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Chapter 3 Scientific Measurement

Chapter 3 Scientific Measurement. 3.1 Measurements and Uncertainty. OBJECTIVES : Convert measurements to scientific notation Distinguish among accuracy, precision, and error of a measurement Determine the number of significant figures in a measurement and in a calculated answer.

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Chapter 3 Scientific Measurement

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  1. Chapter 3Scientific Measurement

  2. 3.1 Measurements and Uncertainty • OBJECTIVES: • Convert measurements to scientific notation • Distinguish among accuracy, precision, and error of a measurement • Determine the number of significant figures in a measurement and in a calculated answer

  3. Measurements • We make measurements every day: buying products, sports activities, and cooking • Qualitative measurements are words, such as heavy or hot • Quantitative measurements involve numbers (quantities), and depend on: • The reliability of the measuring instrument • the care with which it is used and read – this is determined by YOU! • Scientific Notation • Coefficient raised to power of 10 (ex. 1.3 x 107) • Review: Textbook pages R56 & R57 as needed

  4. Accuracy, Precision, Error • It is necessary to make good, reliable measurements in the lab • Accuracy – how close a measurement is to the true/accepted value • Precision – how close repeated measurements are to each other (reproducibility)

  5. Precision and Accuracy Precise, but not accurate Neither accurate nor precise Precise AND accurate

  6. Concept Check • A standard 100 g mass is measured on a triple beam balance repeatedly by several students. An average mass was calculated from the following measurements: 98.45 g, 96.86 g, 101.04 g, 102.98 g, 100.97 g. • Are the measurements accurate? Are they precise? Explain

  7. Accuracy, Precision, and Error • Accepted (expected) value = the correct value based on reliable references (Density Table page 90) • Experimental (observed) value = the value measured in the lab

  8. Accuracy, Precision, and Error • Error • = experimental value – accepted value • Can be positive or negative • Percent error = the error divided by the accepted value, multiplied by 100% exp. value – accepted value accepted value % error = x 100%

  9. Why Is there Uncertainty? • Measurements are performed with instruments, and no instrument can read to an infinite number of decimal places • Which graduate cylinder has the greatest uncertainty in measurement?

  10. LabPractice What volumes are contained in the graduated cylinders pictured below? 1 4 5 3 2

  11. Significant Figures in Measurements • Significant figures in a measurement include all of the digits that are known, plus one more digit that is estimated. • Measurements should be reported to the correct number of significant figures.

  12. Figure 3.5 Significant Figures - Page 67 Which measurement is the best? What is the measured value? We “know” that the measurement is between 0-1 m, and estimate it to be 0.6 m. Thus only one sig fig, the estimated digit. The 6 in this measurement is known, and the 1 is estimated. Thus two sig figs. The board is between 0.60 and 0.61 m. Thus the 6 and 0 are known and the 7 is an estimate. Three sig figs. What is the measured value? What is the measured value?

  13. Rounding Calculated Answers • Addition and Subtraction • The answer should be rounded to the same number of decimal places as the least number of decimal places in the problem.

  14. Practice Problem • Three measurements are recorded. Add them together and express the answer with the correct number of significant figures. 12.72 m 24.052 m 5.1m 41.872 m Only one decimal place here   = 41.9 m So, only one decimal place here

  15. Rules for Significant Figures in Mathematical Operations • Multiplication and Division:# sig figs in the result equals the number in the least precise measurement used in the calculation. • 6.38 x 2.0 = • 12.76 13 (2 sig figs)

  16. Sig Fig Practice Calculation Calculator says: Answer 22.68 m2 3.24 m x 7.0 m 100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 0.02 cm x 2.371 cm 0.04742 cm2 710 m ÷ 3.0 s 236.6666667 m/s 1818.2 N x 3.23 m 5872.786 N·m 2.9561 g/ml 1.030 g x 2.87 ml

  17. Sig Fig Practice Calculation Calculator says: Answer 10.24 m 3.24 m + 7.0 m 100.0 g - 23.73 g 76.27 g 0.02 cm + 2.371 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 1818.2 kg + 3.37 kg 1821.57 kg 0.16 mL 2.030 mL - 1.870 mL

  18. 3.2 International System of Measurement • OBJECTIVES: • List SI units of measurement and common SI prefixes • Distinguish between the mass and weight of an object • Convert between the Celsius and Kelvin temperature scales

  19. International System of Units • Measurements depend upon units that serve as reference standards • The standards of measurement used in science are those of the Metric System

  20. International System of Units • Metric system is revised and called the International System of Units (SI) • 7 base units, but five commonly used in chemistry: meter, kilogram, kelvin, second, and mole.

  21. The Fundamental SI Units(Le Système International, SI)

  22. SI Prefixes – Page 74Common to Chemistry

  23. Nature of Measurements Measurement - quantitative observation consisting of 2 parts: • Part 1 – number • Part 2 - scale (unit) • Examples: • 20 grams • 6.63 x 10-34 Joule·seconds

  24. International System of Units • Some non-SI units used in chemistry • Liter, Celsius degree, calorie • Some are derived units • They are made by joining other units • Speed = miles/hour (distance/time) • Density = grams/mL (mass/volume)

  25. Length • Length basic unit = meter (m) • distance between two points • measured with ruler • How long is the yellow bar?

