chapter 2 measurements. homework do “questions and problems” do “questions and problems” 2.1...

Chapter 2Chapter 2MeasurementsMeasurements

HomeworkHomework

Do “Questions and Problems”Do “Questions and Problems” 2.1 through 2.73 (odd)2.1 through 2.73 (odd)

Do “Understanding the Concepts”Do “Understanding the Concepts” 2.75, 2.792.75, 2.79

Do “Additional Questions and Do “Additional Questions and Problems”Problems” 2.83 through 2.103 (odd)2.83 through 2.103 (odd)

Do “Challenge Questions”Do “Challenge Questions” 2.105-2.113 (odd)2.105-2.113 (odd)

MeasurementMeasurement The most useful tool of the chemistThe most useful tool of the chemist Most of the basic concepts of chemistry Most of the basic concepts of chemistry

were obtained through data compiled were obtained through data compiled by taking measurementsby taking measurements

How much…?How much…? How long…?How long…? How many...?How many...? These questions cannot be answered These questions cannot be answered

without taking measurementswithout taking measurements The concepts of chemistry were The concepts of chemistry were

discovered as data was collected and discovered as data was collected and subjected to the scientific methodsubjected to the scientific method

MeasurementMeasurement The estimation of the magnitude of an The estimation of the magnitude of an

object relative to a unit of measurementobject relative to a unit of measurement Involves a measuring device Involves a measuring device

ie: meterstick, scaleie: meterstick, scale The device is calibrated to compare the The device is calibrated to compare the

object to some standard object to some standard (inch/centimeter, pound/kilogram)(inch/centimeter, pound/kilogram)

Quantitative observation with two parts: Quantitative observation with two parts: A A numbernumber and a and a unitunit Number tells the total of the quantity Number tells the total of the quantity

measuredmeasured Unit tells the scale (dimensions)Unit tells the scale (dimensions)

MeasurementMeasurement A unit is a standard (accepted) quantityA unit is a standard (accepted) quantity Describes what is being added upDescribes what is being added up Units are essential to a measurementUnits are essential to a measurement For example, you need “six of sugar”For example, you need “six of sugar”

teaspoons?teaspoons? ounces?ounces? cups?cups? pounds?pounds?

Units of measurementUnits of measurement Units tells the magnitude of the standardUnits tells the magnitude of the standard Two most commonly used systems of Two most commonly used systems of

units of measurementunits of measurement US systemUS system: Used in everyday : Used in everyday

commerce (USA and Britain*)commerce (USA and Britain*) Metric systemMetric system: Used in everyday : Used in everyday

commerce and science (The rest of the commerce and science (The rest of the world)world)

SI Units (1960): A modern, revised form SI Units (1960): A modern, revised form of the metric system set up to create of the metric system set up to create uniformity of units used worldwide uniformity of units used worldwide (world’s most widely used)(world’s most widely used)

Metric SystemMetric System A decimal system of measurement A decimal system of measurement

based on the meter and the grambased on the meter and the gram It has a single It has a single base unitbase unit per physical per physical

quantity quantity All other units are multiples of 10 of All other units are multiples of 10 of

the base unitthe base unit The power (multiple) of 10 is The power (multiple) of 10 is

indicated by a prefixindicated by a prefix

Metric SystemMetric System In the metric system there is one base In the metric system there is one base

unit for each type of measurementunit for each type of measurement lengthlength volumevolume massmass

The base units multiplied by the The base units multiplied by the appropriate appropriate power of 10power of 10 form smaller or form smaller or larger unitslarger units

The prefixes are always the same, The prefixes are always the same, regardless of the base unitregardless of the base unit millimilligrams and grams and millimilliliters both mean liters both mean

1/1000 of the base unit1/1000 of the base unit

LengthLength

MeterMeter Base unit of length in metric and SI systemBase unit of length in metric and SI system About 3 ½ inches longer than a yardAbout 3 ½ inches longer than a yard

1 m = 1.094 yd1 m = 1.094 yd

LengthLength

Other units of Other units of length are derived length are derived from the meterfrom the meter

Commonly use Commonly use centimeters (cm)centimeters (cm) 1 m = 100 cm1 m = 100 cm 1 inch = 2.54 cm 1 inch = 2.54 cm

(exactly)(exactly)

VolumeVolume

Measure of the amount Measure of the amount of three-dimensional of three-dimensional space occupied by a space occupied by a objectobject

