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Chemistry

Chemistry. Chapter 3: Scientific Measurement (pages 60-99). IA. Accuracy and Precision. Accuracy and Precision.

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Chemistry

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  1. Chemistry Chapter 3: Scientific Measurement (pages 60-99)

  2. IA. Accuracy and Precision

  3. Accuracy and Precision To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

  4. Accuracy vs. Precision • In chemistry, the meanings of accuracy and precision are quite different. • Accuracy - is a measure of how close a measurement comes to the actual or true value of whatever is measured. • Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

  5. Accuracy and Precision Darts on a dartboard illustrate the difference between accuracy and precision. Poor Accuracy, Good Precision Good Accuracy, Good Precision Poor Accuracy, Poor Precision The closeness of a dart to the bull’s-eye corresponds to the degree of accuracy. The closeness of several darts to one another corresponds to the degree of precision.

  6. IB. Significant Figures

  7. Significant Figures Why must measurements be reported to the correct number of significant figures?

  8. Significant Figures Significant figures are used by scientist to figure out how to round an answer in a problem. Significant figures are used in real-world math and not in ideal sense math (like in your math class). It indicates the precision of a measurement and the precision of the instrument used.

  9. Rule # 1 Numbers other than zero are always significant. Example: 96 g 2SF 61.4 g 3SF 0.52 g 2SF

  10. Rule # 2 One or more final zeros (trailing zeros) used after the decimal point are always significant. Example: 4.72 g 3SF 4.7200 g 5SF 82.0 g 3SF

  11. Rule # 3 Zeros between two other numbers (or “trapped” zeros) are always significant. Example: 5.029 m 4SF 306k m 3SF

  12. Rule # 4 Zeros used for spacing the decimal point are not significant. Example: 7000 g 1SF 0.00783 g 3SF

  13. Significant Figures Counting Sig Fig Examples 1. 23.50 1. 23.50 4 sig figs 3 sig figs 2. 402 2. 402 3. 5,280 3. 5,280 3 sig figs 2 sig figs 4. 0.080 4. 0.080

  14. CHEMISTRY&YOU Suppose that the winner of a 100-meter dash finishes the race in 9.98 seconds. The runner in second place has a time of 10.05 seconds. How many significant figures are in each measurement? Is one measurement more accurate than the other? Explain your answer. • There are three significant figures in 9.98 and four in 10.05. Both measurements are equally accurate because both measure the actual time of the runner to the hundredth of a second.

  15. Significant Figures in Calculations • In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated. • The calculated value must be rounded to make it consistent with the measurements from which it was calculated.

  16. Significant Figures in Calculations Rounding • To round a number, you must first decide how many significant figures the answer should have. • This decision depends on the given measurements and on the mathematical process used to arrive at the answer. • Once you know the number of significant figures your answer should have, round to that many digits, counting from the left.

  17. Significant Figures in Calculations Rounding • If the digit immediately to the right of the last significant digit is less than 5, it is simply dropped and the value of the last significant digit stays the same. • If the digit in question is 5 or greater, the value of the digit in the last significant place is increased by 1.

  18. SampleProblem 3.4 Rounding Measurements Round off each measurement to the number of significant figures shown in parentheses. Write the answers in scientific notation. a. 314.721 meters (four) b. 0.001 775 meter (two) c. 8792 meters (two)

  19. Significant Figures Significant Figures in Calculations Multiplication and Division Rule: The result of multiplication or division carries the same number of significant figures as the factor with the fewest significant figures.

  20. Significant Figures in Calculations Multiplication and Division Rule: The intermediate result (in blue) is rounded to two significant figures to reflect the least precisely known factor (0.10), which has two significant figures.

  21. Significant Figures in Calculations Multiplication and Division Rule: The intermediate result (in blue) is rounded to three significant figures to reflect the least precisely known factor (6.10), which has three significant figures.

  22. Significant Figures in Multiplication and Division Perform the following operations. Give the answers to the correct number of significant figures. a. 7.55 m x 0.34m b. 2.4526 m2÷ 8.4 m c. 10 m x 0.70 m d. 0.365 m2 ÷ 0.0200 m

  23. Significant Figures Significant Figures in Calculations Addition and Subtraction Rule: In addition or subtraction calculations, the result carries the same number of decimal places as the quantity carrying the fewest decimal places.

  24. Significant Figures in Calculations Addition and Subtraction Rule: We round the intermediate answer (in blue) to two decimal places because the quantity with the fewest decimal places (5.74) has two decimal places.

