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Section 2.1 Units and Measurements

Section 2.1 Units and Measurements. Pages 32-39. International System of Units (SI System).

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Section 2.1 Units and Measurements

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  1. Section 2.1Units and Measurements Pages 32-39

  2. International System of Units (SI System) • In 1960, the metric system was standardized in the form of the International System of Units (SI). These SI units were accepted by the international scientific community as the system for measuring all quantities.

  3. SI Base Unitsare defined by an object or event in the physical world. • The foundation of the SI is seven independent quantities • and their SI base units. You must learn the first 5 • quantities listed!

  4. SI Prefixes • SI base units are not always convenient to use so prefixes are attached to the base unit, creating a more convenient easier-to-use unit. You must memorize these!

  5. Temperature Temperature is a measure of the average kinetic energy of the particles in a sample of matter. • The Fahrenheit scale is not used in chemistry.

  6. SI Derived Units • In addition to the seven base units, other SI units can be made from combinations of the base units. • Area, volume, and density are examples of derived units. • Volume (m3 or dm3 or cm3 ) length  length  length • 1 cm3 = 1 mL • 1 dm3 = 1 L

  7. m • V • D= Density Density (kg/m3 or g/cm3 or g/mL) is a physical property of matter. • m = mass • V = volume

  8. 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 = 11,220 g • m = 11,200 g (correct sig figs)

  9. Density A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? • WORK: • V = m • D • V = 25 g • 0.87 g/mL • GIVEN: • D = 0.87 g/mL • V = ? • m = 25 g • = 28.736 mL • V = 29 mL (correct sig figs)

  10. Non SI Units The volume unit, liter (L), and temperature unit, Celsius (C), are examples of non-SI units frequently used in chemistry.

  11. SI & English Relationships One meter is approximately 3.3 feet. One kilogram weighs approximately 2.2 pounds at the surface of the earth. Remember: Mass (amount of material in the object) is constant,but weight (force of gravity on the object) may change. One liter or one dm3 is slightly more than a quart, 1.06 quart to be exact.

  12. Section 2.2Scientific Notation Pages 40-43

  13. Scientific Notation

  14. Scientific Notation In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we deal with some very SMALL numbers: Mass of an electron = 0.000000000000000000000000000000091 kg

  15. Imagine the difficulty of calculating the mass of 1 mole of electrons! 0.000000000000000000000000000000091 kg x 602000000000000000000000 • ???????????????????????????????????

  16. Scientific Notation: A method of representing very large or very small numbers in the form: M x 10n • Mis a number between1and10 • nis an integer

  17. 2 500 000 000 . 9 7 6 5 4 3 2 1 8 Step #1: Insert an understood decimal point Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

  18. 2.5 x 109 The exponent is the number of places we moved the decimal.

  19. 0.0000579 • 1 • 2 • 3 • 4 • 5 Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

  20. 5.79 x 10-5 The exponent is negative because the number we started with was less than 1.

  21. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION

  22. Review: Scientific notation expresses a number in the form: M x 10n n is an integer 1  M  10

  23. IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 4 x 106 + 3 x 106 7 x 106

  24. The same holds true for subtraction in scientific notation. 4 x 106 - 3 x 106 1 x 106

  25. If the exponents are NOT the same, we must move a decimal to make them the same. 4 x 106 + 3 x 105

  26. 4.00 x 106 4.00 x 106 + .30 x 106 + 3.00 x 105 4.30 x 106 Move the decimal on the smaller number!

  27. A Problem for you… 2.37 x 10-6 + 3.48 x 10-4

  28. Solution… 002.37 x 10-6 2.37 x 10-6 +3.48 x 10-4

  29. Solution… 0.0237 x 10-4 + 3.48 x 10-4 3.5037 x 10-4

  30. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION Multiplication and Division

  31. Multiplication 4.0 x 106 Exponents do NOT have to be the same. MULTIPLY the coefficients and then ADD the exponents. X3.0 x 105 12 x 1011 1.2 x 1012 Rewrite in proper scientific notation.

  32. Division 4.0 x 106 Exponents do NOT have to be the same. DIVIDE the coefficients and then SUBTRACT the exponents. ÷3.0 x 105 1.3 x 101

  33. Section 2.2Dimensional Analysis Pages 44-46

  34. Dimensional Analysis • Dimensional Analysis A tool often used in science for converting units within a measurement system by using • Conversion Factors A numerical factor by which a quantity expressed in one system of units may be converted to another system

  35. Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 cm = 10 mm Factors: 1 cm and 10 mm 10 mm 1 cm

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

  37. Dimensional Analysis • Steps to solving problems: 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.

  38. How many minutes are in 2.5 hours? conversion factor cancel 60 min 1 hr =150 min 2.5 hr 1 x By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

  39. Convert400 mL to Liters L 400 mL 1 .400 L = 1000 mL =0.4 L =4x10-1 L

  40. Convert0.02 kilometers to m m 0.02 km 1 000 m 20 = 1 km = 2x101 m

  41. Squared and Cubed Conversions Convert 455.5 cm3 to dm3. 1dm=10cm

  42. Multiple Unit Conversions Convert 568 mg/dL to g/L. 1 g = 1000 mg 1L = 10 dL

  43. Section 2.3 Uncertainty in Data Pages 47-49

  44. Types of Observations and Measurements • We make QUALITATIVE observations of reactions — changes in color and physical state. • We also make QUANTITATIVE MEASUREMENTS, which involve numbers.

  45. Measurement – quantitative observation consisting of two parts: Number Scale (unit) Examples: 20 grams 6.63 × 10-34joule·seconds Nature of Measurement

  46. Accuracy vs. Precision • Accuracy - how close a measurement is to the accepted value • Precision - how close a series of measurements are to each other • ACCURATE = CORRECT • PRECISE = CONSISTENT

  47. Accuracy vs. Precision

  48. Precision and Accuracy in Measurements • In the real world, we never know whether the measurement we make is accurate • We make repeated measurements, and strive for precision • We hope (not always correctly) that good precision implies good accuracy

  49. your value • given value Percent Error • Indicates accuracy of a measurement

  50. Percent Error • A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. • (correct sig figs)

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