Derived from lengthDerived from length SI unit = SI unit = cubic meter cubic meter

(m(m33)) Metric unitMetric unit == liter (L) or liter (L) or

10 cm10 cm3 3

Commonly measure Commonly measure smaller volumes in smaller volumes in cubic centimeters (cmcubic centimeters (cm33))

Volume = side × side × side

Volume = side × side × side

VolumeVolume Since it is a three-Since it is a three-

dimensional dimensional measure, its units measure, its units have been cubed have been cubed

SI base unit = SI base unit = cubic meter (mcubic meter (m33))

This unit is too This unit is too large for practical large for practical use in chemistryuse in chemistry

Take a volume Take a volume 1000 times smaller 1000 times smaller than the cubic than the cubic meter, 1dmmeter, 1dm33

VolumeVolume

Metric base unitMetric base unit == 1dm1dm3 3 == liter (L) liter (L)

1L = 1.057 qt1L = 1.057 qt Commonly measure Commonly measure

smaller volumes in smaller volumes in cubic centimeters cubic centimeters (cm(cm33))

Take a volume 1000 Take a volume 1000 times smaller than times smaller than the cubic decimeter, the cubic decimeter, 1cm1cm33

VolumeVolume The most commonly The most commonly

used unit of volume used unit of volume in the laboratory: in the laboratory: milliliter (mL)milliliter (mL)

1 mL = 1 cm1 mL = 1 cm33

1 L= 1 dm1 L= 1 dm3 3 = 1000 = 1000 mLmL

1 m1 m3 3 = 1000 dm= 1000 dm3 3 = = 1,000,000 cm1,000,000 cm3 3

Use a graduated Use a graduated cylinder or a pipette cylinder or a pipette to measure liquids in to measure liquids in the labthe lab

MassMass Measure of the total quantity of Measure of the total quantity of

matter present in an objectmatter present in an object SI unit (base) = SI unit (base) = kilogram (kg) kilogram (kg) Metric unit (base) = Metric unit (base) = gram (g)gram (g) Commonly measure mass in grams Commonly measure mass in grams

(g) or milligrams (mg)(g) or milligrams (mg) 1 kg = 1000 g1 kg = 1000 g 1 g = 1000 mg1 g = 1000 mg 1 kg = 2.205 pounds 1 kg = 2.205 pounds 1 lb = 453.6 g1 lb = 453.6 g

TemperatureTemperature

Measurement of the intensity of heat energy in matter

Hotness or coldness of an object Fahrenheit Scale, °F

Everyday Use in USA Not used in science Water’s freezes at 32°F, boils at

212°F

TemperatureTemperature Celsius Scale, °CCelsius Scale, °C

Metric UnitMetric Unit Used in science (USA) and rest of worldUsed in science (USA) and rest of world Temperature unit larger than the Fahrenheit Temperature unit larger than the Fahrenheit

unitunit Water’s freezes = 0°C, boils at 100°CWater’s freezes = 0°C, boils at 100°C

Kelvin Scale, K Kelvin Scale, K SI UnitSI Unit Used in scienceUsed in science Temperature unit same size as Celsius unitTemperature unit same size as Celsius unit Water’s freezes at 273 K, boils 373 KWater’s freezes at 273 K, boils 373 K Absolute zero is the lowest temperature theoretically Absolute zero is the lowest temperature theoretically

possiblepossible

TemperatureTemperature Scales determined by different degree Scales determined by different degree

sizes and different reference pointssizes and different reference points There are 180 degrees between the There are 180 degrees between the

freezingfreezing and and boiling pointsboiling points on the on the

Fahrenheit scaleFahrenheit scale The number of degree units between the The number of degree units between the

freezing freezing and and boiling pointboiling point on the Celsius on the Celsius

and Kelvin scales are the same: 100 and Kelvin scales are the same: 100

degreesdegreesA change in 1 °C = a change in 1 KA change in 1°C or 1 K = a change of 1.8 °F

Fig2_9

32ºF 0ºC

100ºC Boiling point

Freezing point

212ºF

180Fahrenheitdegrees

100Celsiusdegrees

Prefixes and EqualitiesPrefixes and Equalities One base unit for each type of measurementOne base unit for each type of measurement Length (Length (metermeter), volume (), volume (literliter), and mass (), and mass (gramgram*)*) The base units are then multiplied by the The base units are then multiplied by the

appropriate power of 10 to form larger or smaller appropriate power of 10 to form larger or smaller unitsunits

base unit

Prefixes and Equalities Prefixes and Equalities ((memorizememorize))

