Chapter 2 – Measurements and Calculations

Chapter 2 – Measurements and

Calculations

Honors Chemistry, Chapter 2Page 1

Evidence of Chemical Change

Evolution of a Gas (Bubbles, Odor)Formation of a Precipitate (Formation of Cloudiness in a Clear Solution, Solids Collecting at the Bottom or Top)Release of Energy (Heat, Light)Color Change


Scientific MethodObserving and Collecting Data– Qualitative (Bubbles Formed)– Quantitative (1 gram/liter of catalyst

speeded the reaction by 25%)– Chemists Study Systems (Region

Selected for Study)Formulate Hypothesis – Generalization about Data – Testable Statement


Scientific MethodTesting Hypothesis (Experimentation)– Supported, Retained– Not Supported, Discarded, ModifiedTheorizing – Create a Model– Model: An Explanation of How Phenomena

Occur and How Data or Events are Related.• Visual• Verbal• Mathematical



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(Wisdom is essential in a president, the appearance of wisdom will do in a candidate. – Eric Severeid)


Chapter 2, Section 1 Review

1. What is the purpose of the scientific method?

2. Distinguish between qualitative and quantitative observations.

3. Describe the differences between hypothesis, theories, and models.


Units of MeasureMeasurements Are Quantitative InformationQuantity: Something That Has Size or Amount


SI MeasurementSI Units Are Defined in Terms of Standards of MeasurementSeven Basic UnitsAll Others Derived From Seven Basic Units


SI Base UnitsQuantity Symbol Unit AbbreviationLength l meter mMass m Kilogram KgTime t second sThermodynamic Temperature T Kelvin KAmount of a Substance n mole molElectric Current I ampere ALuminous Intensity Iv candela cd


SI PrefixesPrefix Abbreviation

Exponent Multiplier Meaning Example Using Length

tera- T 1012 1000000000000 1 terameter (Tm)

giga- G 109 1000000000 1 gigameter (Gm)

mega- M 106 1000000 1 megameter (Mm)

kilo- k 103 1000 1 kilometer (km) = 1000 m

hecto- h 102 100 1 hectometer (hm) = 100 m

deka- da 101 10 1 dekameter (dam) = 10 m

100 1 1 meter (m)


SI PrefixesPrefix Abbreviation

Exponent Multiplier Meaning Example Using Length

100 1 1 meter (m)

deci- d 10-1 0.1 1 decimeter (dm)

centi- c 10-2 0.01 1 centimeter (cm)

milli- m 10-3 0.001 1 millimeter (km)

micro- 10-6 0.000001 1 micrometer (m)

nano- n 10-9 0.00000001 1 nanometer (nm)

pico- p 10-12 0.000000000001 1 picometer (pm)



Useful Conversion Factors

• 1000 ml = 1 L• 1 cm3 = 1 ml• 1000 g = 1 kg• 1000 mg = 1 g• 1000 g = 1 mg• 1000000 g = 1 g• 1000 mmol = 1 mol

Metric PrefixesMetric Prefixes

1. 1000 m = 1 1. 1000 m = 1 ______ a) mm b) km c) dma) mm b) km c) dm

2. 0.001 g = 1 2. 0.001 g = 1 ___ ___ a) mg b) kg c) dga) mg b) kg c) dg

3. 0.1 L = 1 3. 0.1 L = 1 ______ a) mL b) cL c) dLa) mL b) cL c) dL

4. 0.01 m = 1 ___ 4. 0.01 m = 1 ___ a) mm b) cm c) dma) mm b) cm c) dm

Learning Check

Units of LengthUnits of Length? kilometer (km) = 500 meters (m)? kilometer (km) = 500 meters (m)2.5 meter (m) = ? centimeters (cm)2.5 meter (m) = ? centimeters (cm)1 centimeter (cm) = ? millimeter (mm)1 centimeter (cm) = ? millimeter (mm)1 nanometer (nm) = 1.0 x 101 nanometer (nm) = 1.0 x 10-9-9 meter meter

