The Metric System

Unit 1: Measurement and Conversions

http://old.unit5.org/roller1CHEMISTRY 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 natures raw materials.

Eyewitness Science Chemistry , Dr. Ann Newmark, DK Publishing, Inc., 1993, pg 6Scientific Notation ReviewOften 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 102= 8 x 10 x 10 = 2.531 x 10 x 10 x 10 = 2.531 x 103= 1.4 / 10 / 10 / 10 = 1.4 x 10-3Change the given number to standard form.

1.87 x 105 =

3.7 x 108 =

7.88 x 101 =

2.164 x 102 = 370,000,0000.000018778.80.02164000000187000000Scientific Notation Practice(-) exponent = number < 1(+) exponent = number > 1Change the given number into scientific notation.

12,340 = 0.369 = 0.008 = 1,000,000,000 = 1.234 x 1043.69 x 1018 x 1031 x 109Scientific Notation PracticeSignificant FiguresA 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 mLNO!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.aboutMeasurement and AccuracyThe 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)262516.416.36050Identifying Significant FiguresCounting SFs in a numberNon-zero numbers: ALWAYS count as SFZeroes Left: NEVER count as SF (0.000345)Middle: ALWAYS count as SF (5001)Right: sometimesw/ decimal point: count as SF (25.10)w/o decimal point: DO NOT count as SF (8200)Exact Numbers: IGNORE SFCounts (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 SFMeasurement Number of SF25 g

0.030 kg

1.240560 x 106 mg

6 x 104 sec

246.31 g

20.06 cm

1.050 m0.12 kg

1240560. cm

6000000 kg

6.00 x 106 kg

409 cm

29.200 dm

0.02500 g2

2

7

1

5

4

42

7

1

3

3

5

4Sig Figs with CalculationsNote: For any calculations, always perform the entire calculation without rounding, and then round the final answer.Addition/SubtractionRound the answer to the LEAST number of decimal places found (least precise)11.31 + 33.264 + 4.1 = 48.674Multiplication/DivisionRound the answer to the smallest number of SF found5.282 x 3.42 = 18.06444 rounded to 48.7 rounded to 18.1 (3.42 only has 3 SF)Back to the original questionA 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 mL93 mLCould I write that as 93.0?NO!More practice with SFIf 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

= -6.118 x 10-9= 3.63 x 109= 15.563report -6 x 10-9 (1 SF) report 3.6 x 109 (2 SF) report 15.6 (tenths place)= 16.27report 20 (tens place)

= 1.7225 x 10-5report 1.7 x 10-5 (2 SF) Practice with Sig Fig CalculationsComplete calculation, and then follow order of operations to determine how many SF would be carried for each stepA

A

A

A

A

The Metric Systemfrom Industry Week, 1981 November 30 SI SystemThe 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 tenUses prefixes to differentiate between powersUsed 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 QuantityNameSymbolDorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 1615Internet Access to the National Institute of Standards and TechnologyTo be or not to be: the English or the Metric systemThe 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 SystemThis 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.htmWhat 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.htmlWhat 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 ____Internet Access to the National Institute of Standards and TechnologyTo be or not to be: the English or the Metric systemAnother 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 systemArea and Volume: Derived UnitsArea = length x width= 5.0 m x 3.0 m= 15 ( m x m)= 15 m2Volume = length x width x height= 5.0 m x 3.0 m x 4.0 m= 60. ( m x m x m)= 60. m3Derived Units Commonly Used in Chemistry Areasquare meter m2 Volumecubic meter m3 Forcenewton N Pressurepascal Pa Energyjoule J Powerwatt W Voltagevolt V Frequencyhertz Hz Electric chargecoulomb C Quantity Name SymbolPrefixes in the SI System Power of 10 for Prefix SymbolMeaning Scientific Notation_______________________________________________________________________

mega-M 1,000,000106

kilo-k 1,000103

deci-d 0.110-1

centi-c 0.0110-2

milli-m 0.00110-3

micro-m 0.00000110-6

nano-n 0.00000000110-9

The Commonly Used Prefixes in the SI System

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118Quantities of MassKelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25Earths atmosphere to 2500 kmOcean linerIndian elephantAverage human1.0 liter of waterGrain of table saltTypical proteinUranium atomWater molecule

1024 g1021 g1018 g1015 g1012 g109 g106 g103 g100 g10-3 g10-6 g10-9 g10-12 g10-15 g10-18 g10-21 g10-24 gGiga- Mega-Kilo-basemilli-micro-nano-pico-femto-atomo-Reporting MeasurementsMust use significant figuresReport what is known with certaintyUsing dashesAdd ONE digit of uncertainty beyond thatUsing 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 certainty20By 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.Practice Measuring4.5 cm4.54 cm3.0 cmTimberlake, Chemistry 7th Edition, page 7cm012345cm012345cm012345

21PRACTICE 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.)