Mega (M) 1,000,000 Mega (M) 1,000,000 10 1066

Kilo Kilo (k)(k) 1,000 1,000 10 1033

BaseBase 1 1 10 1000

DeciDeci (d)(d) 0.1 0.1 10 10-1-1

CentiCenti (c)(c) 0.01 0.01 10 10-2-2

MilliMilli (m)(m) 0.001 0.001 10 10--

33

MicroMicro (µ) 0.000001(µ) 0.000001 10 10--

66

Nano Nano (n)(n) 0.000000001 10 0.000000001 10-9-9

× base unit

meter liter gram

Remembering Metric Remembering Metric SystemSystem

Keep in mind which unit is Keep in mind which unit is largerlargerA kilogram is larger than a A kilogram is larger than a

gram, so there must be a gram, so there must be a number of grams in one number of grams in one kilogramkilogram

This can help you check if you This can help you check if you have the conversion correcthave the conversion correctn < µ < m < c < base < k < Mn < µ < m < c < base < k < M

Scientific NotationScientific Notation

A system in which an ordinary A system in which an ordinary decimal number (m) is expressed as a decimal number (m) is expressed as a product of a number between 1 and product of a number between 1 and 10, multiplied by 10 raised to a 10, multiplied by 10 raised to a power (n)power (n)

Used to write very large or very Used to write very large or very small numberssmall numbers

Based on powers of 10Based on powers of 10n10 m

Scientific NotationScientific Notation

Consists of a Consists of a numbernumber ( (coefficientcoefficient) ) followed by a power of 10 (followed by a power of 10 (x 10x 10nn))

Negative exponentNegative exponent: Number is : Number is less less than 1than 1

Positive exponentPositive exponent: Number is : Number is greater greater than 1than 1

210 7.03

coefficient exponential term

exponent

Scientific NotationScientific Notation In an ordinary cup of water there are:In an ordinary cup of water there are:

Each molecule has a massEach molecule has a mass of:of:

0.0000000000000000000000299 gram0.0000000000000000000000299 gram

In scientific notation:In scientific notation:7.91 7.91 хх 10 102424 molecules molecules

2.99 2.99 хх 10 10-23-23 gram gram

7,910,000,000,000,000,000,000,000 molecules7,910,000,000,000,000,000,000,000 molecules

Writing in Scientific Writing in Scientific NotationNotation

For small numbers (<1):For small numbers (<1):

1)1) Locate the decimal pointLocate the decimal point

2)2) Move the decimal point to the Move the decimal point to the rightright to to give a coefficient between 1 and 10 give a coefficient between 1 and 10

3)3) The new number is now between 1 and The new number is now between 1 and 1010

4)4) Add the termAdd the term x10 x10-n-n

where where nn is the number of places you moved is the number of places you moved the decimal point. It has a negative signthe decimal point. It has a negative sign

If the decimal point is moved to the If the decimal point is moved to the rightright, , then the exponent is a negative numberthen the exponent is a negative number

Writing in Scientific Writing in Scientific NotationNotation

For large numbers (>1):For large numbers (>1):

1)1) Locate the decimal pointLocate the decimal point

2)2) Move the decimal point to the Move the decimal point to the leftleft to to give a coefficient between 1 and 10 give a coefficient between 1 and 10

3)3) Add the term Add the term x10x10nn

where where nn is the number of places you is the number of places you moved the decimal point. It has a moved the decimal point. It has a positive sign.positive sign.

If the decimal point is moved to the If the decimal point is moved to the leftleft, , the exponent is a positive numberthe exponent is a positive number

ExamplesExamples

Write each of the following in Write each of the following in scientific notationscientific notation12,50012,5000.02020.020237,400,00037,400,0000.00001040.0000104

ExamplesExamples12,50012,500

Decimal place is at the far rightDecimal place is at the far rightMove the decimal place to Move the decimal place to

between the 1 and 2 (1.25)between the 1 and 2 (1.25)The decimal place was moved 4 The decimal place was moved 4

places to the left (large number) places to the left (large number) so exponent is positiveso exponent is positive

1.25x101.25x1044

ExamplesExamples

0.02020.0202Move the decimal place to Move the decimal place to


places to the right (small places to the right (small number) so exponent is negativenumber) so exponent is negative