  25. Significant Figures in Calculations Addition and Subtraction Rule: We round the intermediate answer (in blue) to one decimal place because the quantity with the fewest decimal places (4.8) has one decimal place.

  26. SampleProblem 3.5 Significant Figures in Addition and Subtraction Perform the following addition and subtraction operations. Give each answer to the correct number of significant figures. • 12.52 m + 349.0 m + 8.24 m • b. 74.626 m – 28.34 m

  27. Both Multiplication/Division and Addition/Subtraction In calculations involving both multiplication/division and addition/subtraction • do the steps in parentheses first; • determine the correct number of significant figures in the intermediate answer without rounding; • then do the remaining steps.

  28. Both Multiplication/Division and Addition/Subtraction • In the calculation 3.489 × (5.67 – 2.3), do the step in parentheses first. 5.67 – 2.3 = 3.37 • Use the subtraction rule to determine that the intermediate answer has only one significant decimal place. • To avoid small errors, it is best not to round at this point; instead, underline the least significant figure as a reminder. 3.489 × 3.37 = 11.758 = 12 • Use the multiplication rule to determine that the intermediate answer (11.758) rounds to two significant figures (12) because it is limited by the two significant figures in 3.37.

  29. IC. Scientific Notation

  30. Scientific Notation How do you write numbers in scientific notation?

  31. In chemistry, you will often encounter very large or very small numbers. • A single gram of hydrogen, for example, contains approximately 602,000,000,000,000,000,000,000 hydrogen atoms. • You can work more easily with very large or very small numbers by writing them in scientific notation.

  32. In scientific notation, a given number is written as the product of two numbers: a coefficient and 10 raised to a power. • For example, the number 602,000,000,000,000,000,000,000 can be written in scientific notation as 6.02 x 1023. • The coefficient in this number is 6.02. The power of 10, or exponent, is 23.

  33. Writing numbers in Scientific Notation 65,000 kg  6.5 × 104 kg Converting into Sci. Notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1)  positive exponentSmall # (<1)  negative exponent Only include sig figs.

  34. To Convert a Number to Scientific Notation • If the decimal point is moved to the left, the exponent is positive. • If the decimal point is moved to the right, the exponent isnegative.

  35. Scientific Notation Practice Problems 2.4  106 g 1. 2,400,000 g 2. 0.00256 kg 3. 7  10-5 km 4. 6.2  104 mm 2.56  10-3 kg 0.00007 km 62,000 mm

  36. EXE EXP EXP ENTER EE EE Scientific Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = • Calculating with Sci. Notation Type on your calculator: 8.1 4 5.44 7 ÷ = 670 g/mol = 6.7 × 102 g/mol = 671.6049383

  37. II. Units of Measurement

  38. Number vs. Quantity • Quantity - number + unit UNITS MATTER!!

  39. CHEMISTRY&YOU What’s the forecast for tomorrow—hot or cold? Will the high temperature tomorrow be 28°C, which is very warm? Or 28°F, which is very cold? Without the correct units, you can’t be sure.

  40. The metric system was originally established in France in 1795. • The International System of Units (abbreviated SI after the French name, Le Système International d’Unités) is a revised version of the metric system. • The SI was adopted by international agreement in 1960.

  41. There are seven SI base units. • From these base units, all other SI units of measurement can be derived (made). • Derived units are used for measurements such as volume, density, and pressure.

  42. III. Conversion Problems

  43. Dimensional Analysis • The “Factor-Label” Method • Units, or “labels” are canceled, or “factored” out

  44. Prefixes you will use! (handout) PrefixSymbolPower of 10 Giga G 109 mega M 106 Kilo k 103 Base Unit m,L,g,s 100 Deci d 10-1 Centi c 10-2 Milli m 10-3 Micro  10-6 Nano n 10-9 + -

  45. Dimensional Analysis • Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

  46. SI Prefix Conversions 0.2 32 1) 20 cm = ______________m 2) 0.032 L = _____________mL

  47. Dimensional Analysis • How many milliliters are in 1.00 quart of milk? 1 L 1.057 qt 1000 mL 1 L 1.00 qt = 946 mL

  48. Dimensional Analysis • Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? 8.0 cm 1 in 2.54 cm = 3.2 in

  49. Dimensional Analysis • Tellico football needs 550 cm for a 1st down. How many yards is this? 1 ft 12 in 1 yd 3 ft 1 in 2.54 cm 550 cm = 6.0 yd

  50. IV. Density

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