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Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors Accuracy vs. Precision Accuracy Precision Resolution SI units for Measuring Length Comparison of English and SI Units Reporting Measurements Measuring a Pin Practice Measuring

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Measurement 100 mL Graduated Cylinder Units of Measuring Volume Reading a Meniscus Units for Measuring Mass Quantities of Mass SI-English Conversion Factors Accuracy vs. Precision Accuracy Precision Resolution SI units for Measuring Length Comparison of English and SI Units Reporting Measurements Measuring a Pin Practice Measuring

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100 mL Graduated Cylinder Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119

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Instruments for Measuring Volume Graduated cylinder SyringeVolumetric flask BuretPipet

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Units of Measuring Volume 1 L = 1000 mL 1 qt = 946 mL Timberlake, Chemistry 7 th Edition, page 3

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Reading a Meniscus 10 8 6 line of sight too high reading too low reading too high line of sight too low proper line of sight reading correct graduated cylinder 10 mL

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Units for Measuring Mass 1 kg = 2.20 lb Timberlake, Chemistry 7 th Edition, page 3

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Christopherson Scales Made in Normal, Illinois USA Units for Measuring Mass 1 kg = 2.20 lb 1 kg (1000 g) 1 lb 0.20 lb

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Quantities of Mass Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25 Earth’s atmosphere to 2500 km Ocean liner Indian elephant Average human 1.0 liter of water Grain of table salt Typical protein Uranium atom Water molecule 10 24 g 10 21 g 10 18 g 10 15 g 10 12 g 10 9 g 10 6 g 10 3 g 10 0 g 10 -3 g 10 -6 g 10 -9 g 10 -12 g 10 -15 g 10 -18 g 10 -21 g 10 -24 g Giga- Mega- Kilo- base milli- micro- nano- pico- femto- atomo-

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Factor Name Symbol Factor Name Symbol 10 -1 decimeter dm 10 1 decameter dam 10 -2 centimeter cm 10 2 hectometer hm 10 -3 millimeter mm 10 3 kilometer km 10 -6 micrometer m 10 6 megameter Mm 10 -9 nanometer nm 10 9 gigameter Gm 10 -12 picometer pm 10 12 terameter Tm 10 -15 femtometer fm 10 15 petameter Pm 10 -18 attometer am 10 18 exameter Em 10 -21 zeptometer zm 10 21 zettameter Zm 10 -24 yoctometer ym 10 24 yottameter Ym

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Scientific Notation: Powers of Ten Rules for writing numbers in scientific notation: Write all significant figures but only the significant figures. Place the decimal point after the first digit, making the number have a value between 1 and 10. Use the correct power of ten to place the decimal point properly, as indicated below. a) Positive exponents push the decimal point to the right. The number becomes larger. It is multiplied by the power of 10. b) Negative exponents push the decimal point to the left. The number becomes smaller. It is divided by the power of 10. c) 10 o = 1 Examples: 3400 = 3.20 x 103 0.0120 = 1.20 x 10-2 Nice visual display of Powers of Ten (a view from outer space to the inside of an atom) viewed by powers of 10!a view from outer space to the inside of an atom

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Multiples of bytes as defined by IEC 60027-2bytesIEC 60027-2 SI prefixBinary prefixes NameSymbolMultipleName Sy mb ol Multiple kilobytekB10 3 10 3 (or 2 10 )kibibyteKiB2 10 megabyteMB10 6 10 6 (or 2 20 )mebibyteMiB2 20 gigabyteGB10 9 10 9 (or 2 30 )gibibyteGiB2 30 terabyteTB10 12 10 12 (or 2 40 )tebibyteTiB2 40 petabytePB10 15 10 15 (or 2 50 )pebibytePiB2 50 exabyteEB10 18 10 18 (or 2 60 )exbibyteEiB2 60 zettabyteZB10 21 10 21 (or 2 70 ) yottabyteYB10 24 10 24 (or 2 80 ) A yottabyte (derived from the SI prefix )SI prefix

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Metric Article Keys Metric ArticleMetric Article (questions)questions Metric ArticleMetric Article (questions)(questions) http://www.unit5.org/chemistry/intro.html

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SI-US Conversion Factors RelationshipConversion Factors Length Volume Mass 2.54 cm = 1 in. 1 m = 39.4 in. 946 mL = 1 qt 1 L = 1.06 qt 454 g = 1 lb 1 kg = 2.20 lb 1 in 2.54 cm 39.4 in 1 m 39.4 in. 946 mL 1 qt 946 mL 1.06 qt 1 L 1.06 qt 454 g 1 lb 454 g 2.20 lb 1 kg 2.20 lb 2.54 cm 1 in and

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Accuracy vs. Precision Random errors: reduce precision Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Systematic errors: reduce accuracy (person)(instrument)

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Accuracy vs. Precision Random errors: reduce precision Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Systematic errors: reduce accuracy

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Precision Accuracy reproducibility check by repeating measurements poor precision results from poor technique correctness check by using a different method poor accuracy results from procedural or equipment flaws.