2.02x102.02x10-2-2

ExamplesExamples

37,400,00037,400,000Decimal place is at the far rightDecimal place is at the far rightMove the decimal place to Move the decimal place to


places to the left (big number) so places to the left (big number) so exponent is positiveexponent is positive

3.74x103.74x1077

ExamplesExamples

0.00001040.0000104Move the decimal place to Move the decimal place to

between the 1 and 0 (1.04)between the 1 and 0 (1.04)The decimal place 5 places to The decimal place 5 places to

the right (small number) so the right (small number) so exponent is negativeexponent is negative

1.04x101.04x10-5-5

ExampleExample 6.442x106.442x1055

5 is positive, move the decimal 5 5 is positive, move the decimal 5 places to the right (to make the places to the right (to make the number bigger)number bigger)

644,200644,200 5.583x105.583x10-2-2

2 is negative, move the decimal 2 2 is negative, move the decimal 2 places to the left (to make the number places to the left (to make the number smaller)smaller)

0.055830.05583

Scientific Notation and Scientific Notation and CalculatorsCalculators

1)1) Enter the coefficient (number)Enter the coefficient (number)

2)2) Push the key: Push the key:

Then enter only the power of 10Then enter only the power of 10

3)3) If the exponent is negative, use the If the exponent is negative, use the key:key:

4)4) DO NOTDO NOT use the multiplication use the multiplication key: key:

to express a number in sci. to express a number in sci. notationnotation

(+/-)(+/-)

XX

EXPEXPEEEE or

Converting Back to a Standard Converting Back to a Standard NumberNumber

1)1) Determine the Determine the signsign of the exponent, of the exponent, nn If If nn is is ++ the decimal point will move to the decimal point will move to

the right (gives a number greater than the right (gives a number greater than one)one)

If If nn is is –– the decimal point will move to the the decimal point will move to the left (gives a number less than one)left (gives a number less than one)

2)2) Determine the value of the exponent of 10Determine the value of the exponent of 10 The “power of ten” determines the The “power of ten” determines the

number of places to move the decimal number of places to move the decimal pointpoint

Using Scientific NotationUsing Scientific Notation To compare numbers written in scientific To compare numbers written in scientific

notationnotation FirstFirst compare the exponents of 10 compare the exponents of 10

The larger the exponent, the larger the The larger the exponent, the larger the numbernumber

If the exponents are the If the exponents are the samesame, then , then compare coefficients directlycompare coefficients directly Which number is larger?Which number is larger?

21.8 21.8 хх 10 1033 or 2.05 or 2.05 хх 10 1044

2.18 2.18 хх 10 1044 > 2.05 > 2.05 хх 10 1044

Measured Numbers and Measured Numbers and Significant FiguresSignificant Figures

Two kinds of numbersTwo kinds of numbersCounted (exact)Counted (exact)Measured Measured

Exact NumbersExact Numbers Numbers known with certainty Numbers known with certainty Unlimited number of significant Unlimited number of significant

figuresfigures They are eitherThey are either

counting numberscounting numbers10 beds, 6 pills, 4 chairs10 beds, 6 pills, 4 chairs

defined numbersdefined numbers100 cm = 1 m; 12 in = 1 ft; 1 in = 100 cm = 1 m; 12 in = 1 ft; 1 in = 2.54 cm2.54 cm

1 kg = 1000 g; 1 lb = 16 oz1 kg = 1000 g; 1 lb = 16 oz1000 mL = 1 L; 1 gal = 4 qts.1000 mL = 1 L; 1 gal = 4 qts.1 minute = 60 seconds1 minute = 60 seconds

Measured NumbersMeasured Numbers

A measurement always has some A measurement always has some amount of uncertainty amount of uncertainty Involves reading a measuring Involves reading a measuring

devicedevice Uncertainty comes from the tool Uncertainty comes from the tool

used for comparisonused for comparison i.e. Some rulers show smaller i.e. Some rulers show smaller

divisions (markings) than othersdivisions (markings) than others

Measured NumbersMeasured Numbers Always have to Always have to

estimate the value estimate the value between the two between the two smallest divisions on smallest divisions on a measuring devicea measuring device

Every person will Every person will estimate it slightly estimate it slightly differently, so there differently, so there is some uncertainty is some uncertainty present as to the present as to the true valuetrue value 2.8 to 2.9 cm

Significant FiguresSignificant Figures

To indicate the uncertainty of a single To indicate the uncertainty of a single measurement scientists use a system measurement scientists use a system called significant figurescalled significant figures