O—H distance =O—H distance =9.4 x 109.4 x 10-11 -11 mm9.4 x 109.4 x 10-9 -9 cmcm0.094 nm0.094 nm

Learning Check Select the unit you would use to measure Select the unit you would use to measure 1. Your height1. Your height a) millimeters a) millimeters b) metersb) meters c) kilometers c) kilometers2. Your mass2. Your mass a) milligramsa) milligrams b) gramsb) grams c) kilograms c) kilograms3. The distance between two cities3. The distance between two cities a) millimetersa) millimeters b) metersb) meters c) kilometers c) kilometers4. The width of an artery4. The width of an arterya) millimetersa) millimeters b) metersb) meters c) kilometers c) kilometers

Derived UnitsArea A m2

Volume V m3

Density D kg/m3 (=m/V)Molar Mass M kilograms/molConcentration c mol/literMolar Volume Vm m3/molEnergy E joule


Helpful HintRelationship Between D, m, and V:


D

m

V

PROBLEM:PROBLEM: Mercury (Hg) has a density Mercury (Hg) has a density of 13.6 g/cmof 13.6 g/cm33. What is the mass of 95 . What is the mass of 95 mL of Hg in grams? In pounds?mL of Hg in grams? In pounds?

StrategyStrategy1.1.Use density to calc. mass (g) from Use density to calc. mass (g) from volume.volume.2.2.Convert mass (g) to mass (lb)Convert mass (g) to mass (lb)

Need to know conversion factorNeed to know conversion factor= 454 g / 1 lb= 454 g / 1 lb

PROBLEM:PROBLEM: Mercury (Hg) has a density of Mercury (Hg) has a density of 13.6 g/cm13.6 g/cm33. What is the mass of 95 mL of . What is the mass of 95 mL of Hg?Hg?

First, note thatFirst, note that 1 cm1 cm33 = 1 mL = 1 mL

1.1.Convert volume to massConvert volume to mass

PROBLEM:PROBLEM: Mercury (Hg) has a density of Mercury (Hg) has a density of 13.6 g/cm13.6 g/cm33. What is the mass of 95 mL of . What is the mass of 95 mL of Hg?Hg?

95 cm3 • 13.6 gcm3 = 1.3 x 103 g

1.3 x 103 g • 1 lb454 g

= 2.8 lb

2.2. Convert mass (g) to mass (lb)Convert mass (g) to mass (lb)

Learning CheckLearning Check

Osmium is a very dense metal. What is its Osmium is a very dense metal. What is its density in g/cmdensity in g/cm3 3 if 50.00 g of the metal if 50.00 g of the metal occupiesoccupiesa volume of 2.22cma volume of 2.22cm33??

1) 2.25 g/cm1) 2.25 g/cm33

2)2) 22.5 g/cm22.5 g/cm33

3)3) 111 g/cm111 g/cm33

Solution

2) Placing the mass and volume of the 2) Placing the mass and volume of the osmium metal into the density setup, we osmium metal into the density setup, we obtainobtain

D = D = massmass = = 50.00 g 50.00 g = = volumevolume 2.22 cm2.22 cm33

= 22.522522 g/cm= 22.522522 g/cm3 3 == 22.5 g/cm22.5 g/cm33

Volume DisplacementVolume Displacement

A solid displaces a matching volume of A solid displaces a matching volume of water when the solid is placed in water.water when the solid is placed in water.

33 mL33 mL25 mL 25 mL


What is the density (g/cmWhat is the density (g/cm33) of 48 g of a metal ) of 48 g of a metal if the metal raises the level of water in a if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? graduated cylinder from 25 mL to 33 mL? 1) 0.2 g/ cm1) 0.2 g/ cm33 2) 6 g/m 2) 6 g/m33 3) 252 3) 252 g/cmg/cm33

33 mL33 mL 25 mL25 mL


Which diagram represents the Which diagram represents the liquid layers in the cylinder?liquid layers in the cylinder?(K) Karo syrup (1.4 g/mL), (V) (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL)water (1.0 g/mL)

1)1) 2) 2) 3)3)

K

K

W

W

W

V

V

VK


The density of octane, a component of The density of octane, a component of gasoline, is 0.702 g/mL. What is the gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane?mass, in kg, of 875 mL of octane?1) 0.614 kg1) 0.614 kg2) 614 kg2) 614 kg3) 1.25 kg3) 1.25 kg


If blood has a density of 1.05 g/mL, If blood has a density of 1.05 g/mL, how many liters of blood are donated how many liters of blood are donated if 575 g of blood are given?if 575 g of blood are given?

