1. Chapter 3 Scientific 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: 1) The reliability of the measuring instrument 2) 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 10 7 )  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 Neither accurate nor precise Precise, but not accurate 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 exp. value – accepted value accepted value accepted value x 100% % error =

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

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.

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 5.1m 41.872 m = 41.9 m Only one decimal place here   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 3.24 m x 7.0 m CalculationCalculator says:Answer 22.68 m 2 100.0 g ÷ 23.7 cm 3 4.219409283 g/cm 3 0.02 cm x 2.371 cm 0.04742 cm 2 710 m ÷ 3.0 s 236.6666667 m/s 1818.2 N x 3.23 m5872.786 N·m 1.030 g x 2.87 ml 2.9561 g/ml

17. Sig Fig Practice 3.24 m + 7.0 m CalculationCalculator says:Answer 10.24 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 kg1821.57 kg 2.030 mL - 1.870 mL 0.16 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 74 Common to Chemistry Prefix Unit Abbreviation MeaningExponent Kilo-k thousand 10 3 Centi-c hundredth 10 -2 Milli-m thousandth 10 -3 Micro- millionth 10 -6

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

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 = m 3, cm 3 )  Everyday unit = Liter (L), non-SI.  (Note: 1 mL = 1 cm 3 )  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 20 o C, ~ room temperature

29. Mass vs Weight  Mass measure 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 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 (Measured with a thermometer.)

32. Units of Temperature Celsius scale defined by two readily determined temperatures: –F.P. of water at sea level = 0 o C –B.P. of water at sea level = 100 o C Kelvin scale does not use degree sign, it’s just K absolute zero = 0 K (thus no negative values) absolute zero = 0 K (thus no negative values) formula to convert: K = o C + 273formula to convert: K = o C + 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: 1) Joule (J) = the SI unit of energy 2) calorie (cal) = the heat needed to raise 1 gram of water by 1 o C  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 one meter is one hundred centimeters write it as an equation write it as an equation 1 m = 100 cm 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. Conversion factors 100 cm1 m = 100 cm 1 = = 1 m

37. Conversion factors 1 1 day = 24 hr = 1 L 1000 cm 3 1 (1 L = 1000 ml = 1000 cm 3 )

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 xx= 7 days 1 week 24 hrs 1 day 60 min 1 hr 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? (cm 3 to m 3, etc.)

45. Useful Complex Units The density of manganese is 7.21 g/cm 3. 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 cm 3, then convert cm 3  ml (1 cm 3 = 1 ml) 7.21 g Mn 1 cm 3 7.21 g Mn

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/cm 3, (or for gases, often g/L ) Common units: g/mL, g/cm 3, (or for gases, often g/L ) Density is an intensive physical property, thus does not depend upon sample size Density is an intensive physical property, thus does not depend upon sample size

49. - Page 90 Note temperature and density units

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

51. Density and Water  Water is an important exception to the previous statement.  Over certain temperatures, the volume of water increases as the temperature decreases (Do you want your water pipes to freeze in the winter?)  Does ice float in liquid water?  Why?

52. Practice Problem What is the volume of a pure silver coin that has a mass of 14 g? The density of silver is 10.5 g/cm 3.