Significant figures: All digits known Significant figures: All digits known with certainty plus one digit that is with certainty plus one digit that is uncertainuncertain

The last digit written in a The last digit written in a measurement is the number that is measurement is the number that is considered to be uncertainconsidered to be uncertain

Unless stated otherwise, the Unless stated otherwise, the uncertainty in the last digit is ±1uncertainty in the last digit is ±1

Counting Significant Counting Significant FiguresFigures

Nonzero integers are always Nonzero integers are always significantsignificant

Zeros (may or may not be Zeros (may or may not be significant)significant) Leading zeros Leading zeros nevernever count as count as

significant figuressignificant figures Captive zeros are Captive zeros are alwaysalways significant significant Trailing zeros are significant if the Trailing zeros are significant if the

number has a decimal pointnumber has a decimal point Exact numbers have an Exact numbers have an unlimitedunlimited

number of significant figuresnumber of significant figures

Rounding Off RulesRounding Off Rules

If the digit to be removedIf the digit to be removed• is less than 5, the preceding digit is less than 5, the preceding digit

stays the samestays the same• is equal to or greater than 5, the is equal to or greater than 5, the

preceding digit is increased by 1preceding digit is increased by 1 In a series of calculations, carry In a series of calculations, carry

the extra digits to the final result the extra digits to the final result and and thenthen round off round off

Significant Figures in CalculationsSignificant Figures in Calculations

Calculations cannot improve the Calculations cannot improve the precision of experimental measurementsprecision of experimental measurements

The number of significant figures in any The number of significant figures in any mathematical calculation is limited by mathematical calculation is limited by the least precise measurement used in the least precise measurement used in the calculationthe calculation

Two operational rules to ensure no Two operational rules to ensure no increase in measurement precisionincrease in measurement precision addition and subtractionaddition and subtraction multiplication and divisionmultiplication and division

Multiplication/DivisionMultiplication/Division

Product or quotient has the same Product or quotient has the same number of significant figures as the number of significant figures as the number with the number with the smallest numbersmallest number of of significant figuressignificant figures

Count the number of significant Count the number of significant figures in each numberfigures in each number

Round the result so it has the same Round the result so it has the same number of significant figures as the number of significant figures as the number with the number with the smallest numbersmallest number of of significant figuressignificant figures

ExampleExample

The number with the fewest The number with the fewest significant figures is 1.1 so the significant figures is 1.1 so the answer has 2 significant figuresanswer has 2 significant figures

0.1021 0.082103 273 1.1

2.0804382 SF

5 SF 3 SF

2.1

4 SF

2 SF

Addition/SubtractionAddition/Subtraction

Sum or difference is limited Sum or difference is limited by the number with the by the number with the smallest numbersmallest number of of decimal decimal placesplaces

Find number with the fewest Find number with the fewest decimal placesdecimal places

Round answer to the same Round answer to the same decimal placedecimal place

ExampleExample

The number with the fewest The number with the fewest decimal places is 171.5 so decimal places is 171.5 so the answer should have 1 the answer should have 1 decimal placedecimal place

171.5 72.915 8.23 236.1851 d.p. 3 d.p. 2 d.p.

236.2

1 d.p.

EqualitiesEqualities A fixed relationship between two A fixed relationship between two

quantitiesquantities Shows the relationship between two Shows the relationship between two

units that measure the same quantityunits that measure the same quantity The relationships are The relationships are exact, exact, not not

measuredmeasured 1 min = 60 s1 min = 60 s 12 inches = 1 ft12 inches = 1 ft 1 dozen = 12 items (units)1 dozen = 12 items (units) 1L = 1000 mL1L = 1000 mL 4 quarts = 1 gallon4 quarts = 1 gallon 1 pound = 454 grams1 pound = 454 grams

Conversion FactorsConversion Factors Many problems in chemistry involve a Many problems in chemistry involve a

conversion of unitsconversion of units Conversion factor: Conversion factor: An equality An equality

expressed as a fraction expressed as a fraction Used as a multiplier to convert a Used as a multiplier to convert a

quantity in one unit to its equivalent in quantity in one unit to its equivalent in another unitanother unit May be exact or measuredMay be exact or measured Both parts of the conversion factor should Both parts of the conversion factor should

have the same number of significant have the same number of significant figuresfigures

Problem SolvingProblem Solving Conversion Factors Stated Within a Conversion Factors Stated Within a

ProblemProblem The average person in the U.S. The average person in the U.S.

consumes one-half pound of consumes one-half pound of sugar per day. How many sugar per day. How many pounds of sugar would be pounds of sugar would be consumed in one year?consumed in one year?

