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Chapter 3 “ Scientific Measurement ”

Chapter 3 “ Scientific Measurement ”. Olympic High School Chemistry - Mr Daniel Credits: Stephen L. Cotton Charles Page High School. Section 3.1 Measurements and Their Uncertainty. OBJECTIVES: Convert measurements to scientific notation. Section 3.1 Measurements and Their Uncertainty.

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Chapter 3 “ Scientific Measurement ”

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  1. Chapter 3“Scientific Measurement” Olympic High School Chemistry - Mr Daniel Credits: Stephen L. Cotton Charles Page High School

  2. Section 3.1Measurements and Their Uncertainty • OBJECTIVES: • Convert measurements to scientific notation.

  3. Section 3.1Measurements and Their Uncertainty • OBJECTIVES: • Distinguish among accuracy, precision, and error of a measurement.

  4. Section 3.1Measurements and Their Uncertainty • OBJECTIVES: • Determine the number of significant figures in a measurement and in a calculated answer.

  5. Measurements • Qualitative measurements are descriptive words, such as “heavy” or “warm” • Quantitative measurements involve numbers (quantities), and depend on: • The reliability of the measuring instrument • the care with which it is read – this is determined by YOU!

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

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

  8. Accuracy, Precision, and Error Error = accepted value – experimental value Can be positive or negative • Accepted value = the correct value based on reliable references • Experimental value = the value measured in the lab

  9. Accuracy, Precision, and Error Percent error = the absolute value of the error divided by the accepted value, then multiplied by 100. | error | acceptedvalue accepted (true) value % error = x 100

  10. Chemistry“Scientific Notation Review” Olympic High School Mr. Daniel

  11. 1. Scientific Notation …Is also called Exponential Notation • Scientists often use very large or very small numbers • 602 000 000 000 000 000 000 000 Called Avogadro’s Number • 0.000 000 000 114 m The radius of a bromine atom

  12. 1. Scientific Notation • Large numbers are very inconvenient, even difficult • Thus, very large or small numbers should be written in Scientific Notation • In Scientific Notation, the number is the product of two different components: • A coefficient • Exponent: A power of 10

  13. 1. Scientific Notation • 2300 is: 2.3 x 103 • A coefficient is a number greater than or equal to one, and less than ten • The coefficient here is 2.3 • The exponent is how many times the coefficient is multiplied by ten… • The product of 2.3 x 10 x 10 x 10 equals 2300 (2.3 x 103)

  14. 1. Scientific Notation • The value of the exponent changes to indicate the number of places the decimal has moved left or right. • 12 000 000 = • 0.00356 = • 85 130 = • 0.000 05 = • 0.0342 = 1.2 x 107 3.56 x 10-3 8.513 x 104 5 x 10-5 3.42 x 10-2

  15. 1. Scientific Notation • Multiplication and Division • Use of a calculator is permitted • use it correctly • No calculator? Multiply the coefficients, and add the exponents: (3 x 104) x (2 x 102) = (3.5 x 106) x (4.0 x 1012) = 6 x 106 1.4 x 1019

  16. 1. Scientific Notation • Multiplication and Division • In division, divide the coefficients, and subtract the exponent in the denominator from the numerator 3.0 x 105 5 x 102 = 6.0 x 102

  17. 1. Scientific Notation • Addition and Subtraction • Before numbers can be added or subtracted, the exponents must be the same • Calculators will take care of this • Doing it manually, you will have to make the exponents the same - it does not matter which one you change.

  18. 1. Scientific Notation • Addition and Subtraction (6.6 x 10-8) + (4.0 x 10-9) = (3.42 x 10-5) – (2.5 x 10-6) = 7.0 x 10-8 3.2 x 10-5 (Note that these answers have been expressed in standard form)

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

  20. Significant Figures!!

  21. 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 must be reported to the correct number of significant figures.

  22. Figure 3.5 Significant Figures - Page 67 Which measurement is the best? What is the measured value? What is the measured value? What is the measured value?

  23. Rules for Counting Significant Figures Non-zerosalways count as significant figures: 3456kmhas 4significant figures

  24. Rules for Counting Significant Figures Zeros Captive zerosalways count as significant figures: 16.07 cmhas 4 significant figures

  25. Rules for Counting Significant Figures Zeros Leading zerosnever count as significant figures: 0.0486 mL has 3 significant figures

  26. Rules for Counting Significant Figures Zeros Trailing zerosare significant only if the number contains a written decimal point: 9.300 g has 9300 g has 9300. g has 4 significant figures 2 significant figures 4 significant figures

  27. Rules for Counting Significant Figures Two special situations have an unlimited number of significant figures: • Counted items • 23 people, or 425 thumbtacks • Exactly defined quantities • 60 minutes = 1 hour

  28. Sig Fig Practice #1 How many significant figures in the following? 1.0070 m 5 sig figs 17.10 kg 4 sig figs 100,890 L 5 sig figs These come from measurements 3.20 x 103 s 3 sig figs 0.0054 cm 2 sig figs 3,200,000 g 2 sig figs This is a counted value 5 dogs unlimited

  29. Significant Figures in Calculations • A calculated answer is only as accurate as the least accurate measurement from which it is calculated. Just like a chain which is only as strong as the weakest link… …sometimes, calculated values need to be rounded off.