1) 1) 0.548 L0.548 L2) 2) 1.25 L1.25 L3) 3) 1.83 L1.83 L

Conversion FactorsConversion Factors

Fractions in which the numerator and Fractions in which the numerator and denominator are EQUAL quantities expressed in denominator are EQUAL quantities expressed in different unitsdifferent units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

Learning Check

Write conversion factors that relate Write conversion factors that relate each of the following pairs of units:each of the following pairs of units:1. Liters and mL1. Liters and mL

2. Hours and minutes2. Hours and minutes

3. Meters and kilometers3. Meters and kilometers

How many minutes are in 2.5 hours?

Conversion factor

2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min 1 hr1 hr

cancelBy using dimensional analysis / factor-label method, the By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!and the UNITS are calculated as well as the numbers!

Factor Label MethodExpress 4.5 kg as gramsBegin by Expressing as a Fraction: 4.5 kg 1Identify Conversion Factor: 1 kg = 1000 gramsExpress as a Fraction:


1 kg 1000 g1 = --------------- or -------------- 1000 g 1 kg

Factor LabelContinued

Write Equation Including Proper FactorCancel UnitsMultiply Numbers to Get Final Result


4.5 kg 1000 g--------- x -------------- = 4500 g 1 1 kg


Factor Label Steps

1. Express as a Fraction2. Identify Conversion Factor3. Express Conversion Factor as Two

Fractions4. Select Proper Factor (units in denom.)5. Write Equation Including Proper Factor6. Cancel Units7. Multiply Numbers to Get Final Result


1. Distinguish between a quantity, a unit, and a measurement standard.

2. Name SI units for length, mass, time, volume, and density.

3. Distinguish between mass and weight.4. Perform a density calculation.5. Transform a statement of equality to a

conversion factor (factor label method).


Scientific MeasurementsAccuracy – The Closeness of Measurements to the Correct or Accepted ValuePrecision – The Closeness of a Set of Measurements


Accuracy vs. Precision


XXXX

XXXX

High PrecisionHigh Accuracy

High PrecisionLow Accuracy


Accuracy vs. Precision

X XX X

X X

X X

Low PrecisionLow Accuracy

Low PrecisionHigh Accuracy(on average)

Percent Error Valueaccepted - Valueexperimental

%Error = --------------------------------------- Valueaccepted

X 100Honors Chemistry, Chapter 2Page 40

Significant FiguresAll the Digits Known With Certainty Plus One Final Digit Which is Somewhat Uncertain


| I I I I | I I I I | I I I I | I I I I |

7 8 9

8.36

Rules for Significant Figures

1. Zeros Appearing Between Nonzero Digits are Significant

2. Zeros Appearing in Front of All Nonzero Digits are Not Significant

3. Zeros Appearing to the Right of the Decimal Point And at the End of the Number are Significant



Rules for Significant Figures

4. Zeros at the End of a Number but to the Left of the Decimal Point May or May Not be Significant. If a Zero Has Not Been Measured or Estimated but is Just a Placeholder, it is Not Significant. A Decimal Point Placed After Zeros Indicates They are Significant.

Rules for RoundingIf the Digit Following the Last Digit

to be Retained is:> 5 Then Round Up< 5 Then Round Down5 Followed by non Zero Digits

Then Round Up



Rules for Rounding

If the Digit Following the Last Digit to be Retained is:5 Followed by Non-Zero Digit(s), and Preceeded by an Odd Digit

Round Up5 Followed by Non-Zero Digit(s), and

Preceeded by an Even DigitLeave Unchanged

Significant Figures With Addition/Subraction

When Adding or Subtracting Decimals, the Answer Must Have the Same Number of Digits to the Right of the Decimal Point as There are in the Measurement Having the Fewest Digits to the Right of the Decimal Point.



