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Chapter 3 Observation, Measurement and Calculations.

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Chapter 3 Chapter 3 Observation, Observation, Measurement Measurement and Calculations and Calculations
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Page 1: Chapter 3 Observation, Measurement and Calculations.

Chapter 3Chapter 3Observation,Observation,MeasurementMeasurement

and Calculationsand Calculations

Page 2: Chapter 3 Observation, Measurement and Calculations.

MeasurementMeasurement

MeasurementMeasurement – a quantity that has both a number and a unit.

• Measurements are fundamental to the experimental sciences

• Units typically used in the sciences are the International System of Measurements (SI)

Page 3: Chapter 3 Observation, Measurement and Calculations.

In science, we deal with some In science, we deal with some very very LARGELARGE numbers: numbers:

1 mole = 6020000000000000000000001 mole = 602000000000000000000000

In science, we deal with some In science, we deal with some very very SMALLSMALL numbers: numbers:

Mass of an electron = Mass of an electron = 0.000000000000000000000000000000091 kg0.000000000000000000000000000000091 kg

Scientific NotationScientific Notation

Page 4: Chapter 3 Observation, Measurement and Calculations.

Imagine the difficulty of Imagine the difficulty of calculating the mass of 1 mole calculating the mass of 1 mole of electrons!of electrons!

0.00000000000000000000000000000000.000000000000000000000000000000091 kg 91 kg x 602000000000000000000000x 602000000000000000000000

???????????????????????????????????

Scientific NotationScientific Notation

Page 5: Chapter 3 Observation, Measurement and Calculations.

Scientific Scientific Notation:Notation:

A method of representing very large A method of representing very large or very small numbers in the or very small numbers in the form: form:

M x 10M x 10n n

MM is a number between is a number between 11 and and 10 10 nn is an integer is an integer

Page 6: Chapter 3 Observation, Measurement and Calculations.

2 500 000 000

Step #1: Insert an understood decimal pointStep #1: Insert an understood decimal point

.

Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal point

123456789

Step #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn

Page 7: Chapter 3 Observation, Measurement and Calculations.

2.5 x 102.5 x 1099

The exponent is the number of places we moved the decimal.

Page 8: Chapter 3 Observation, Measurement and Calculations.

0.00005790.0000579

Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal pointStep #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn

1 2 3 4 5

Page 9: Chapter 3 Observation, Measurement and Calculations.

5.79 x 105.79 x 10-5-5

The exponent is negative because the number we started with was less than 1.

Page 10: Chapter 3 Observation, Measurement and Calculations.

PERFORMING PERFORMING CALCULATIONCALCULATION

S IN S IN SCIENTIFIC SCIENTIFIC NOTATIONNOTATION

ADDITION AND ADDITION AND SUBTRACTIONSUBTRACTION

Page 11: Chapter 3 Observation, Measurement and Calculations.

ReviewReview::Scientific notation Scientific notation expresses a number in the expresses a number in the form:form: M x 10M x 10nn

1 1 M M 1010

n is an n is an integerinteger

Page 12: Chapter 3 Observation, Measurement and Calculations.

4 x 104 x 1066

+ 3 x 10+ 3 x 1066

IFIF the exponents the exponents are the same, we are the same, we simply add or simply add or subtract the subtract the numbers in front numbers in front and bring the and bring the exponent down exponent down unchanged.unchanged.

77 x 10x 1066

Page 13: Chapter 3 Observation, Measurement and Calculations.

4 x 104 x 1066

- 3 x 10- 3 x 1066

The same holds The same holds true for true for subtraction in subtraction in scientific scientific notation.notation.

11 x 10x 1066

Page 14: Chapter 3 Observation, Measurement and Calculations.

4 x 104 x 1066

+ 3 x 10+ 3 x 1055

If the exponents If the exponents are NOT the are NOT the same, we must same, we must move a decimal to move a decimal to makemake them the them the same.same.

Page 15: Chapter 3 Observation, Measurement and Calculations.

4.00 x 104.00 x 1066

+ + 3.00 x 103.00 x 1055 + + .30 x 10.30 x 1066

4.304.30 x 10x 1066

Move the Move the decimal decimal on the on the smallersmaller number!number!

4.00 x 104.00 x 1066

Page 16: Chapter 3 Observation, Measurement and Calculations.

A Problem for A Problem for you…you…

2.37 x 102.37 x 10-6-6

+ 3.48 x 10+ 3.48 x 10-4-4

Page 17: Chapter 3 Observation, Measurement and Calculations.