  26. Volume • Volume = space occupied by matter. • Units: volume is calculated from units of length; thus derived from units of length. • Common SI units = m3, cm3) • Everyday unit = Liter (L), non-SI. • (Note: 1 mL = 1 cm3) • Measured with: • Ruler - if a regular, geometrical shape • Graduated cylinder – for liquids and irregularly shaped solids (displacement method)

  27. Devices for Measuring Precise Liquid Volumes

  28. Volume Changes! • Volumes of solids and liquids generally increase slightly with increasing temperature • Much more prominent for GASES • Therefore, measuring instruments are calibrated for a specific temperature • usually 20oC, ~ room temperature

  29. Mass vs Weight • Massmeasure of quantity of matter present • Weight is a force that measures the pull by gravity • it changes with location: the moon vs the earth • Mass is constant, it’s the same everywhere

  30. Mass • SI unit of mass = kilogram(kg) • In chemistry, a more convenient everyday unit is the gram (g) • Measuring instrument is the balance

  31. Units of Temperature (Measured with a thermometer.) • Temperature is a measure of how hot or cold an object is. • Heat moves from the object at the higher temperature to the object at the lower temperature. • We use two units of temperature: • Celsius • Kelvin

  32. Units of Temperature • Celsius scale defined by two readily determined temperatures: • F.P. of water at sea level = 0oC • B.P. of water at sea level = 100oC • Kelvin scale does not use degree sign, it’s just K • absolute zero = 0 K (thus no negative values) • formula to convert: K = oC + 273

  33. Units of Energy • Energy is the capacity to do work, or to produce heat. • Energy can also be measured, and two common units are: • Joule (J) = the SI unit of energy • calorie (cal) = the heat needed to raise 1 gram of water by 1oC • Conversions: 1 cal = 4.184 J

  34. 3.3 Conversion Problems • OBJECTIVES: • Construct conversion factors from equivalent measurements • Apply the techniques of dimensional analysis to a variety of conversion problems • Solve problems by breaking the solution into steps • Convert complex units, using dimensional analysis

  35. Conversion factors • A “ratio” of equivalent measurements • Start with two things that are the same: one meter is one hundred centimeters • write it as an equation 1 m = 100 cm • We can divide on each side of the equation to come up with two ways of writing the number “1”

  36. 1 m 100 cm 100 cm 100 cm Conversion factors 100 cm = = 1 m 1 =

  37. Conversion factors 1 day 1 = 24 hr 1 L 1 = 1000 cm3 (1 L = 1000 ml = 1000 cm3)

  38. Conversion Factors • A useful way of writing the number 1 • Provide a value that will let you convert a known/given value with particular units into an unknown value with different units

  39. Practice by writing conversion factors for the following: • Between kilograms and grams • Between hours and minutes • Between tricycles and wheels • Between insects and legs

  40. Conversion Factors • Called conversion factors because they allow us to convert units • really just multiplying by one, in a creative way

  41. Practice • Question: How many minutes in 1 week? 1 week x x x = 7 days 1 week 60 min 1 hr 24 hrs 1 day 10,080 min

  42. Dimensional Analysis • A way to analyze and solve problems, by using units (or dimensions) of the measurement • Dimension = a unit (such as moles, g, L, mL) • Analyze = to solve • Using the units to solve the problems.

  43. Converting Between Units • Problems in which measurements with one unit are converted to an equivalent measurement with another unit are easily solved using dimensional analysis • Sample: Express 750 cm in meters. • Many complex problems are best solved by breaking the problem into manageable parts.

  44. Converting Complex Units? • Complex units are those that are expressed as a ratio of two units: • Speed = m/sec • Such units are useful conversion factors • Ex: 15 m/s = 15 m/1 s = 1 s/15 m • In a problem, this “known” value would allow you to convert from meters to seconds, or from seconds to meters! • How do we work with units that are squared or cubed? (cm3 to m3, etc.)

  45. Useful Complex Units The density of manganese is 7.21 g/cm3. How many milliliters of water would be displaced if a 100 g cube of manganese was placed into a beaker of water? Given: 100 g Mn and = Asked: volume in milliliters Analyze: How do we get from the units given to the one asked for? Solution: use density value to cancel g and replace with cm3, then convert cm3 ml (1 cm3 = 1 ml) 1 cm3 7.21 g Mn 7.21 g Mn 1 cm3

  46. 3.4 Density • OBJECTIVES: • Calculate the density of a material from experimental data • Describe how density varies with temperature

  47. Density • = mass per unit of volume = mass/volume • = how heavy something is for its size • Which is heavier- a kilogram of lead or a kilogram of feathers? • Many will answer lead, but the mass is exactly the same • They are normally thinking about equal volumes of the two

  48. Density • Common units: g/mL, g/cm3, (or for gases, often g/L) • Density is an intensive physical property, thus does not depend upon sample size

  49. Note temperature and density units - Page 90

  50. Density and Temperature • What happens to the density as the temperature of an object increases? • Mass remains same (numerator) • Most substances increase in volume as T increases (denominator) • Thus, density generally decreases as temperature increases

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