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Slide 2 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 Slide 3 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 Slide 4 100 mL Graduated Cylinder Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119 Slide 5 Instruments for Measuring Volume Graduated cylinder SyringeVolumetric flask BuretPipet Slide 6 Units of Measuring Volume 1 L = 1000 mL 1 qt = 946 mL Timberlake, Chemistry 7 th Edition, page 3 Slide 7 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 Slide 8 Units for Measuring Mass 1 kg = 2.20 lb Timberlake, Chemistry 7 th Edition, page 3 Slide 9 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 Slide 10 Quantities of Mass Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25 Earths 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- Slide 11 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 Slide 12 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 Slide 13 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 Slide 14 Metric Article Keys Metric ArticleMetric Article (questions)questions Metric ArticleMetric Article (questions)(questions) http://www.unit5.org/chemistry/intro.html Slide 15 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 Slide 16 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) Slide 17 Accuracy vs. Precision Random errors: reduce precision Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Systematic errors: reduce accuracy Slide 18 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. Slide 19 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 Slide 20 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. Cant be corrected. Can only be accounted for by using statistics. Slide 21 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 Slide 22 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 Slide 23 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. Slide 24 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 Slide 25 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 Slide 26 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 Slide 27 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 Slide 28 Measuring a Pin Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 122 Slide 29 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 Slide 30 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. Slide 31 20 10 ? 15 mL ? 15.0 mL1.50 x 10 1 mL Slide 32 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 Slide 33 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 Slide 34 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 Slide 35 750 740 760 If we do another reading with the vernier at a differ