Significant Figures With Multiplication/Division

• When Multiplying or Dividing, the Answer Can Have no More Significant Figures Than are in the Measurement with the Fewest Number of Significant Figures.

• (Conversion Factors Have Unlimited Digits of Accuracy.)

Significant FiguresSignificant Figures

The numbers reported in a The numbers reported in a measurement are limited by the measurement are limited by the measuring toolmeasuring tool

Significant figures in a Significant figures in a measurement include the known measurement include the known digits plus one estimated digitdigits plus one estimated digit

Counting Significant FiguresCounting Significant Figures

RULE 1. All non-zero digits in a measured RULE 1. All non-zero digits in a measured

number are significant. Only a zero could number are significant. Only a zero could indicate that rounding occurred.indicate that rounding occurred.

Number of Significant Figures

38.15 cm38.15 cm 445.6 ft5.6 ft 2265.6 lb65.6 lb ______122.55 m122.55 m ___

Leading ZerosLeading Zeros

RULE 2. Leading zeros in decimal numbers RULE 2. Leading zeros in decimal numbers are are NOTNOT significant. significant.


0.008 mm0.008 mm 110.0156 oz0.0156 oz 330.0042 lb0.0042 lb ________0.000262 mL 0.000262 mL ____

Sandwiched ZerosSandwiched Zeros

RULE 3. Zeros between nonzero numbers are RULE 3. Zeros between nonzero numbers are significant. (They can not be rounded unless they significant. (They can not be rounded unless they are on an end of a number.)are on an end of a number.)


50.8 mm50.8 mm332001 min2001 min 440.702 lb0.702 lb ________0.00405 m0.00405 m ____

Trailing ZerosTrailing Zeros

RULE 4. Trailing zeros in numbers without RULE 4. Trailing zeros in numbers without decimals are NOT significant. They are decimals are NOT significant. They are only serving as place holders.only serving as place holders.


25,000 in. 25,000 in. 22 200. yr200. yr 33 48,600 gal48,600 gal ________

25,005,000 g 25,005,000 g ________


A. Which answers contain 3 significant figures?A. Which answers contain 3 significant figures?1) 0.47601) 0.4760 2) 0.00476 2) 0.00476 3) 4760 3) 4760

B. All the zeros are significant inB. All the zeros are significant in 1) 0.00307 1) 0.00307 2) 25.300 2) 25.300 3) 2.050 x 10 3) 2.050 x 1033

C. 534,675 rounded to 3 significant figures isC. 534,675 rounded to 3 significant figures is 1) 535 1) 535 2) 535,000 2) 535,000 3) 5.35 x 10 3) 5.35 x 1055


In which set(s) do both numbers In which set(s) do both numbers contain the contain the samesame number of number of significant figures?significant figures? 1) 22.0 and 22.00 1) 22.0 and 22.00

2) 400.0 and 40 2) 400.0 and 40 3) 0.000015 and 150,0003) 0.000015 and 150,000

State the number of significant figures in each State the number of significant figures in each of the following:of the following:A. 0.030 mA. 0.030 m 1 1 2 2 3 3B. 4.050 LB. 4.050 L 2 2 3 3 4 4C. 0.0008 gC. 0.0008 g 1 1 2 2 4 4D. 3.00 mD. 3.00 m 1 1 2 2 3 3E. 2,080,000 beesE. 2,080,000 bees 3 3 5 5 7 7


Significant Numbers in CalculationsSignificant Numbers in Calculations

A calculated answer cannot be more A calculated answer cannot be more precise than the measuring tool. precise than the measuring tool.

A calculated answer must match the least A calculated answer must match the least precise measurement.precise measurement.

Significant figures are needed for final Significant figures are needed for final answers fromanswers from 1) adding or subtracting1) adding or subtracting

2) multiplying or dividing2) multiplying or dividing

Adding and SubtractingAdding and SubtractingThe answer has the same number of The answer has the same number of decimal places as the measurement with decimal places as the measurement with the fewest decimal places.the fewest decimal places.