1)1) State the initial quantity given (unit): State the initial quantity given (unit): One yearOne year State the final quantity needed (unit): State the final quantity needed (unit): PoundsPounds

2)2) Write a sequence of units (Write a sequence of units (planplan) which ) which begins with the initial unit and ends begins with the initial unit and ends with the desired unit:with the desired unit:year day pounds

Problem SolvingProblem SolvingDimensional Analysis ExampleDimensional Analysis Example

3)3) For each unit change,For each unit change,

State the equalities:State the equalities: Every equality will have two Every equality will have two

conversion factorsconversion factors

1 cal 4.184 J1 cal 4.184 J1 cal 4.184 J

year day pounds

0.5 lb sugar 0.5 lb sugar =1day=1day

365 days = 1 365 days = 1 yearyear

Problem SolvingProblem SolvingDimensional Analysis ExampleDimensional Analysis Example

State the conversion factors:State the conversion factors:

4)4) Set Up the problem:Set Up the problem:

year1year1day(s) 365

sugar lbs. 183

sugar lb. 0.5day1

day1 sugar lb.0.5 and

day1sugar lb 0.5

Guide to Problem Solving when Guide to Problem Solving when Working Dimensional Analysis Working Dimensional Analysis

ProblemsProblems Identify the known or given quantity and the Identify the known or given quantity and the

units of the new quantity to be determinedunits of the new quantity to be determined Write out a sequence of units which starts Write out a sequence of units which starts

with your initial units and ends with the with your initial units and ends with the desired units (“the unit pathway”)desired units (“the unit pathway”)

Write out the necessary equalities and Write out the necessary equalities and conversion factors conversion factors

Perform the mathematical operations that Perform the mathematical operations that connect the unitsconnect the units

Check that the units cancel properly to Check that the units cancel properly to obtain the desired unitobtain the desired unit

Does the answer make sense?Does the answer make sense?

DensityDensity The ratio of the mass of an object to the The ratio of the mass of an object to the

volume occupied by that objectvolume occupied by that object Tells how tightly the matter within an object Tells how tightly the matter within an object

is packed togetheris packed together Units for solids and liquids = g/cmUnits for solids and liquids = g/cm33

1 cm1 cm33 = 1 mL so also g/mL = 1 mL so also g/mL Unit for gases = g/LUnit for gases = g/L Density: solids > liquids >>> gasesDensity: solids > liquids >>> gases

Density mass

volume

Determining DensityDetermining Density

Weigh the objectWeigh the objectUse a scaleUse a scale

Determine the volume of the Determine the volume of the objectobjectCalculate it if possible (cube)Calculate it if possible (cube)Can also calculate volume by Can also calculate volume by

determining what volume of water determining what volume of water is displaced by an objectis displaced by an objectVolume of Water Displaced = Volume of ObjectVolume of Water Displaced = Volume of Object

Densities of SubstancesDensities of Substances Can use density as a conversion factor Can use density as a conversion factor

between mass and volumebetween mass and volume Given in Table 2.9, page 47Given in Table 2.9, page 47 You will be given any densities on tests You will be given any densities on tests

EXCEPTEXCEPT water water Density of water isDensity of water is 1.000 g/mL1.000 g/mL at at

room temperatureroom temperature 1.00 mL of water weighs how much?1.00 mL of water weighs how much? How many mL of water weigh 15 g?How many mL of water weigh 15 g?

Density ProblemDensity Problem Iron has a density of 7.87 g/cmIron has a density of 7.87 g/cm33. If . If

52.4 g of iron is added to 75.0 mL of 52.4 g of iron is added to 75.0 mL of water in a graduated cylinder, to water in a graduated cylinder, to what volume reading will the water what volume reading will the water level in the cylinder rise?level in the cylinder rise?

m 52.4 g

d 7.87 g cm3

Vi 75.0 mL

Vf ?

Density ProblemDensity Problem

volumemassdensity

1 mL iron7.87 g iron

6.658 mL iron52.4 g iron

6.658 mL iron + 75.0 mL water = 81.7 mL total

1 cm3 = 1 mLdensitymassvolume

Solve for volume of iron

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