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Measurements and Calculations

Measurements and Calculations. Chapter 2. Scientific Method. A logical approach to solving problems by: Observing and collecting data Formulating hypotheses Testing hypotheses, and Formulating theories that are supported by data. Observing. Using the five senses to gather information

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Measurements and Calculations

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  1. Measurements and Calculations Chapter 2 Chemistry Chapter 2

  2. Scientific Method • A logical approach to solving problems by: • Observing and collecting data • Formulating hypotheses • Testing hypotheses, and • Formulating theories that are supported by data Chemistry Chapter 2

  3. Observing • Using the five senses to gather information • Often involves making measurements and collecting data Chemistry Chapter 2

  4. Qualitative data • Descriptive • Not numerical • Example – the sky is blue Chemistry Chapter 2

  5. Quantitative data • Numerical • Measurable or countable • Example – the temperature of the water went up 1 °C Chemistry Chapter 2

  6. System • A specific portion of matter in a given region of space • Has been selected for study during an experiment or observation • Must be defined by the experimenter Chemistry Chapter 2

  7. Formulating hypotheses • Hypothesis – testable statement • Generalizations about data • Basis for making predictions and designing experiments • Usually if-then statements Chemistry Chapter 2

  8. Testing hypotheses • Doing experiments • You must be ready to reject a hypothesis that is proven wrong Chemistry Chapter 2

  9. Theorizing • Model – an explanation of how phenomena occur and how data or events are related • May include a physical object or drawing • May be visual, verbal, or mathematical • Theory – a broad generalization that explains a body of facts or phenomena • Must predict to be successful Chemistry Chapter 2

  10. Discuss • Section Review • Page 31 Chemistry Chapter 2

  11. Quantity • Something that has magnitude, size, or amount. Chemistry Chapter 2

  12. SI Measurement • Le Système International d’Unités • Metric system • Seven base units – the rest are derived Chemistry Chapter 2

  13. Standards of measurement • Objects or phenomena that are of constant value, easy to preserve and reproduce, and practical in size. • Note – ten thousand is written 10 000, not 10,000. Some countries use the comma as a decimal point. Chemistry Chapter 2

  14. Mass • Measure of the quantity of matter • Kilogram is base unit • kg • Your textbook has a mass of about 1 kg • A paper clip has a mass of about 1 g, or 1/1000 of a kg Chemistry Chapter 2

  15. Mass vs. weight • Weight is the measure of the gravitational pull on matter. • The weight of an object on the moon is 1/6 its weight on earth, but its mass is the same. Chemistry Chapter 2

  16. Length • Meter • m • About 39 inches – width of a doorway • 1 km = 1000 m • 1 m = 100 cm Chemistry Chapter 2

  17. Other base units • Time – seconds – s • Temperature – kelvin – K • Amount of substance – mole – mol • Electric current – ampere – A • Luminous intensity – candela – cd Chemistry Chapter 2

  18. Prefixes • Used to indicate multiples of 10 • See table 2-2 on page 35 Chemistry Chapter 2

  19. Derived SI units • Combinations of base units • Can also use prefixes Chemistry Chapter 2

  20. Volume • Amount of space occupied by an object. • SI unit is cubic meters, or m3 • We often use cubic centimeters, or cm3 • Important – 1 cm3 = 1 mL • 1 m3 = 1 000 000 cm3 • We also use the liter, or L • Equal to 1 cubic dm, or dm3 • There are 1000 mL in 1 L Chemistry Chapter 2

  21. Density • The ratio of mass to volume Chemistry Chapter 2

  22. Density • SI unit is kg/m3 • We often use g/mL or g/cm3 in Chemistry • g/L or kg/m3 might be used for gases Chemistry Chapter 2

  23. Conversion factors • Used to convert from one unit to another • A ratio derived from equality Chemistry Chapter 2

  24. Example • How many seconds are in 1 day? Chemistry Chapter 2

  25. Example • How many centigrams are there in 6.25 kg? Chemistry Chapter 2

  26. Units • When doing conversions, keep track of your units. • They should cancel out to get units you want at the end. Chemistry Chapter 2

  27. Examples using table • Convert 10 cm to m. • Convert 25 mL to L. • Convert 50 mg to kg. • Convert 33 cm3 to mm3. Chemistry Chapter 2

  28. Discuss • Section Review • Page 42 Chemistry Chapter 2

  29. Accuracy vs. Precision • Accuracy – closeness to correct or accepted value • Precision – closeness of a set of measurements of the same quantity made the same way • See page 44, figure 2-3 Chemistry Chapter 2