2.37 x 102.37 x 10-6-6

+ 3.48 x 10+ 3.48 x 10-4-4

Solution…Solution…002.37 x 10002.37 x 10--

66

Page 18: Chapter 3 Observation, Measurement and Calculations.

+ 3.48 x 10+ 3.48 x 10-4-4

Solution…Solution…0.0237 x 100.0237 x 10-4-4

3.5037 x 103.5037 x 10-4-4

Page 19: Chapter 3 Observation, Measurement and Calculations.

Scientific Notation Calculation Summary

Adding and SubtractingYou must express the numbers as the same power

of 10. This will often involve changing the decimal place of the coefficient.

(2.0 x 106) + ( 3.0 x 107)

(0.20 x 107) + (3.0 x 107) = 3.20 x 107

(4.8 x 105) - ( 9.7 x 104)

(4.8 x 105) - ( 0.97 x 105) = 3.83 x 105

Page 20: Chapter 3 Observation, Measurement and Calculations.

Scientific NotationMultiplying

Multiply the coefficients and add the exponents

(xa) (xb) = x a + b

(2.0 x 106) ( 3.0 x 107) = 6.0 x 1013

Dividing(xa) / (xb) = x a - b

(2.0 x 106) / ( 3.0 x 107) = 0.67 x 10-1

Divide the coefficients and subtract the exponents

Page 21: Chapter 3 Observation, Measurement and Calculations.

Nature of MeasurementNature of Measurement

Part 1 - Part 1 - number number Part 2 - Part 2 - scale (unit) scale (unit)

Examples: Examples: 2020 grams grams

6.63 x 106.63 x 10-34-34 Joule secondsJoule seconds

Measurement - quantitative Measurement - quantitative observation observation consisting of 2 partsconsisting of 2 parts

Page 22: Chapter 3 Observation, Measurement and Calculations.

Uncertainty in Uncertainty in MeasurementMeasurement

A digit that must be A digit that must be estimatedestimated is called is called uncertainuncertain. A . A measurementmeasurement always has always has some degree of some degree of uncertainty.uncertainty.

Page 23: Chapter 3 Observation, Measurement and Calculations.

Precision and AccuracyPrecision and AccuracyAccuracyAccuracy – measure of how close a – measure of how close a measurement comes to the actual or measurement comes to the actual or truetrue value of whatever is being measured.value of whatever is being measured.

PrecisionPrecision – measure of how close a series of – measure of how close a series of measurements are to one another.measurements are to one another.

Neither accurate nor

precise

Precise but not accurate

Precise AND accurate

Page 24: Chapter 3 Observation, Measurement and Calculations.

Why Is there Uncertainty?Why Is there Uncertainty? Measurements are performed with instruments No instrument can read to an infinite number of decimal places

Which of these balances has the greatest uncertainty in measurement?

Page 25: Chapter 3 Observation, Measurement and Calculations.

Determining ErrorDetermining Error

Accepted ValueAccepted Value – – the correct value based on reliable references

Error(can be +or-)=experimental value – accepted value

Percent error = absolute value of error x 100% accepted value

Experimental ValueExperimental Value – – the value measured in the lab

Page 26: Chapter 3 Observation, Measurement and Calculations.

Significant Figures in Significant Figures in MeasurementMeasurement

In a supermarket, you can use the scales to measure the weight of produce.

If you use a scale that is calibrated in 0.1 lb intervals, you can easily read the scale to the nearest tenth of a pound.

You can also estimate the weight to the nearest hundredth of a pound by noting the position of the pointer between calibration marks.

Page 27: Chapter 3 Observation, Measurement and Calculations.

Significant Figures in Significant Figures in MeasurementMeasurement

If you estimate a weight that lies between 2.4 lbs and 2.5 lbs to be 2.462.46 lbs, the number in this estimated measurement has three digits.

The first two digits (2 and 4 ) are known with certainty.

The rightmost digit (6) has been estimated and involves some uncertainty.

Page 28: Chapter 3 Observation, Measurement and Calculations.

Significant Figures in Significant Figures in MeasurementMeasurement

Significant figures in a measurement include all of the digits that are know, plus a last digit that is estimated.

Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation.

Page 29: Chapter 3 Observation, Measurement and Calculations.

Rules for Counting Rules for Counting SignificantSignificant

FiguresFigures

Nonzero integersNonzero integers always count always count as significant figures. as significant figures.

34563456 hashas

44 sig figs.sig figs.

Page 30: Chapter 3 Observation, Measurement and Calculations.

