Unit 1: Measurement and Conversions “CHEMISTRY IS THE SCIENCE OF CHANGE. It looks at all the different kinds of substances and how they interact with each other. It is going on all around us all the time, as well as in the scientific laboratory and in the chemical industry. People in widely differing walks of life use chemistry everyday – the doctor and the chef, the farmer and the builder. Chemistry comes to the aid of the manufacturer of food, and also to the brewer and wine maker. The technician in the hospital laboratory uses chemistry to check for infections in blood samples. The forensic scientists uses chemistry to solve crimes. In agriculture, chemistry is used to increase the yields of crops and to control many pests. Chemicals keep the water supply safe and swimming pools clean. One of the largest industries in the world is the petrochemical industry – this industry is mainly associated with gasoline and the chemicals that come from crude oil. Drugs, synthetic dyes, plastics, and fabrics are produced by chemical means from nature’s raw materials.” Eyewitness Science “Chemistry” , Dr. Ann Newmark, DK Publishing, Inc., 1993, pg 6 http://old.unit5.org/roller

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 10exponent 800 2531 0.0014 = 8 x 10 x 10 = 8 x 102 = 2.531 x 10 x 10 x 10 = 2.531 x 103 = 1.4 / 10 / 10 / 10 = 1.4 x 10-3

Scientific Notation Practice Change the given number to standard form. 1.87 x 10–5 = 3.7 x 108 = 7.88 x 101 = 2.164 x 10–2 = 000000187000000 0.0000187 370,000,000 78.8 0.02164 (-) exponent = number < 1 (+) exponent = number > 1

Scientific Notation Practice Change the given number into scientific notation. 12,340 = 0.369 = 0.008 = 1,000,000,000 = 1.234 x 104 3.69 x 10–1 8 x 10–3 1 x 109

Significant Figures about… 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.

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) 60 26 50 25 16.4 16.3

Identifying Significant Figures Counting SF’s 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 1023) Conversions (1 in = 2.54 cm) Relative to the non-zero numbers.

How many Sig Figs? Measurement Number of SF Measurement Number of SF 0.030 kg 1.240560 x 106 mg 6 x 104 sec 246.31 g 20.06 cm 1.050 m 2 7 1 5 4 0.12 kg 1240560. cm 6000000 kg 6.00 x 106 kg 409 cm 29.200 dm 0.02500 g 2 7 1 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 102 mL

Practice with Sig Fig Calculations = -6.118 x 10-9 report -6 x 10-9 (1 SF) = 3.63 x 109 report 3.6 x 109 (2 SF) = 15.563 report 15.6 (tenths place) = 16.27 report 20 (tens place) = 1.7225 x 10-5 report 1.7 x 10-5 (2 SF) Complete calculation, and then follow order of operations to determine how many SF would be carried for each step

The Metric System from Industry Week, 1981 November 30

SI System The International System of Units abbreviated SI from the French Le Système international d'unités 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 Quantity Name Symbol Volume liter L Length meter m Mass kilogram kg Time second s Amount of substance mole mol Thermodynamic temperature Kelvin K Electric current amperes amps Luminous intensity candela cd Internet Access to the National Institute of Standards and Technology “To be or not to be”: the English or the Metric system   The English system of measurement used today in the United States originated in the decrees of English monarchs. The French Revolution produced the overthrow of the French monarchy and in 1799 it also led to the creation of the set of weights and measures we call the metric system. The metric system was legalized for use in the United States in 1866 along with the traditional English system. Today the only countries in the world that do not use the metric system are the United States of America, Liberia and Myanamar. United States government policy toward the Metric System This part is to access the following URLs for the National Institute of Standards and Technology, NIST, and review the evolution of the relationship between the United States and the Metric System. You can answer the first question after reviewing this NIST page. http://ts.nist.gov/ts/htdocs/200/202/ic1136a.htm What was the year when the United States signed the “Treaty of the Meter”? Access this FDA page to answer the following question. http://www.fds.goc/ora/inspect_ref/itg30.html What does the term “Both timeless and toothless” have to do with the Metric Conversions Act of 1975? In your opinion does this influence the pace of metrification in the United States? Name ____________________ Hr ____ Another part of your assignment is to write a brief argument on the back of this page for adopting the metric system and replacing the English system. Lastly you are to write an argument for continuing the current pattern of using two systems. Argument for adopting the Metric system and dropping the English system. Argument for retaining both the English system and the Metric system Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd 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 m2 Volume = length x width x height = 5.0 m x 3.0 m x 4.0 m = 60. ( m x m x m) = 60. m3

Derived Units Commonly Used in Chemistry Quantity Name Symbol Area square meter m2 Volume cubic meter m3 Force newton N Pressure pascal Pa Energy joule J Power watt W Voltage volt V Frequency hertz Hz Electric charge coulomb C

Prefixes in the SI System The Commonly Used Prefixes in the SI System Power of 10 for Prefix Symbol Meaning Scientific Notation _______________________________________________________________________ mega- M 1,000,000 106 kilo- k 1,000 103 deci- d 0.1 10-1 centi- c 0.01 10-2 milli- m 0.001 10-3 micro- m 0.000001 10-6 nano- n 0.000000001 10-9 Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118

Quantities of Mass Giga- Mega- Kilo- base milli- micro- nano- pico- Earth’s atmosphere to 2500 km 1018 g Quantities of Mass 1015 g 1012 g Ocean liner Giga- Mega- Kilo- base milli- micro- nano- pico- femto- atomo- 109 g Indian elephant 106 g Average human 103 g 1.0 liter of water 100 g 10-3 g 10-6 g Grain of table salt 10-9 g 10-12 g 10-15 g 10-18 g Typical protein 10-21 g Uranium atom 10-24 g Water molecule Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25