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Types of errors Systematic Instrument not ‘zeroed’ properly Reagents made at wrong concentration Random Temperature in room varies ‘wildly’ Person running test is not properly trained

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Errors Systematic Errors in a single direction (high or low) Can be corrected by proper calibration or running controls and blanks. Random Errors in any direction. Can’t be corrected. Can only be accounted for by using statistics.

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Accuracy Precision Resolution subsequent samples time offset [arbitrary units] not accurate, not precise accurate, not precise not accurate, precise accurate and precise accurate, low resolution -2 -3 0 1 2 3

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Accuracy Precision Resolution subsequent samples time offset [arbitrary units] not accurate, not precise accurate, not precise not accurate, precise accurate and precise accurate, low resolution -2 -3 0 1 2 3

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Standard Deviation The standard deviation, SD, is a precision estimate based on the area score: where x i is the i- th measurement x is the average measurement N is the number of measurements. y 0 x One standard deviation away from the mean in either direction on the horizontal axis (the red area on the graph) accounts for around 68 percent of the people in this group. Two standard deviations away from the mean (the red and green areas) account for roughly 95 percent of the people. Three standard deviations (the red, green and blue areas) account for about 99 percent of the people.

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SI Prefixes kilo-1000 deci- 1 / 10 centi- 1 / 100 milli- 1 / 1000 Also know… 1 mL = 1 cm 3 and 1 L = 1 dm 3

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SI System for Measuring Length Unit Symbol Meter Equivalent _______________________________________________________________________ kilometerkm 1,000 m or 10 3 m meter m 1 m or 10 0 m decimeterdm 0.1 m or 10 -1 m centimetercm 0.01 m or 10 -2 m millimetermm 0.001 m or 10 -3 m micrometer m 0.000001 m or 10 -6 m nanometernm 0.000000001 m or 10 -9 m The SI Units for Measuring Length Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118

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Comparison of English and SI Units 1 inch 2.54 cm 1 inch = 2.54 cm Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119

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Reporting Measurements Using significant figures Report what is known with certainty Add ONE digit of uncertainty (estimation) Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

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Measuring a Pin Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 122

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Practice Measuring 4.5 cm 4.54 cm 3.0 cm Timberlake, Chemistry 7 th Edition, page 7 cm 0 12345 0 12345 0 12345

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Implied Range of Uncertainty 5 64 3 Implied range of uncertainty in a measurement reported as 5 cm. 5 64 3 Implied range of uncertainty in a measurement reported as 5.0 cm. Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32 5 64 3 Implied range of uncertainty in a measurement reported as 5.00 cm.

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20 10 ? 15 mL ? 15.0 mL1.50 x 10 1 mL

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Reading a Vernier A Vernier allows a precise reading of some value. In the figure to the left, the Vernier moves up and down to measure a position on the scale. This could be part of a barometer which reads atmospheric pressure. The "pointer" is the line on the vernier labeled "0". Thus the measured position is almost exactly 756 in whatever units the scale is calibrated in. If you look closely you will see that the distance between the divisions on the vernier are not the same as the divisions on the scale. The 0 line on the vernier lines up at 756 on the scale, but the 10 line on the vernier lines up at 765 on the scale. Thus the distance between the divisions on the vernier are 90% of the distance between the divisions on the scale. http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html 756

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Reading a Vernier A Vernier allows a precise reading of some value. In the figure to the left, the Vernier moves up and down to measure a position on the scale. This could be part of a barometer which reads atmospheric pressure. The "pointer" is the line on the vernier labeled "0". Thus the measured position is almost exactly 756 in whatever units the scale is calibrated in. If you look closely you will see that the distance between the divisions on the vernier are not the same as the divisions on the scale. The 0 line on the vernier lines up at 756 on the scale, but the 10 line on the vernier lines up at 765 on the scale. Thus the distance between the divisions on the vernier are 90% of the distance between the divisions on the scale. 756 750 760 770 Scale 5 0 10 Vernier http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html

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If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately 746.5 on the scale. If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is 746.5. 5 0 10 750 740 760 What is the reading now? 741.9 http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html

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750 740 760 If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately 746.5 on the scale. If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is 746.5. 5 0 10 What is the reading now? 756.0 http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html

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750 740 760 Here is a final example, with the vernier at yet another position. The pointer points to a value that is obviously greater than 751.5 and also less than 752.0. Looking for divisions on the vernier that match a division on the scale, the 8 line matches fairly closely. So the reading is about 751.8. In fact, the 8 line on the vernier appears to be a little bit above the corresponding line on the scale. The 8 line on the vernier is clearly somewhat below the corresponding line of the scale. So with sharp eyes one might report this reading as 751.82 ± 0.02. This "reading error" of ± 0.02 is probably the correct error of precision to specify for all measurements done with this apparatus. 5 0 10 http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html