Rules for Counting Rules for Counting Significant FiguresSignificant Figures

Leading zerosLeading zeros do not count as do not count as significant figuressignificant figures..

0.04860.0486 has has

33 sig figs. sig figs.

Page 31: Chapter 3 Observation, Measurement and Calculations.

Rules for Counting Rules for Counting Significant FiguresSignificant Figures

Zeros at the end of a number Zeros at the end of a number and to the right of a decimal and to the right of a decimal point point are always significant.are always significant.

9.0009.000 has has

44 sig figs sig figs

1.010 1.010 hashas

4 4 sig figssig figs

Page 32: Chapter 3 Observation, Measurement and Calculations.

Rules for Counting Rules for Counting Significant FiguresSignificant Figures

Captive zerosCaptive zeros always count always count as as

significant figures.significant figures.

16.0716.07 has has

44 sig figs. sig figs.

Page 33: Chapter 3 Observation, Measurement and Calculations.

Rules for Counting Rules for Counting Significant FiguresSignificant Figures

Zeros at the rightmost end Zeros at the rightmost end that lie at the left of an that lie at the left of an understood decimal pointunderstood decimal point are are not significant. not significant.

7000 7000 hashas

11 sig fig sig fig

2721027210 has has

44 sig figs sig figs

Page 34: Chapter 3 Observation, Measurement and Calculations.

Rules for Counting Rules for Counting Significant FiguresSignificant Figures

Exact numbersExact numbers have an infinite have an infinite number of significant figures. number of significant figures.

11 inch = inch = 2.542.54 cm, exactlycm, exactly

Page 35: Chapter 3 Observation, Measurement and Calculations.

Rules for Significant Figures in Rules for Significant Figures in Mathematical OperationsMathematical Operations

Multiplication and DivisionMultiplication and Division:: # sig # sig figs in the result equals the number figs in the result equals the number in the in the least precise measurementleast precise measurement used in the calculation. used in the calculation.

6.38 x 2.0 = 6.38 x 2.0 =

12.76 12.76 13 (2 sig figs)13 (2 sig figs)

Page 36: Chapter 3 Observation, Measurement and Calculations.

Rules for Significant Figures Rules for Significant Figures in Mathematical Operationsin Mathematical Operations

Addition and SubtractionAddition and Subtraction: The : The number of decimal places in the number of decimal places in the result equals the number of decimal result equals the number of decimal places in the least precise places in the least precise measurement. measurement.

6.8 + 11.934 = 6.8 + 11.934 =

18.734 18.734 18.7 ( 18.7 (3 sig figs3 sig figs))

Page 37: Chapter 3 Observation, Measurement and Calculations.

Sig Fig Practice #1Sig Fig Practice #1How many significant figures in each of the following?

1.0070 m

5 sig figs

17.10 kg 4 sig figs

100,890 L 5 sig figs

3.29 x 103 s 3 sig figs

0.0054 cm 2 sig figs

3,200,000 2 sig figs

Page 38: Chapter 3 Observation, Measurement and Calculations.

Sig Fig Practice #2Sig Fig Practice #2

3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m2 23 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2

710 m ÷ 3.0 s 236.6666667 m/s 240 m/s

1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft

1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Page 39: Chapter 3 Observation, Measurement and Calculations.

Sig Fig Practice #3Sig Fig Practice #3

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Page 40: Chapter 3 Observation, Measurement and Calculations.

Questions

1) 78ºC, 76ºC, 75ºC 2) 77ºC, 78ºC, 78ºC3) 80ºC, 81ºC, 82ºC

The sets of measurements were made of the boiling point of a liquid under similar conditions. Which set is the most precise?

Set 2 – the three measurements are closest together.

What would have to be known to determine which set is the most accurate?

The accepted value of the liquid’s boiling point

Page 41: Chapter 3 Observation, Measurement and Calculations.

QuestionsHow do measurements relate to experimental

science?

Making correct measurements is fundamental to the experimental sciences.

How are accuracy and precision evaluated?

Accuracy is the measured value compared to the correct values. Precision is comparing more than one measurement.

Page 42: Chapter 3 Observation, Measurement and Calculations.

QuestionsWhy must a given measurement always be reported to the

correct number of significant figures?

The significant figures in a calculated answer often depend on the number of significant figures of the measurements used in the calculation.

How does the precision of a calculated answer compare to the precision of the measurements used to obtain it?

A calculated answer cannot be more precise than the least precise measurement used in the calculation.