Reporting Measurements Must use significant figures Report what is known with certainty Using dashes Add ONE digit of uncertainty beyond that Using estimation By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement. The implication is that for any measurement, the last digit is an estimate and uncertain, and the next to last is known with certainty Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

Practice Measuring cm 1 2 3 4 5 4.5 cm cm 1 2 3 4 5 4.54 cm cm 1 2 3 4 1 2 3 4 5 4.5 cm cm 1 2 3 4 5 4.54 cm PRACTICE MEASURING Estimate one digit of uncertainty. a) 4.5 cm b) * 4.55 cm c) 3.0 cm *4.550 cm is INCORRECT while 4.52 cm or 4.58 cm are CORRECT (although the estimate is poor) By adding additional numbers to a measurement – you do not make it more precise. The instrument determines how precise it can make a measurement. Remember, you can only add ONE digit of uncertainty to a measurement. In applying the rules for significant figures, many students lose sight of the fact that the concept of significant figures comes from estimations in measurement. The last digit in a measurement is an estimation. How could the measurement be affected by the use of several different rulers to measure the red wire? (Different rulers could yield different readings depending on their precision.) Why is it important to use the same measuring instrument throughout an experiment? (Using the same instrument reduces the discrepancies due to manufacturing defects.) cm 1 2 3 4 5 3.0 cm Timberlake, Chemistry 7th Edition, page 7

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 mL b. 18 mL c. 23.45 mL Mark every 1 mL Mark every 10 mL Mark every 0.1 mL

Implied Range of Uncertainty 50 60 40 30 Implied range of uncertainty in a measurement reported as 50. cm (±5) 5 6 4 3 Implied range of uncertainty in a measurement reported as 5.0 cm (±0.5) When the plus-or-minus notation is not used to describe the uncertainty in a measurement, a scientist assumes that the measurement has an implied range, as illustrated above. The part of each scale between the arrows shows the range for each reported measurement. 5 6 4 3 Implied range of uncertainty in a measurement reported as 5.00 cm (±0.05) Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32

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

20 ? 1.50 x 101 mL 15 mL ? 15.0 mL A student reads a graduated cylinder that is marked at 15.00 mL, as shown in the illustration. Is this correct? NO Express the correct reading using scientific notation. 15.0 mL or 1.50 x101 mL 10

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

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

( ) ( ) ( ) ____ _____ ____ 2. How many seconds is 4.38 days? 24 h 1 d 60 min 1 min 60 s 4.38 d 378,432 s = If we are accounting for significant figures, we would change this to… 3.78 x 105 s

( ) ( ) ( ) ( ) 3. Convert 41.2 cm2 to m2 ______ ______ ______ = 0.412 m2 WRONG! = 0.412 cm.m Recall that… 41.2 cm2 = 41.2 cm.cm ( ) ______ ( ) ______ 41.2 cm.cm 100 cm 1 m 100 cm 1 m = 0.00412 m2 ( ) ________ (100)2 cm2 1 m2 41.2 cm2 = 0.00412 m2

( ) 4. Convert 41.2 cm2 to mm2 _____ Recall that… 1 cm = 10 mm ( )2 ( )2 ( )2 ( ) _____ 1 cm2 102 mm2 41.2 cm2 = 4,120 mm2

( ) ( ) ( ) ( ) ( ) 5. Convert to 480 cm3 to m3 _____ _____ _____ cm.cm.cm ( ) _____ ( ) _____ ( ) _____ 100 cm 1 m 480 cm 3 2 100 cm 1 m 100 cm 1 m = or ( ) _____ 100 cm 1 m 3 480 cm3 = 0.00048 m3 or 1 m 1000000 cm ( ) _________ 3 480 cm3 4.8 x 10-4 m3 =

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 Equality Conversion Factors Length 2.54 cm 1 in 1 in 2.54 cm 2.54 cm = 1 in. and 39.4 in 1 m 1 m 39.4 in. 1 m = 39.4 in. and Volume 946 mL 1 qt 1 qt 946 mL 946 mL = 1 qt and 1.06 qt 1 L 1 L 1.06 qt and Dominoes Activity 1 L = 1.06 qt Mass 453.6 g 1 lb 1 lb 453.6 g 453.6 g = 1 lb and 2.20 lb 1 kg 1 kg 2.20 lb 1 kg = 2.20 lb 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 m V D Density = Typical units: g/cm3 for solids g/mL for fluids Glass: liquid or solid? liquids and gases

Monty Python’s 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 cm3. Find sample’s density. m V D = 11 2. Another sample of lead occupies 16.2 cm3 of space. Find sample’s mass. V m = D V = 180 g

More Density Review Problems… 3. A 119.5 g solid cylinder has radius 1.8 cm and height 1.5 cm. Find sample’s 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?

3. A 119.5 g solid cylinder has radius 1.8 cm and height 1.5 cm. Find sample’s density. 1.5 cm 1.8 cm m V D 2 SF V = p r2 h = p (1.8 cm)2(1.5 cm) = 15.2681 cm3 = 7.8

this object sink in water? 8.2 cm 5.1 cm 4.7 cm 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? (Find object’s density and compare it to water’s density.) 2 SF m V D V = l w h = 8.2 cm (5.1 cm)(4.7 cm) = 196.554 cm3 = 0.78 < 1 No; it floats.

Will bowling balls sink or float in H2O? If DBB > 1, it will sink If DBB < 1, it will float 21.6 cm in diameter Vsphere = 4/3 p r3 V = 4/3 p (10.8 cm)3 m V D V = 5,276.7 cm3 m = D V m = (1.0 g/cm3)(5276.7 cm3) m = 5276.7 g Since the mass of a BB varies, let’s figure out at what mass it will sink v. float …or 11.6 lbs

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