Unit 1: Measurement and Conversions .

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Scientific Notation Review Often used to express very large or very small numbers. Also used to maintain correct number of significant figures. Form: (# from 1 to 9.999) x 10 exponent 800 2531 0.0014 = 8 x 10 2 = 8 x 10 x 10 = 2.531 x 10 x 10 x 10 = 2.531 x 10 3 = 1.4 / 10 / 10 / 10 = 1.4 x 10 -3

Change the given number to standard form. 1.87 x 10 5 = 3.7 x 10 8 = 7.88 x 10 1 = 2.164 x 10 2 = 370,000,000 0.0000187 78.8 0.02164 000000187000000 Scientific Notation Practice (-) exponent = number < 1 (+) exponent = number > 1

Change the given number into scientific notation. 12,340 = 0.369 = 0.008 = 1,000,000,000 = 1.234 x 10 4 3.69 x 10 1 8 x 10 3 1 x 10 9 Scientific Notation Practice

Significant Figures A student is combining separate water samples, all of differing volumes, into one large bucket. Samples A, B and C are 25.5 mL, 16.37 mL and 51 mL, respectively. Once combined, what is the total volume of all the samples? 92.87 mL NO! Because the samples were each measured with a different level of precision, we must factor that into our calculations by identifying what are called significant figures. about

Measurement and Accuracy The last digit of any measured number is assumed to be an estimate (uncertain) The second to last digit is assumed to be known with certainty (based on a line) A (25.5 mL)B (16.37 mL)C (51 mL) 26 25 16.4 16.3 60 50

Identifying Significant Figures Counting SFs in a number Non-zero numbers: ALWAYS count as SF Zeroes Left: NEVER count as SF (0.000345) Middle: ALWAYS count as SF (5001) Right: sometimes w/ decimal point: count as SF (25.10) w/o decimal point: DO NOT count as SF (8200) Exact Numbers: IGNORE SF Counts (28 students in this class) Constants (1 mol = 6.022 x 10 23 ) Conversions (1 in = 2.54 cm) Relative to the non-zero numbers.

How many Sig Figs? Measurement Number of SF 1.25 g 2.0.030 kg 3.1.240560 x 10 6 mg 4.6 x 10 4 sec 5.246.31 g 6.20.06 cm 7.1.050 m 8.0.12 kg 9.1240560. cm 10.6000000 kg 11.6.00 x 10 6 kg 12.409 cm 13.29.200 dm 14.0.02500 g 2 2 7 1 5 4 4 2 7 1 3 3 5 4

Sig Figs with Calculations Note: For any calculations, always perform the entire calculation without rounding, and then round the final answer. Addition/Subtraction Round the answer to the LEAST number of decimal places found (least precise) 11.31 + 33.264 + 4.1 = 48.674 Multiplication/Division Round the answer to the smallest number of SF found 5.282 x 3.42 = 18.06444 rounded to 48.7 rounded to 18.1 (3.42 only has 3 SF)

Back to the original question A student is combining separate water samples, all of differing volumes, into one large bucket. Samples A, B and C are 25.5 mL, 16.37 mL and 51 mL, respectively. Once combined, what is the total volume of all the samples? 25.5 mL + 16.37 mL + 51 mL = 92.87 mL 93 mL Could I write that as 93.0? NO!

More practice with SF If you made measurements of three samples of water (128.7 mL, 18 mL and 23.45 mL), and then poured all of the water together in one, unmarked container, what total volume of water should you report? Support your answer. 128.7 mL + 18 mL + 23.45 mL = 170.15 mL 170. mL or 1.70 x 10 2 mL

= -6.118 x 10 -9 = 3.63 x 10 9 = 15.563 report -6 x 10 -9 (1 SF) report 3.6 x 10 9 (2 SF) report 15.6 (tenths place) = 16.27 report 20 (tens place) = 1.7225 x 10 -5 report 1.7 x 10 -5 (2 SF) Practice with Sig Fig Calculations Complete calculation, and then follow order of operations to determine how many SF would be carried for each step 1.A 2.A 3.A 4.A 5.A

The Metric System from Industry Week, 1981 November 30

SI System The International System of Units abbreviated SI from the French Le Systme international d'units Based on the metric system (with small variations) Based on powers of ten Uses prefixes to differentiate between powers Used in nearly country except U.S. (Liberia and Myanmar are some others)

The International System of Units Volumeliter L Lengthmeter m Masskilogram kg Timesecond s Amount of substancemole mol Thermodynamic temperatureKelvin K Electric currentamperes amps Luminous intensitycandela cd QuantityNameSymbol Dorin, Demmin, Gabel, Chemistry The Study of Matter, 3 rd Edition, 1990, page 16

Area and Volume: Derived Units Area = length x width = 5.0 m x 3.0 m = 15 ( m x m) = 15 m 2 Volume = length x width x height = 5.0 m x 3.0 m x 4.0 m = 60. ( m x m x m) = 60. m 3

Derived Units Commonly Used in Chemistry Areasquare meter m 2 Volumecubic meter m 3 Forcenewton N Pressurepascal Pa Energyjoule J Powerwatt W Voltagevolt V Frequencyhertz Hz Electric chargecoulomb C Quantity Name Symbol