25.25.22 one decimal placeone decimal place

+ 1.+ 1.3434 two decimal placestwo decimal places 26.5426.54answer 26.5answer 26.5 one decimal placeone decimal place

Adding and SubtractingAdding and SubtractingThe answer has the same number of The answer has the same number of decimal places as the measurement with decimal places as the measurement with the fewest decimal places.the fewest decimal places.

25.25.22 one decimal placeone decimal place

+ 1.+ 1.3434 two decimal placestwo decimal places 26.5426.54answer 26.5answer 26.5 one decimal placeone decimal place

Learning CheckLearning Check In each calculation, round the answer to In each calculation, round the answer to the correct number of significant figures.the correct number of significant figures.A. 235.05 + 19.6 + 2.1 = A. 235.05 + 19.6 + 2.1 =

1) 256.751) 256.75 2) 256.8 2) 256.8 3) 2573) 257

B. 58.925 - 18.2B. 58.925 - 18.2 ==1) 40.7251) 40.725 2) 40.73 2) 40.73 3) 40.73) 40.7

Multiplying and Dividing

Round (or add zeros) to the Round (or add zeros) to the calculated answer until you have the calculated answer until you have the same number of significant figures same number of significant figures as the measurement with the fewest as the measurement with the fewest significant figures.significant figures.


A. 2.19 X 4.2 =A. 2.19 X 4.2 = 1) 91) 9 2) 9.2 2) 9.2 3) 9.1983) 9.198

B. 4.311 ÷ 0.07 =B. 4.311 ÷ 0.07 = 1)1) 61.5861.58 2) 62 2) 62 3) 603) 60

C. C. 2.54 X 0.00282.54 X 0.0028 = = 0.0105 X 0.060 0.0105 X 0.060 1) 11.31) 11.3 2) 112) 11 3) 0.041 3) 0.041

Reading a MeterstickReading a Meterstick

. l. l22. . . . I . . . . I. . . . I . . . . I33 . . . .I . . . . I . . . .I . . . . I44. . cm. . cm

First digit (known)First digit (known) = 2 = 2 2.?? cm2.?? cmSecond digit (known)Second digit (known) = 0.7 = 0.7 2.7? cm2.7? cmThird digit (estimated) between 0.05- 0.07Third digit (estimated) between 0.05- 0.07Length reportedLength reported == 2.75 cm 2.75 cm

oror 2.74 cm 2.74 cm

oror 2.76 cm2.76 cm

Known + Estimated DigitsKnown + Estimated DigitsIn 2.76 cm…In 2.76 cm…

• Known digitsKnown digits 2 andand 7 are 100% certainare 100% certain

• The third digit 6 is estimated (uncertain)The third digit 6 is estimated (uncertain)

• In the reported length, all three digits (2.76 In the reported length, all three digits (2.76 cm) are significant including the estimated cm) are significant including the estimated oneone


. l8. . . . I . . . . I9. . . .I . . . . I10. . cmWhat is the length of the line?What is the length of the line?

1) 9.6 cm 1) 9.6 cm 2) 9.62 cm 2) 9.62 cm 3) 9.63 cm3) 9.63 cmHow does your answer compare with your How does your answer compare with your neighbor’s answer? Why or why not?neighbor’s answer? Why or why not?

Zero as a Measured NumberZero as a Measured Number

. l3. . . . I . . . . I4 . . . . I . . . . I5. . cmWhat is the length of the line?What is the length of the line?

First digitFirst digit 5.?? cm5.?? cmSecond digitSecond digit 55.0? cm.0? cmLast (estimated) digit isLast (estimated) digit is 5.05.00 cm0 cm

Always estimate ONE place past the smallest mark!Always estimate ONE place past the smallest mark!

Scientific NotationMove the Decimal Point Left or Right Until the Mantissa is Greater Than or Equal to 1.0 and Less Than 10Express the Number as: M x 10n Where n Represents the Number of Places the Decimal Point was Moved, Positive if the Decimal is Moved Left and Negative if the Decimal is Moved Right


What is Scientific What is Scientific Notation?Notation?