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How to Read a Thermometer (Celcius) 10 5 0 4.0 o C 10 5 0 8.3 o C 100 50 0 64 o C 5 0 3.5 o C

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0oC0oC 10 o C 20 o C 30 o C 40 o C 50 o C 60 o C 0oC0oC 1oC1oC 2oC2oC 3oC3oC 4oC4oC 5oC5oC 6oC6oC 0oC0oC 5oC5oC 10 o C 15 o C 20 o C 25 o C 0oC0oC 20 o C 40 o C 60 o C 80 o C 100 o C 0oC0oC 20 o C 40 o C 60 o C 80 o C 100 o C Record the Temperature (Celcius) A B C D E 30.0 o C 3.00 o C19.0 o C 48 o C 60. o C

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Measurements Metric (SI) units Prefixes Uncertainty Significant figures Significant figures Conversion factors Conversion factors Length Density Mass Volume Problem solving with conversion factors Problem solving with conversion factors Timberlake, Chemistry 7 th Edition, page 40

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I II III Using Measurements MEASUREMENT Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Accuracy vs. Precision Accuracy Accuracy - how close a measurement is to the accepted value Precision Precision - how close a series of measurements are to each other ACCURATE = Correct PRECISE = Consistent Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Percent Error Indicates accuracy of a measurement your value accepted value Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Percent Error A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 % Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Significant Figures Indicate precision of a measurement. Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Significant Figures Counting Sig Figs (Table 2-5, p.47) Count all numbers EXCEPT: Leading zeros -- 0.0025 Trailing zeros without a decimal point -- 2,500 Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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4. 0.080 3. 5,280 2. 402 1. 23.50 Significant Figures Counting Sig Fig Examples 1. 23.50 2. 402 3. 5,280 4. 0.080 4 sig figs 3 sig figs 2 sig figs Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Significant Figures Calculating with Sig Figs Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm 3 )(23.3cm 3 ) = 324.103g 324 g 4 SF3 SF Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Significant Figures Calculating with Sig Figs (con’t) Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g 7.9 mL 350 g 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Significant Figures Calculating with Sig Figs (con’t) Exact Numbers do not limit the # of sig figs in the answer. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Significant Figures 5. (15.30 g) ÷ (6.4 mL) Practice Problems = 2.390625 g/mL 18.1 g 6. 18.9g - 0.84 g 18.06 g 4 SF2 SF 2.4 g/mL 2 SF Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Scientific Notation Converting into scientific notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1) positive exponent Small # (<1) negative exponent Only include sig. figs. 65,000 kg 6.5 × 10 4 kg Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Scientific Notation 7. 2,400,000 g 8. 0.00256 kg 9.7 10 -5 km 10.6.2 10 4 mm Practice Problems 2.4 10 6 g 2.56 10 -3 kg 0.00007 km 62,000 mm Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Scientific Notation Calculating with scientific notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 EXP EE ÷ ÷ EXP EE ENTER EXE 78.1 4 = 671.6049383= 670 g/mol= 6.7 × 10 2 g/mol Type on your calculator: Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Proportions Direct Proportion Inverse Proportion y x y x Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

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Reviewing Concepts Measurement Why do scientists use scientific notation? What system of units do scientists use for measurements? How does the precision of measurements affect the precision of scientific calculations? List the SI units for mass, length, and temperature.

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Rules for Counting Significant Figures 1. Nonzero integers always count as significant figures. 2. Zeros: There are three classes of zeroes. a.Leading zeroes precede all the nonzero digits and DO NOT count as significant figures. Example: 0.0025 has ____ significant figures. b.Captive zeroes are zeroes between nonzero numbers. These always count as significant figures. Example: 1.008 has ____ significant figures. c.Trailing zeroes are zeroes at the right end of the number. Trailing zeroes are only significant if the number contains a decimal point. Example: 1.00 x 10 2 has ____ significant figures. Trailing zeroes are not significant if the number does not contain a decimal point. Example: 100 has ____ significant figure. 3.Exact numbers, which can arise from counting or definitions such as 1 in = 2.54 cm, never limit the number of significant figures in a calculation. 2 4 3 1 Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination 2006, page 53

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Significant figures: Rules for zeros Leading zeros are not significant. Captive zeros are significant. Trailing zeros are significant. Leading zero Captive zero Trailing zero 0.421 4012 114.20 – three significant figures – four significant figures – five significant figures

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Significant Digits Keys Significant Digits http://www.unit5.org/chemistry/intro.html

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How to pick a lab partner ?

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