Page 43: Chapter 3 Observation, Measurement and Calculations.

Question

A technician experimentally determined the boiling point of octane to be 124.1ºC. The actual boiling point of octane is 125.7ºC. Calculate the error and the percent error.

Error = experimental value – accepted value

error = 124.1ºC – 125.7ºC = -1.6ºC

Absolute error / accepted value x 100%

% error = -1.6ºC / 125.7ºC x 100% = 1.3%

Page 44: Chapter 3 Observation, Measurement and Calculations.

Question

Determine the number of significant figures in each of the following

11 soccer playerunlimited

0.070 020 meter5

10,800 meters3

5.00 cubic meters3

Page 45: Chapter 3 Observation, Measurement and Calculations.

QuestionSolve the following and express each answer in scientific

notation and to the correct number of significant figures.

(5.3 x 104) + (1.3 x 104)6.6 x 104

(7.2 x 10-4) / (1.8 x 103)4.0 x 10-7

(104)(10-3) (106)107

(9.12 x 10-1) - (4.7 x 10-2)8.65 x 10-1

(5.4 x 104) (3.5 x 109)18.9 x 1013 or 1.9 x 10 14

Page 46: Chapter 3 Observation, Measurement and Calculations.

End of section 3.1

Page 47: Chapter 3 Observation, Measurement and Calculations.

International Systems of Units• The standards of measurement used in science are

those of the metric system

• All metric units are based on multiples of 10

• Metric system was originally establish in France in 1795

• The International System of Units (SI) is a revised version of the metric system.

• The SI comes from the French name, le Systeme International d’Unites.

• The SI was adopted by international agreement in 1960.

Page 48: Chapter 3 Observation, Measurement and Calculations.

International Systems of Units

There are seven SI base units

SI Base Units

Quantity SI base unit SymbolLength Meter m

Mass kilogram kg

Temperature kelvin K

Time second s

Amount mole mol

Luminous intensity candela cd

Electric current ampere A

Page 49: Chapter 3 Observation, Measurement and Calculations.

Metric Prefixes

Meter (m)

Deka(da) 101

Hecto (hm) 102

Kilo (k) 103

Deci (d) 10-1

Centi (c) 10-2

Milli (m) 10-3

Micro (µ) 10-6

Nano (nm) 10-9

Pico (pm) 10-12

Mega (M)

left

right

Page 50: Chapter 3 Observation, Measurement and Calculations.

Metric Conversions

1.0 decimeter (dm) = ? hectometers

0.001 hectometer (hm)

2.5 hectometer (hm) = ? millimeters

250,000 millimeters (mm)

9.7 centimeters (cm) = ? kiometers

0.000097 kilometers (km)

7.4 grams (g) = ? Milligrams (mg)

7400 milligrams (mg)

Page 51: Chapter 3 Observation, Measurement and Calculations.

Other Common Conversions

1 cm3 = 1ml

1dm3 = 1L

1 inch = 2.54 cm

1kg = 2.21 lb

454 g = 1 lb

4.18 J = 1 cal

1 mol = 6.02 x 1023 pieces

1 GA = 3.79 L

Page 52: Chapter 3 Observation, Measurement and Calculations.

Units of Length

metermeter – the basic SI unit of length or linear measure

Common metric units of length include the centimeter (cm), meter (m), and kilometer (km)

Page 53: Chapter 3 Observation, Measurement and Calculations.

Units of Volume

VolumeVolume -the space occupied by any sample of matter

Volume (cube or rectangle) = length x width x height

The SI unit of volume is the amount of space occupied by a cube that is 1m along each edge. (mm33)

Liter Liter (L) – non SI unit – the volume of a cube that is 10cm along each edge (1000cm1000cm33)

The units milliliter and cubic centimeter are used interchangeably.

1 cm3 = 1ml

1dm3 = 1L

Page 54: Chapter 3 Observation, Measurement and Calculations.

Units of MassCommon metric units of mass include the kilogram,

gram, milligram and microgram.

Weight Weight – is a force that measures the pull on a given mass by gravity.

Weight is a measure of force and is different than mass.

MassMass – measure of the quantity of matter.

Although, the weight of an object can change with its location, its mass remains constant regardless of its location.

Objects can become weightless, but not massless

Page 55: Chapter 3 Observation, Measurement and Calculations.

Units of Temperature

TemperatureTemperature – measure of how hot or cold an object is.

The objects temperature determines the direction of heat transfer.

When two objects at different temperatures are in contact, heat moves from the object at the higher temperature to the object at the lower temperature.