Scientific notation is a way of Scientific notation is a way of expressing really big numbers or expressing really big numbers or really small numbers.really small numbers.For very large and very small For very large and very small numbers, scientific notation is numbers, scientific notation is more concise.more concise.

Scientific notation Scientific notation consists of two parts:consists of two parts:A number between 1 and 10A number between 1 and 10

A power of 10A power of 10

N x 10N x 10xx

To change standard To change standard form to scientific form to scientific

notation…notation…Place the decimal point so that there is Place the decimal point so that there is one non-zero digit to the left of the one non-zero digit to the left of the decimal point.decimal point.Count the number of decimal places the Count the number of decimal places the decimal point has “moved” from the decimal point has “moved” from the original number. This will be the original number. This will be the exponent on the 10.exponent on the 10.If the original number was less than 1, If the original number was less than 1, then the exponent is negative. If the then the exponent is negative. If the original number was greater than 1, original number was greater than 1, then the exponent is positive.then the exponent is positive.

ExamplesExamplesGiven: 289,800,000Given: 289,800,000Use: 2.898 (moved 8 places)Use: 2.898 (moved 8 places)Answer:Answer: 2.898 x 102.898 x 1088

Given: 0.000567Given: 0.000567Use: 5.67 (moved 4 places)Use: 5.67 (moved 4 places)Answer:Answer: 5.67 x 105.67 x 10-4-4

To change scientific To change scientific notation to standard notation to standard

form…form…Simply move the decimal point to Simply move the decimal point to the right for positive exponent 10. the right for positive exponent 10. Move the decimal point to the left Move the decimal point to the left for negative exponent 10.for negative exponent 10.

(Use zeros to fill in places.)(Use zeros to fill in places.)

ExampleExampleGiven: 5.093 x 10Given: 5.093 x 1066

Answer: Answer: 5,093,0005,093,000 (moved 6 (moved 6 places to the right)places to the right)

Given: 1.976 x 10Given: 1.976 x 10-4-4

Answer: Answer: 0.00019760.0001976 (moved 4 (moved 4 places to the left)places to the left)

Learning CheckExpress these numbers in Express these numbers in Scientific Notation:Scientific Notation:

1)1) 4057894057892)2) 0.0038720.0038723)3) 300000000030000000004)4) 225)5) 0.4782600.478260

Direct ProportionY = kXExample Mass vs. Volume Data for AluminumSlope of the Line (k) is the Density


Measurement of a Series of Blocks

Block Number Mass (g) Volume (cm3)

1 1.20 0.442 3.69 1.393 5.72 2.104 12.80 4.685 15.30 5.716 18.80 6.907 22.70 8.458 26.50 9.649 34.00 12.80

10 36.40 13.50


Plot Mass vs. VolumeMass (g) As a Function of Volume (V)

05

10

15202530

3540

0 5 10 15

Volume - cubic centimeters

Mas

s - g

ram

s

Mass (g)


Calculate Slope and Intercept

Y = mX + b = slope x Volume + interceptSlope = 2.69 g/cm3

Intercept = 0.09 grams (!) (Actually Zero)From Table of Densities: Sample is Aluminum (Al)


Inversely Proportionalk = XY or Y = k/XAs X Increases, Y DecreasesExample: Pressure-Volume Data


Pressure Volume Data for Nitrogen

Pressure (k-Pa) Volume (cm3) P x V100 500 50000150 333 49950200 250 50000250 200 50000300 166 49800350 143 50050400 125 50000450 110 49500


Volume vs. Pressure For Nitrogen

0

100

200

300

400

500

600

0 200 400 600

Pressure (kPa)

Volu

me

(cm

3)

Volume (cm3)




1. Distinguish between accuracy and precision.2. Determine the number of significant figures in

a measurement.3. Perform mathematical operations (+,-,x,/)

involving significant digits.4. Convert measurements into scientific notation.5. Distinguish between inversely proportional and

directly proportional relationships.

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Chapter 2 – Measurements and Calculations

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