Prefixes in the SI System Power of 10 for Prefix SymbolMeaning Scientific Notation _______________________________________________________________________ mega-M 1,000,00010 6 kilo-k 1,00010 3 deci-d 0.110 -1 centi-c 0.0110 -2 milli-m 0.00110 -3 micro- 0.00000110 -6 nano-n 0.00000000110 -9 The Commonly Used Prefixes in the SI System Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118

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-

Reporting Measurements Must use significant figures Report what is known with certainty Using dashes Add ONE digit of uncertainty beyond that Using estimation Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46 The implication is that for any measurement, the last digit is an estimate and uncertain, and the next to last is known with certainty

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

Measurement/Sig Fig Practice Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water and explain your answers (the numbers given are as precise as possible): a. 128.7 mLb. 18 mLc. 23.45 mL Mark every 1 mLMark every 10 mLMark every 0.1 mL

Implied Range of Uncertainty 50 6040 30 Implied range of uncertainty in a measurement reported as 50. cm (5) 5 64 3 Implied range of uncertainty in a measurement reported as 5.0 cm (0.5) 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 (0.05)

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

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

How many cm are in 1.32 meters? applicable conversion factors: equality: or 1.32 m = 1 m = 100 cm ______1 m 100 cm We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose. ______ 1 m 100 cm 1 m 100 cm 132 cm (or 0.01 m = 1 cm) Conversion Factors

1. How many kilometers is 15,000 decimeters? 15,000 dm = 1.5 km 1,000 m 1 km 10 dm 1 m () ______ 15,000 dm () ____ 1,000 m 1 km 10 dm 1 m OR Both ways are equally good!

2. How many seconds is 4.38 days? = 1 h 60 min24 h 1 d1 min 60 s ____ ()() () _____ 4.38 d 378,432 s3.78 x 10 5 s If we are accounting for significant figures, we would change this to

3. Convert 41.2 cm 2 to m 2 100 cm 1 m () ______ 41.2 cm 2 41.2 cm. cm Recall that41.2 cm 2 = 41.2 cm. cm 100 cm 1 m () ______ 41.2 cm 2 =0.412 m 2 =0.412 cm. m WRONG! () ______ 100 cm 1 m =0.00412 m 2 () ________ (100) 2 cm 2 1 m 2 =0.00412 m 2

4. Convert 41.2 cm 2 to mm 2 41.2 cm 2 Recall that1 cm = 10 mm =4,120 mm 2 1 cm 2 10 2 mm 2 () _____ ( ) 2

5. Convert to 480 cm 3 to m 3 480 cm 3 =0.00048 m 3 100 cm 1 m 3 () _____ 480 cm 3 = 480 100 cm 1 m () _____ 100 cm 1 m () _____ 100 cm 1 m () _____ = or cm. cm. cm 1 m 1000000 cm ( ) _________ 3 3 4.8 x 10 -4 m 3 or 3 2 cm

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

SI-US Conversion Factors EqualityConversion Factors Length Volume Mass 2.54 cm = 1 in. 1 m = 39.4 in. 946 mL = 1 qt 1 L = 1.06 qt 453.6 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 453.6 g 1 lb 453.6 g 2.20 lb 1 kg 2.20 lb 2.54 cm 1 in and

Practical Conversions Teachers get a lot of grief from normal workers because they only work 36 weeks a year. How many extra hours, per day, would a teacher have to put in to match the typical worker, assuming a teacher works 8 hrs per day for those 36 weeks? What assumptions must we make?

Density Review how tightly packed the particles are Density = Typical units: g/cm 3 for solids g/mL for fluids m V D liquids and gases Glass: liquid or solid?

Monty Pythons take on analytical science and density with regard to witches

Density Review 1. A sample of lead (Pb) has mass 22.7 g and volume 2.0 cm 3. Find samples density. m V D 2. Another sample of lead occupies 16.2 cm 3 of space. Find samples mass. m = D V= 180 = 11 g V

3. A 119.5 g solid cylinder has radius 1.8 cm and height 1.5 cm. Find samples density. 4. A 153 g rectangular solid has edge lengths 8.2 cm, 5.1 cm, and 4.7 cm. Will this object sink in water? More Density Review Problems

3. A 119.5 g solid cylinder has radius 1.8 cm and height 1.5 cm. Find samples density. 1.5 cm 1.8 cm m V D m V = r 2 h = (1.8 cm) 2 (1.5 cm) = 15.2681 = 7.8 cm 3 2 SF

4. A 153 g rectangular solid has edge lengths 8.2 cm, 5.1 cm, and 4.7 cm. Will this object sink in water? 8.2 cm 5.1 cm 4.7 cm m V D (Find objects density and compare it to waters density.) V = l w h = 8.2 cm (5.1 cm)(4.7 cm) = 196.554 = 0.78 cm 3 < 1 No; it floats. 2 SF

Will bowling balls sink or float in H 2 O? 21.6 cm in diameter V sphere = 4/3 r 3 V = 4/3 (10.8 cm) 3 V = 5,276.7 cm 3 If D BB > 1, it will sink If D BB < 1, it will float Since the mass of a BB varies, lets figure out at what mass it will sink v. float m = (1.0 g/cm 3 )(5276.7 cm 3 ) m V D m = 5276.7 g m = D V or 11.6 lbs

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

Unit 1: Measurement and Conversions .

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