Scientist use two equivalent units of temperature, the degree Celsius and the Kelvin.

Page 56: Chapter 3 Observation, Measurement and Calculations.

Units of Temperature

The Celsius scale of the metric system is named after Swedish astronomer Anders Celsius.

The Celsius scale sets the freezing point of water at 0ºC and the boiling point of water at 100ºC

The Kelvin scale is named for Lord Kelvin, a Scottish physicist and mathematician.

On the Kelvin scale, the freezing point of water is 273.15 kelvins (K), & the boiling point is 373.15 K.

With the Kelvin scale the degree (º) sign is not used

Page 57: Chapter 3 Observation, Measurement and Calculations.

Units of Temperature

A change of 1 º on the Celsius scale is equivalent to one kelvin on the Kelvin scale.

The zero point on the Kelvin scale, 0K, or absolute zero, is equal to -273.15º C.

K = ºC + 273

ºC = K - 273

.

Page 58: Chapter 3 Observation, Measurement and Calculations.
Page 59: Chapter 3 Observation, Measurement and Calculations.

Units of Energy

EnergyEnergy – the capacity to do work or to produce heat.

The joule and the calorie are common units of energy.

The jouleThe joule (J) is the SI unit of energy named after the English physicist James Prescott Joule.

1 calorie1 calorie (cal) - is the quanity of heat that raises the temperature of 1 g of pure water by 1ºC.

1 J = 0.2390 cal

1 cal = 4.184 J

Page 60: Chapter 3 Observation, Measurement and Calculations.

End of Section 3.2

Page 61: Chapter 3 Observation, Measurement and Calculations.

Conversion Factors1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies

Different ways to express the same amount of money

1 meter =10 decimeters =100 centimeters =1000 millimeters

Different ways to express length

Whenever two measurements are equivalent, a ratio of the two measurements will equal 1.

1 m = 100 cm = 1 1m

Conversion factor

Page 62: Chapter 3 Observation, Measurement and Calculations.

Conversion Factors

Conversion factor – a ratio of equivalent measurements

100 cm / 1 m

1000 mm / 1 m

The measurement on the top is equivalent to the measurement on the bottom

Read “one hundred centimeters per meter” and “1000 millimeters per meter”

Smaller number 1 m larger unitLarger number 100 cm smaller unit

Page 63: Chapter 3 Observation, Measurement and Calculations.

Conversion FactorsWhen a measurement is multiplied by a conversion factor,

the numerical value is generally changed, but the actual size of the quantity measured remains the same.

Conversion factors within a system of measurements are defined quantities or exact quantities.

Therefore, they have an unlimited number of significant figures and do not affect the rounding of a calculated answer.

How many significant figures does a conversion factor within a system of measurements have?

Page 64: Chapter 3 Observation, Measurement and Calculations.

Dimensional AnalysisDimensional analysis – a way to analyze and solve

problems using the units, or dimensions, of the measurements.

How many minutes are there in exactly one week?

60 minutes = 1 hour 24 hours = 1 day7 days = 1 week

1 week 7 days 24 hours 60 minutes = 10,080 min 1 week 1 day 1 hour

1.0080 x 104 min

Page 65: Chapter 3 Observation, Measurement and Calculations.

Dimensional AnalysisHow many seconds are in exactly a 40-hr work

week?

60 minutes = 1 hour 24 hours = 1 day7 days = 1 week 60 seconds = 1

minute

40 hr 60 min 60 sec = 144,000 s 1 hr 1 min

1.44000 x 105 s

Page 66: Chapter 3 Observation, Measurement and Calculations.

Dimensional AnalysisAn experiment requires that each student use an

8.5 cm length of Mg ribbon. How many students can do the experiment if there is a 570 cm length of Mg ribbon available?

570 cm ribbon 1 student = 67 students 8.5 cm ribbon

2 sig figs

Page 67: Chapter 3 Observation, Measurement and Calculations.

Dimensional AnalysisA 1.00º increase on the Celsius scale is equivalent to a 1.80º increase on the Fahrenheit scale. If a temperature increases by 48.0ºC, what is the corresponding temperature increase on the Fahrenheit scale?

48.0ºC 1.80ºF = 86.4ºF 1.00ºC

A chicken needs to be cooked 20 minutes for each pound it weights. How long should the chicken be cooked if it weighs 4.5 pounds?

4.5 lb 20 min = 90 min lb

Page 68: Chapter 3 Observation, Measurement and Calculations.