  30. Percent error • Finds accuracy of a single value or an average value. • See sample problem 2-3 on page 45 Chemistry Chapter 2

  31. Reading instruments • Estimate the last digit. • Example – a ruler is marked to a tenth of a centimeter. • Your measurement should be to the nearest hundredth of a centimeter. • Example – a thermometer is marked to the nearest degree. • Your measurement should be to the nearest tenth of a degree Chemistry Chapter 2

  32. Significant Figures • All the digits known in a measurement, plus one that is somewhat uncertain. • All nonzero digits are significant • Zeros are governed by four rules • Zeros between nonzero digits are significant • 203 has 3 sig figs • 5.0279 has 5 sig figs Chemistry Chapter 2

  33. Significant Figures • Zeros in front of all nonzero digits are not significant • 0.0035 has 2 sig figs • 0.0008 has 1 sig fig • Zeros at the end of a number and after the decimal point are significant. • 75.000 has 5 sig figs • 0.000800 has 3 sig figs Chemistry Chapter 2

  34. Significant Figures • Zeros at the end of a number but before the decimal point may or may not be significant. • If a zero is just a placeholder, it is not significant. • If it has been measured, it is significant. To show all zeros are significant, use a decimal point. • To show some are, use scientific notation (tomorrow) • 2000 has 1 sig fig • 2000. has 4 sig figs Chemistry Chapter 2

  35. 2.5 2 sig figs 2.50 3 sig figs 250 2 sig figs 2.50 x 102 3 sig figs 250.0 4 sig figs 0.0025 2 sig figs 0.00250 3 sig figs 0.002501 4 sig figs How many sig figs? Chemistry Chapter 2

  36. Rounding • If the next digit is less than five, round down. • 3.044 → 3.04 • If the next digit is more than five, round up. • 3.046 → 3.05 • If the next digit is a five and there are nonzero digits after it, round up • 3.0452 → 3.05 • If the next digit is a five and not followed by nonzero digits round to the even number • 3.045 → 3.04 • 3.035 → 3.04 Chemistry Chapter 2

  37. Adding or subtracting with sig figs • The answer must have the same number of digits after the decimal point as there are in the measurement with the fewest digits after the decimal point. Chemistry Chapter 2

  38. Example • Since 1.040 only has 3 sig figs after the decimal, the answer can only have 3 sig figs after the decimal. Round the answer to 1.253 Chemistry Chapter 2

  39. Multiplication and Division • The result should have the same number of significant figures as the least number of significant figures in any factor. Chemistry Chapter 2

  40. Example • Since 1.2 only has 2 sig figs, our answer can only have 2 sig figs. We would round our answer to 1.6 Chemistry Chapter 2

  41. Conversion factors • Are not considered when finding the number of significant figures. • Are exact Chemistry Chapter 2

  42. Discuss • How do you round a number that ends in a five if you are rounding to the place before the five? • What is the difference between accuracy and precision? • How many significant figures are in the answer when you multiply? When you subtract? Chemistry Chapter 2

  43. Scientific Notation • Useful when writing very small or very large numbers • 696 000 000 m = 6.96 x 108 m • 4 000 000 km = 4 x 106 km • 0.012 kg = 1.2 x 10-2 kg • 0.000 000 000 567 s = 5.67 x 10-10 s Chemistry Chapter 2

  44. Scientific notation • The mantissa (number in front) is greater than or equal to 1 but less than 10. • Only significant figures are shown. • All digits shown are significant figures. • 2000 has 1 sig fig • 2000. has 4 sig figs • 2.0 x 103 has 2 sig figs • 2.00 x 103 has 3 sig figs Chemistry Chapter 2

  45. Multiplying in Scientific Notation • Multiply the mantissas. • Multiply the units. • Add the exponents. Chemistry Chapter 2

  46. Example Chemistry Chapter 2

  47. Dividing in scientific notation • Divide the mantissas. • Divide the units • Subtract the exponents. Chemistry Chapter 2

  48. Example Chemistry Chapter 2

  49. Addition and subtraction • If the exponents (and units) are the same, you can simply add or subtract the mantissas and keep the exponents and units the same. • If the exponents are different, do it on your calculator. • Your book shows you how, but most people don’t like to do it that way. • If the units are different, you can’t add or subtract. Chemistry Chapter 2

  50. Direct proportions • Two quantities are directly proportional if dividing one by the other gives a constant. • Graph is a straight line that passes through the origin • General forms of the equation: Chemistry Chapter 2

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