“Scientific Measurement & Problem Solving”

1. “Scientific Measurement & Problem Solving” SAVE PAPER AND INK!!! If you print out the notes on PowerPoint, print "Handouts" instead of "Slides“ in the print setup. Also, turn off the backgrounds (Tools>Options>Print>UNcheck "Background Printing")!

2. Types of Observations and Measurements • We makeQUALITATIVEobservations of reactions — Describes using words Ex. Odor, color, texture, and physical state. • We also makeQUANTITATIVE observations, using numbers- measurements • Ex. 25.3 mL, 4.239 g

3. Standards of Measurement When we measure, we use a measuring tool to compare some dimension of an object to a standard. For example, at one time the standard for length was the king’s foot. What are some problems with this standard?

4. Our measurements must be both Accurate & precise! Accuracy – how close a measurement comes to the true value of what is measured Precision – is concerned with the reproducibility of the measurement

5. Can you hit the bull's-eye? Three targets with three arrows each to shoot. How do they compare? Both accurate and precise Precise but not accurate Neither accurate nor precise

6. Stating a Measurement In every measurement there is a • Number followed by a • Unit from a measuring device The number should also be as precise as the measurement!

7. SI Measurement • Le Systeme International d’Unites : SI Metrics • System of measurement agreed on all over the world in 1960 • Contains 7 base units • units are defined in terms of standards of measurement that are objects or natural occurrence that are of constant value or are easily reproducible • We still use some non-SI units!

8. Le Système international d'unités • SI units— based on the metric system • The only countries that have not officially adopted SI are Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but now these are reportedly using metric regularly • Among countries with non-metric usage, the U.S. is the only country significantly holding out.The U.S. officially adopted SI in 1866. Information from U.S. Metric Association

9. The 7 Base Units of SI

10. S.I. (the ones you’re responsible for knowing!)

11. Derived Unitsmade by combining Base Units! • Volume length cubed m3 cm3 • Density mass/volume g/mL kg/L g/ cm3 g/L • Speed length /time mi/hr m/s km/hr • Area length squared m2 cm2

12. We use prefixes to expand on the base units!

13. kilo k 103 deci d 10-1 centi c 10-2 milli m 10-3 micro m 10-6 nano n 10-9

14. Metric System • These prefixes are based on powers of 10. • From each prefix every “step” is either: • 10 times larger or • 10 times smaller • For example • Centimeters are 10 times larger than millimeters • 1 centimeter = 10 millimeters

15. Metric System • An easy way to move within the metric system is by moving the decimal point one place for each “step” desired Example: change meters to centimeters 1.00 meter = 10.0 decimeters = 100. centimeters

16. A 1 kg bar will weigh 1 kg on earth 0.1 kg on moon • mass – measure of the quantity of matter • SI unit of mass is the kilogram (kg) • 1 kg = 1000 g = 1 x 103 g weight– mass + gravity force that gravity exerts on an object Mass does not vary from place to place! A 1 kg bar has a mass of 1 kg on earth and on the moon

17. Volume – Amount of space occupied by matter SI derived unit for volume is cubic meter (m3) m3 = m x m x m We often use the Liter (L) when working with liquid volumes! 1 L = 1000 mL= 1000 cm3 = 1 dm3 1 mL = 1 cm3 1 dm3 = 1 L

18. Anders Celsius 1701-1744 Lord Kelvin (William Thomson) 1824-1907 Temperature Scales • Fahrenheit • Celsius • Kelvin

19. TEMPERATURE SCALES In Chemistry, the terms heat and temperature are often used to describe specific properties of a sample. HEAT is the most common form of energy in nature and is directly related to the motion of particles of matter. The faster the motion of particles in a sample the greater its heat content.

20. TEMPERATURE is associated only with the intensity of heat and is not affected by the size of the sample. A forest fire and a lit match may both be at the same temperature, but there is a large difference in the amount of heat each possess. Heat always spontaneously flows from a hotter system (higher temp.) to a colder system (lower temp.).

21. 212 ˚F 100 ˚C 373 K 100 K 180˚F 100˚C 32 ˚F 0 ˚C 273 K Temperature Scales Fahrenheit Celsius Kelvin Boiling point of water Freezing point of water Notice that 1 Kelvin = 1 degree Celsius

23. Temperature Scientists do not know of any limit on how high a temperature may be. The temperature at the center of the sun is about 15,000,000 °C. However, nothing can have a temperature lower than –273°C. This temperature is called absolute zero. It forms the basis of the Kelvin scale. Because the Kelvin scale begins at absolute zero, 0 K equals –273°C, and 273 K equals 0 °C.

