero digits. 3 Significant Figures 401

  21. Significant Figures A zero is significant when it is between nonzero digits. 5 Significant Figures 9 3 . 0 0 6

  22. Significant Figures A zero is significant when it is between nonzero digits. 3 Significant Figures 9 . 0 3

  23. Significant Figures A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures 5 5 . 0 0 0

  24. Significant Figures A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures 2 . 1 9 3 0

  25. Significant Figures A zero is not significant when it is before the first nonzero digit. 1 Significant Figure 0 . 0 0 6

  26. Significant Figures A zero is not significant when it is before the first nonzero digit. 3 Significant Figures 0 . 7 0 9

  27. Significant Figures A zero is not significant when it is at the end of a number without a decimal point. 1 Significant Figure 5 0 0 0 0

  28. Significant Figures A zero is not significant when it is at the end of a number without a decimal point. 4 Significant Figures 6 8 7 1 0

  29. Rounding Off Numbers Often when calculations are performed extra digits are present in the results. It is necessary to drop these extra digits so as to express the answer to the correct number of significant figures. When digits are dropped the value of the last digit retained is determined by a process known as rounding off numbers.

  30. Rounding Off Numbers Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed. 4 or less 80.873

  31. Rounding Off Numbers Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed. 4 or less 1.875377

  32. 5 or greater drop these figures Rounding Off Numbers Rule 2. When the first digit after those you want to retain is 5 or greater, that digit and all others to its right are dropped. The last digit retained is increased by 1. increase by 1 5.459672 6

  33. CALCULATIONS AND SIGNIFICANT FIGURES The results of a calculation cannot be more precise than the least precise measurement. Learn how to determine number of sig figs in answers after performing calculations, including multiply/divide and add/subtract. In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures.

  34. CALCULATIONS AND SIGNIFICANT FIGURES The results of an addition or a subtraction must be expressed to the same precision as the least precise measurement. - The result must be rounded to the same number of decimal places as the value with the fewest decimal places.

  35. Drop these three digits. 2.3 has two significant figures. (190.6)(2.3) = 438.38 190.6 has four significant figures. Answer given by calculator. The answer should have two significant figures because 2.3 is the number with the fewest significant figures. Round off this digit to four. 438.38 The correct answer is 440 or 4.4 x 102

  36. 125.17 129. 52.2 Add 125.17, 129 and 52.2 Least precise number. Answer given by calculator. 306.37 Round off to the nearest unit. Correct answer. 306.37

  37. 0.018286814 Drop these 6 digits. Correct answer. Answer given by calculator. Two significant figures. The answer should have two significant figures because 0.019 is the number with the fewest significant figures.

  38. The Metric System The metric or International System (SI, Systeme International) is a decimal system of units. It is built around standard units. It uses prefixes representing powers of 10 to express quantities that are larger or smaller than the standard units.

  39. International System’s Standard Units of Measurement Quantity Name of Unit Abbreviation Length meter m Mass kilogram kg Temperature Kelvin K Time second s Amount of substance mole mol

  40. Prefixes and Numerical Values for SI Units Power of 10 Prefix Symbol Numerical Value Equivalent exa E 1,000,000,000,000,000,000 1018 peta P 1,000,000,000,000,000 1015 tera T 1,000,000,000,000 1012 giga G 1,000,000,000 109 mega M 1,000,000 106 kilo k 1,000 103 hecto h 100 102 deca da 10 101 — —1 100

  41. Prefixes and Numerical Values for SI Units Power of 10 Prefix Symbol Numerical Value Equivalent deci d 0.1 10-1 centi c 0.01 10-2 milli m 0.001 10-3 micro 0.000001 10-6 nano n 0.000000001 10-9 pico p 0.000000000001 10-12 femto f 0.00000000000001 10-15 atto a 0.000000000000000001 10-18

  42. GROUP RACE FOR ANSWERS IN METRIC a. one millionth of a scope = ____scope b. 0.01 mental = ____mental c. 1,000,000 phones = ___phones d. 2000 mockingbird =___bird e. 1/1000 tary =___tary

  43. MEMORIZE THESE ENGLISH/METRIC CONVERSIONS: (table 2.3 plus others) 1 lb = 453.59 grams 1 inch = 2.54 cm (exactly) 1 mile = 1.609 km 1.0567 qt = 1 L 1000 mL = 1 L 1 mL = 1 cm3 1 cal = 4.184 Joule 1 atm = 760.00 torr oF = 1.8oC + 32 K = oC + 273.15

  44. Dimensional Analysis Dimensional analysis converts one unit to another by using conversion factors. unit1 x conversion factor = unit2 Basic Steps 1. Read the problem carefully. Determine what is to be solved for and write it down. 2. Tabulate the data given in the problem. Label all factors and measurements with the proper units.

  45. Dimensional Analysis Basic steps – continued: 3. Determine which principles are involved and which unit relationships are needed to solve the problem. You may need to refer to tables for needed data. 4. Set up the problem in a neat, organized and logical fashion. Make sure unwanted units cancel. Use sample problems in the text as guides for setting up the problem.

  46. Dimensional Analysis Basic steps continued: 5. Proceed with the necessary mathematical operations. Make certain that your answer contains the proper number of significant figures. 6. Check the answer to make sure it is reasonable.

  47. Metric Units of Length Exponential Unit Abbreviation Metric Equivalent Equivalent kilometer km 1,000 m 103 m meter m 1 m 100 m decimeter dm 0.1 m 10-1 m centimeter cm 0.01 m 10-2 m millimeter mm 0.001 m 10-3 m micrometer m 0.000001 m 10-6 m nanometer nm 0.000000001 m 10-9 m

  48. How many millimeters are there in 2.5 meters? Use the conversion factor with millimeters in the numerator and meters in the denominator.

  49. Convert 3.7 x 103 cm to micrometers. Centimeters can be converted to micrometers by writing down conversion factors in succession. cm  m meters

  50. Convert 3.7 x 103 cm to micrometers. Centimeters can be converted to micrometers by two stepwise conversions. cm  m meters

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