Dimensional AnalysisGold has a density of 19.3 g/cm3. What is the density in kg/m3

19.3 g 1 kg 1 x 106 cm3 = 1.93 x 104 kg / m3 cm3 1000 g m3

There are 7.0 x 106 red blood cell (RBC) in 1.0 mm3 of blood. How many red blood cells are in 1.0 L of blood?

7.0 x 106 RBC 1 x 106 mm3 1 dm3 = 7.0 x 1012

1.0 mm3 dm3 1 L

Page 69: Chapter 3 Observation, Measurement and Calculations.

Dimensional Analysis1.00 L of neon gas contains 2.69 x 1022 neon atoms. How many neon atoms are in 1.00mm3 of neon gas under the same conditions?

2.69 x 1022 atoms 1 L dm3

1.00 L 1 dm3 1 x 106 mm3

2.69 x 1016 atoms in 1.00mm3 of gas

Page 70: Chapter 3 Observation, Measurement and Calculations.

QuestionsWhat conversion factor would you use to convert between these pairs of units?

Minutes to hours

1 hour / 60 minutes

grams to milligrams

1000 mg / 1 g

Cubic decimeters to milliliters

1000 ml / 1 dm3

Page 71: Chapter 3 Observation, Measurement and Calculations.

QuestionsAn atom of gold has a mass of 3.271 x 10-22g. How many atoms of gold are in 5.00 g of gold?

1.53 x 1022 atoms of gold

Light travels at a speed of 3.00 x 1010 cm/sec. What is the speed of light in km/hour?

1.08 x 109 km/hr

Page 72: Chapter 3 Observation, Measurement and Calculations.

QuestionsConvert the following. Express your answers in scientific notation.

7.5 x 104 J to kJ

7.5 x 101 kJ

3.9 x 105 mg to dg

3.9 x 103dg

2.21 x 10-4 dL to µL

2.21 x 101µL

Page 73: Chapter 3 Observation, Measurement and Calculations.

QuestionsMake the following conversions. Express your answers in standard exponential form.

14.8 g to µg

1.48 x 107 µg

3.75 x 10-3 kg to g

3.72 g

66.3 L to cm3

6.63 x 104 cm3

Page 74: Chapter 3 Observation, Measurement and Calculations.

End of Section 3.3

Page 75: Chapter 3 Observation, Measurement and Calculations.

DensityIf a piece of led and a feather of the same volume are weighted, the lead would have a greater mass than the feather.

It would take a much larger volume of feather to equal the mass of a given volume of lead.

Density = mass / volumeD = m / v

Mass is a extensive property (a property that depends on the size of the sample)

Density is an intensive property (depends on the composition of a substance, not on the size of the sample)

Page 76: Chapter 3 Observation, Measurement and Calculations.

Density

A helium filled balloon rapidly rises to the ceiling when released.

Whether a gas-filled balloon will sink or rise when released depends on how the density of the gas compares with the density of air.

Helium is less dense than air, so a helium filled balloon rises.

Page 77: Chapter 3 Observation, Measurement and Calculations.

Density and TemperatureThe volume of most substances increase as the temperature increases.

The mass remains the same despite the temperature and volume changes.

So if the volume changes with temperature while the mass remains constant, then the density must also change with temperature.

The density of a substance generally decreases as its temperature increases. (water is the exception: ice floats because it is less dense than liquid water)

Page 78: Chapter 3 Observation, Measurement and Calculations.

Questions

A student finds a shiny piece of metal that she thinks is aluminum. In the lab, she determines that the metal has a volume of 245cm3 and a mass of 612g. Was is the density? Is it aluminum?

D = 612g / 245cm3 = 2.50g/cm3

D of aluminum is 2.70 g/cm3; no it is not aluminum

A bar of silver has a mass of 68.0 g and a volume of 6.48 cm3. What is the density?

D = 68.0g / 6.48 cm3 = 10.5 g/cm3

Page 79: Chapter 3 Observation, Measurement and Calculations.

Questions

The density of boron is 2.34 g/cm3. Change 14.8 g of boron to cm3 of boron.

D = m / v or v = m / D

V = 14.8 g cm3 = 6.32 cm 3

2.34 g

Convert 4.62 g of mercury to cm3 by using the density of mercury -13.5 g/cm3.

V = 46.2 g cm3 = 0.342 cm 3

13.5 g

Page 80: Chapter 3 Observation, Measurement and Calculations.

Density

D = m / v

v = m / D

m = D · v

Page 81: Chapter 3 Observation, Measurement and Calculations.

End of Chapter 3


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