24. Calculations Using Temperature • Many chemistry equations require temp’s to be in Kelvin • K = ˚C + 273 • Body temp = 37 ˚C + 273 = 310 K • Liquid nitrogen = 273 -77 K = -196 ˚C ˚C = K - 273

25. Platinum Mercury Aluminum DENSITY – an important and useful physical property (Derived Unit)ratio of mass per unit of volume platinum mercury 13.6 g/cm3 21.5 g/cm3 2.7 g/cm3

26. Get out those calculators! ProblemA piece of copper has a mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. Calculate density (g/cm3). Copper ore Pure copper metal

27. SOLUTION 1. Get dimensions in common units. 2. Calculate volume in cubic centimeters. 3. Calculate the density. (9.36 cm)(7.23 cm)(0.095 cm) = 6.4 cm3

28. Learning Check Which diagram represents the liquid layers in the cylinder? (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) 1) 2) 3) V W K V W K W V K

29. Solution (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) 1) WATER!! Denser materials ‘sink’ in less dense materials! V W Most solids sink in their liquid form. Can you think of an exception to this?! K

30. Volume of an Irregular SolidWater Displacement A solid displaces a matching volume of water when the solid is placed in water. Volume of solid is 8 mL 33 mL 25 mL

31. Calculator Time! What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? a) 0.2 g/ cm3 b) 6.0 g/m3 c) 252 g/cm3 33 mL 25 mL

32. Percent Error • Percent Error: • Measures the inaccuracy of experimental data • Can have + or – value • Accepted value : correct value based on reliable references • Experimental value: value you measured in the lab

33. The number of atoms in 12 g of carbon: 602,200,000,000,000,000,000,000 The mass of a single carbon atom in grams: 0.0000000000000000000000199 Scientific Notation 6.022 x 1023 1.99 x 10-23 N x 10n N is a number between 1 and 10 n is a positive or negative integer

34. To change standard form to scientific notation… • Place the decimal point so that there is one non-zero digit to the left of the decimal point. • Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. • If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

35. Examples • Given: 289,800,000 • Use: 2.898 (moved 8 places) • Answer:2.898 x 108 • Given: 0.000567 • Use: 5.67 (moved 4 places) • Answer:5.67 x 10-4

36. To change scientific notation to standard form… • Simply move the decimal point to the right for positive exponent 10. • Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

37. Example • Given: 5.093 x 106 • Answer: 5,093,000 (moved 6 places to the right) • Given: 1.976 x 10-4 • Answer: 0.0001976 (moved 4 places to the left)

38. Learning Check • Express these numbers in Scientific Notation: • 405789 • 0.003872 • 3000000000 • 2 • 0.478260

39. move decimal left move decimal right Scientific Notation 568.762 0.00000772 n > 0 n < 0 568.762 = 5.68762 x 102 0.00000772 = 7.72 x 10-6 Addition or Subtraction • Write each quantity with the same exponent n • Combine N1 and N2 • The exponent, n, remains the same 4.31 x 104 + 3.9 x 103 = 4.31 x 104 + 0.39 x 104 = 4.70 x 104

40. Scientific Notation Calculations Multiplication (4.0 x 10-5) x (7.0 x 103) = (4.0 x 7.0) x (10-5+3) = 28 x 10-2 = 2.8 x 10-1 • Multiply N1 and N2 • Add exponentsn1and n2 • Put in proper format, if necessary Division 8.5 x 104÷ 5.0 x 109 = (8.5 ÷ 5.0) x 104-9 = 1.7 x 10-5 • Divide N1 and N2 • Subtract exponentsn1and n2 • Put in proper format, if necessary

41. Significant Figures • The numbers reported in a measurement are limited by the measuring tool • Significant Figures in a measurement include all certain digits plus one estimated digit

42. Significant Figures • All certain digits plus one estimated digit (used when recording measurements)

43. Known + Estimated Digits In 2.85 cm… • Known digits2and8are 100% certain (there are lines on the ruler for these!) • The third digit, 5, is estimated (uncertain) • In the reported length, all three digits (2.76 cm) are significant including the estimated one

44. Figure 5.5: Measuring a pin. There are not really lines on the scale here – just estimate!

45. Reading a Meterstick . l2. . . . I . . . . I3 . . . .I . . . . I4. . cm First digit (known) = 2 2.?? cm Second digit (known) = 0.8 2.8? cm Third digit (estimated) between 0.03- 0.05 Length reported =2.83 cm or 2.84 cm or 2.85 cm

46. Learning Check . l8. . . . I . . . . I9. . . . I . . . . I10. . cm What is the length of the line? 1) 9.3 cm 2) 9.40 cm 3) 9.30 cm How does your answer compare with your neighbor’s answer?

47. Rules forCounting Significant Figures RULE 1. All non-zero digits in a measured number are significant. Number of Significant Figures? 38.15 cm 5.6 mL 65.6 kg 122.55 m 4 2 3 5

48. Sandwiched Zeros RULE 2. Zeros between nonzero numbers are significant. Number of Significant Figures? 50.8 mm 2001 min .702 mg 400005 m 3 4 3 6

49. Leading Zeros (in front) RULE 3. Leading zeros in decimal numbers are NOT significant. Number of Significant Figures? 0.008 mm 0.0156 g 0.0042 cm 0.0002602 mL 1 3 2 4

50. Trailing Zeros (at end) RULE 4. Trailing zeros in numbers without decimals are NOT significant. They are only serving as place holders. Number of Significant Figures? 25,000 m 200 L 48,600 mg 25,005,000 kg 2 1 3 5