Measurement/Sig Fig PracticeDraw 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 mLImplied Range of Uncertainty50604030Implied range of uncertainty in a measurement reported as 50. cm (5)5643Implied range of uncertainty in a measurement reported as 5.0 cm (0.5)Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 325643Implied range of uncertainty in a measurement reported as 5.00 cm (0.05)23When 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.Reading a Meniscus1086line of sight too highreading too lowreading too highline of sight too lowproper line of sightreading correctgraduatedcylinder10 mL2010? 15 mL ?15.0 mL1.50 x 101 mL25A 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 mLHow many cm are in 1.32 meters?

applicable conversion factors:

equality:

or 1.32 m=1 m = 100 cm

______1 m100 cmWe use the idea of unit cancellationto decide upon which one of the twoconversion factors we choose.______1 m100 cm1 m100 cm132 cm(or 0.01 m = 1 cm)Conversion Factors1. How many kilometers is 15,000 decimeters? 15,000 dm=1.5 km1,000 m1 km10 dm1 m()______

15,000 dm()____1,000 m1 km10 dm1 mORBoth ways are equally good!2. How many seconds is 4.38 days?=1 h60 min24 h1 d1 min60 s____()()____()_____4.38 d378,432 s3.78 x 105 sIf we are accounting for significant figures, we would change this to

3. Convert 41.2 cm2 to m2 100 cm1 m()______ 41.2 cm2 41.2 cm.cmRecall that41.2 cm2 = 41.2 cm.cm100 cm1 m()______ 41.2 cm2=0.412 m2=0.412 cm.mWRONG!()______100 cm1 m=0.00412 m2()________(100)2 cm21 m2=0.00412 m24. Convert 41.2 cm2 to mm2 41.2 cm2Recall that1 cm = 10 mm=4,120 mm21 cm2102 mm2()_____( )2( )2

5. Convert to 480 cm3 to m3 480 cm3=0.00048 m3100 cm1 m3()_____ 480 cm3= 480 100 cm1 m()_____100 cm1 m()_____100 cm1 m()_____=orcm.cm.cm1 m1000000 cm()_________334.8 x 10-4 m3or32cmComparison of English and SI Units

1 inch2.54 cm1 inch = 2.54 cmZumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119SI-US Conversion FactorsEqualityConversion FactorsLengthVolumeMass2.54 cm = 1 in.1 m = 39.4 in.946 mL = 1 qt1 L = 1.06 qt453.6 g = 1 lb1 kg = 2.20 lb 1 in2.54 cm 39.4 in 1 m 1 m 39.4 in.946 mL 1 qt 1 qt 946 mL 1.06 qt 1 L 1 L 1.06 qt 453.6 g 1 lb 1 lb 453.6 g 2.20 lb 1 kg 1 kg 2.20 lb2.54 cm 1 inandandandandandand33Dominoes ActivityPractical ConversionsTeachers 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/cm3 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 Review1. A sample of lead (Pb) has mass 22.7 g and volume 2.0 cm3. Find samples density.

m V D

2. Another sample of lead occupies 16.2 cm3 of space. Find samples mass.

m = D V= 180

= 11gV3. 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 DmV = p r2 h

= p (1.8 cm)2(1.5 cm)= 15.2681

= 7.8cm32 SF4. 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 cm5.1 cm4.7 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

= 0.78cm3< 1No; it floats.2 SF

Will bowling balls sink or float in H2O?21.6 cm in diameterVsphere = 4/3 p r3V = 4/3 p (10.8 cm)3V = 5,276.7 cm3If DBB > 1, it will sinkIf DBB < 1, it will floatSince the mass of a BB varies, lets figure out at what mass it will sink v. floatm = (1.0 g/cm3)(5276.7 cm3) m V Dm = 5276.7 gm = D Vor 11.6 lbsMeasurementsMetric (SI) unitsPrefixesUncertaintySignificant figuresConversionfactorsLengthDensityMassVolumeProblem solving withconversion factorsTimberlake, Chemistry 7th Edition, page 40