  30. Rounding Calculated Answers • A quick reminder about Rounding • Determine how many significant figures are needed • Locate that final digit by counting from the left • Is the next digit to the right less than 5? • No change to the final digit • Is the next digit to the right 5 or greater? • Increase the final digit by 1

  31. - Page 59 Round off each measurement to the number of significant figures shown in parentheses: • 314.721 meters (four) • 0.001775 meter (two) c)8792 meters (two) 314.7 meters 0.0018 meter 8800 meters

  32. Rules for Significant Figures in Mathematical Operations Multiplication and Division:The number of significant figures in an answer equals the number in the least accurate measurement used in the calculation. 6.38 cm x 2.0 cm = 12.76 cm2 sigfig answer : 13 cm2 (2 sig figs)

  33. Sig Fig Practice #2 Calculation Calculator says: Answer 22.68 m2 3.24 m x 7.0 m 23 m2 100.0 g ÷ 23.7 cm3 4.21 g/cm3 4.214409283 g/cm3 0.02 cm x 2.371 cm 0.05 cm2 0.04742 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 5870 lb·ft 1818.2 lb x 3.23 ft 5871.786 lb·ft 1.030 g x 2.87 mL 2.9561 g/mL 2.96 g/mL

  34. Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the answer equals the number of decimal places in the least accurate measurement. 6.8 cm +11.934 cm = 18.734 cm sigfig answer  18.7 cm (3 sig figs)

  35. Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 10.24 m 10.2 m 100.0 g - 23.73 g 76.3 g 76.27 g 0.02 cm + 2.371 cm 2.39 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1821.6 lb 1818.2 lb + 3.37 lb 1821.57 lb 2.030 mL - 1.870 mL 0.160 mL 0.16 mL *Note the zero that has been added.

  36. Section 3.3The International System of Units • 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.

  37. International System of Units • Measurements depend upon units that serve as reference standards • The Metric system was first introduced by the French following the French Revolution • It was revised and renamed the International System of Units (SI), as of 1960. • The standards of measurement used in science are those of the SI.

  38. International System of Units SI has several advantages: -Used world-wide -Simple -Based on powers of 10 • There are eight base units which are commonly used in chemistry: meter, cubic meter, kilogram, kelvin, second, joule, pascal and mole.

  39. The Fundamental SI Units(Le Système International, SI) (Liter) (gram) (ºCelsius) (calorie)

  40. Nature of Measurements Measurement - quantitative observation consisting of 2 parts: 1 ) number 2 ) unit Examples:20 grams 6.63 x 10-34 joules-seconds

  41. International System of Units Derived units: These are not measured directly, but are calculated, showing the relationship between two other measurements: • Speed = miles/hour (distance/time) • Density = grams/mL (mass/volume)

  42. Length • In SI, the basic unit of length is the meter (m) • The meter is one ten millionth (0.000 000 1 ) the distance from the equator to the North Pole. • Or more accurately for the 21st century: 1 meter equals 1,650,763.73 wavelengths of light given off from an isotope of Krypton… We make use of prefixes for units larger or smaller…

  43. SI Prefixes Common to Chemistry Learn These!!!

  44. Converting Measurements in the SIe.g. 1.2 mm= µm 1) Mark the value of prefixes of both units 1.2 mm= µm 2) Determine the difference in the number of place values of the two prefixes by subtracting. This is how many places the decimal is to be moved. -3-(-6) = 10-6 10-3 +3

  45. Converting Measurements in the SI(continued) 3) If the difference is a positive number, move the decimal place to the right to make the numerical value larger If the difference is a negative number, move the decimal place to the left to make the numerical value smaller The difference is positive (+3) therefore 1.2 becomes 1200 The final answer is 1200 µm

  46. Volume • The space occupied by any sample of matter. • Calculated for a solid by multiplying the length x width x height; thus derived from units of length. • SI unit = cubic meter (m3) • Everyday unit = Liter (L), which is non-SI. Note: 1000mL = 1 L 1mL = 1cm3

  47. Devices for Measuring Liquid Volume • Graduated cylinders • Pipets • Burets • Volumetric Flasks • Syringes

  48. The Volume Changes! • Volumes of a solid, liquid, or gas will generally increase with temperature • Therefore, measuring instruments are calibrated for a specific temperature, usually 20 oC, which is about room temperature

  49. Units of Mass • Mass is a measure of the quantity of matter present • Mass is constant, regardless of location Weight is a force that measures the pull by gravity- it changes with location

  50. Working with Mass • The SI unit of mass is the kilogram (kg), even though a more convenient everyday unit is the gram • It’s measuring instrument is the balance

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