unit 2 text

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CH_TER SOLUTIONSMANUAL

Sedion

2 1

Units

o

easurement

p ges 25 30

Practice Problems

p ge 29

1.

A piece of metal with a mass of 147 g is placed

in a 50-mL graduated cylinder. The water level

rises from 20

mL

to 41 mL. What is the density

of the metal?

density =

mass

volume

volume

=

41

mL

- 20 mL

=

21

mL

. 147 g

d

enslty = 21 mL = 7.0 g/mL

2. What is the volume

of

a sample that has a mass

of

20 g and a density of 4 glmL?

volume = mass

density

20R

volume = 4 g/jPt = 5 mL

3.

A metal cube has a mass of 20 g and a volume

of 5 cm

3

. Is the cube made

of

pure aluminum?

Explain your answer.

No;

the

density of aluminum is 2 7 g/cm

3

;

the

density of the cube is 4 g/cm

3

Section 2 1 Assessment

p ge

30

4.

List SI units of measurement for length, mass,

time, and temperature.

length: meter;

mass:

kilogram; time: second;

temperature: kelvin

5.

Describe the relationship between the mass,

volume, and density

of

a material.

Density is

the

mass-to-volume ratio

of

a material.

6. Which ofthese samples have the same density?

DensityData

Sample Mass Volume

A 80g

20mL

B 12 g 4 cm

3

C

33

g

11 ml

Band C

7.

What is the difference between a base unit and a

derived unit?

Base units are defined based on a physical object

or

process. Derived units are defined based

on

a

combination of base units.

8. How does adding the prefix mega to a unit

affect the quantity being described?

It multiplies the

quantity by

10

6

9. How many milliseconds are in a second? How

many centigrams are in a gram?

1000 ms/s; 100 cg/g

10.

Thinking Critically Why does oil float on

water?

Oil is less dense than water.

11. Using Numbers You measure a piece of wood

with a meterstick and it is exactly one meter

long. How many centimeters long is it?

100cm

Solutions Manual

Chemistry: Matter and Change Chapter 2

7

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CHAPTER

D

Sedion

2.2

ScientificNotation

andDimensionalAnalysis

p ges 37-35

PracticeProblems

p ge

32

12.

Expressthefollowingquantitiesinscientific

notation.

a.

700m

7x1 )2 m

b. 38000 m

3.8X 10

4

m

c. 4500 000m

4.5x10

6

m

d. 685000000000m

6.85x

10

11

m

e.

0.0054kg

5.4x10 -

3

kg

f. 0.00000687kg

6.87

x

10-

6

kg

g.

0.000000076kg

7.6

x

10 -

8

kg

h. 0.0000000008kg

8

X

10 -

10

kg

13. Expressthefollowingquantitiesinscientific

notation.

a.

360000s

3.6

x

10S 5

b. 0.000054s

5.4X 10-

5

5

c. 5060s

5.06

x

10

3

5

d. 89000000000s

8.9

X 10

10

5

Chemistry:Matter and

Change.

Chapter2

SOLUTIONS MANUAL

Solve

the

followingadditionand

subtraction

problems.

Express

your answersin scientific

notation.

14. a. 5x 10-

5

m

+

2 X

10-

5

m

7x10-

5

m

b. 7X

10

8

m 4 X 10

8

m

3x

10

8

m

c. 9 X

10

2

m 7 X

10

2

m

2

x

10

2

m

d. 4X10-

12

m+1X lO-

12

m

5

x10-

12

m

e.

1.26X lQ4 kg+2.5 X10

3

kg

1.26

x1()4

kg

+

0.25

X 10

4

kg=1.51

x

1()4 kg

f. 7.06X 10-

3

kg+1.2X10-

4

kg

7.06

X 10-

3

kg

+

0.12

X 10-

3

kg

=7.18X 10 -

3

kg

g.

4.39X

105

kg - 2.8X lQ4 kg

4.39

x

10S

kg-

0.28

x

10S

kg

=4.11 X

10

5

kg

h. 5.36X10-

1

kg 7.40X

10-

2

kg

5.36

x

10-

1

kg- 0.740X 10-

1

kg

=

4.62

X

10-

1

kg

PracticeProblems

p ge 33

Solvethefollowingmultiplicationand division

problems.Expressyour

answers

inscientific

notation.

15. Calculatethefollowingareas.Reportthe

answersinsquarecentimeters,cm

2

a. (4 X10

2

em) X

1

X

10

8

em)

4

x

10

10

cm

2

b. (2 X10-

4

em) X

(3

X

10

2

cm)

6

x

10-

2

cm

2

c. (3 X10

1

cm)X (3 X10 -

2

cm)

9 x 10 -

1

cm

2

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CHAPTER

SOLUTIONS

M NU L

d. (1

X

10

3

cm)

X

(5

X

10-

1

cm)

5x 10

2

cm

2

16. Calculatethefollowingdensities.Reportthe

answers

in

glcm

3

.

a.

(6 X 10

2

g)

+-

(2 X 10

1

cm

3

)

3

x

10

1

g/cm

3

b.

(8

X 10

4

g)

(4

X 10

1

cm

3

)

2

x10

3

g/cm

3

c. (9 X

UP g)

+- (3 X 10-

1

cm

3

)

3 x10

6

g/cm

3

d.

(4 X 10-

3

g)

+-

(2 X 10-

2

cm

3

)

2

x

10 -

1

g/cm

3

Practice Problems

p ge 34

Refer to Table2-2to figure

out

the relationship

betweenunits.

17.

a. Convert360stoms.

360..8"X

1 ~ ; S = 360000ms

b. Convert4800gtokg.

1

kg

4800Ax

1000.....-=4.8

kg

c. Convert5600dm tom.

1m

5600.Pnrx 10

JIn I

= 560m

d.

Convert72gtomg.

1000mg

72Ji'x

= 72000mg

18. a. Convert245mstos.

1

s

245,JM'x 1000JRS" =0.245s

b.

Convert5mtocm.

5

Jl{x

100

cm

= 500cm

1

)It'"

Solutions Manual

c.

COllvert6800

cm

tom.

#J

1

m

6800,....x 1 =68

m

d.

Convert25kgtoMg.

1 Mg

25..kf(x

1000)4(= 0.025Mg

Practice Problems

page3S

19.

Howmanysecondsaretherein

24

hours?

60.JRirr 60s

24 J{ x 1JY x 1

p:Hrr =

86400s

20.

Thedensityof goldis 19.3glmL.Whatis

gold'sdensityindecigramsperliter?

19.3,..f( 10 dg

1000..,mt"=

193000 d L

1 jRI:." x

1JY

x 1L 9

21.

Acaristraveling90.0kilometers

per

hour.

Whatisitsspeed

in

miles

per

minute?

One

kilometer 0.62miles.

90.0"kRr'x 0.62mi x

...t1l =

0.930

mi/min

1

J:r' J...krtt 60

min

Section 2.2 Assessment

page3S

22. Isthenumber5X 10-

4

greateror lessthan

1.0?Explainyouranswer.

less than one because the exponent is negative

23.

WhenmUltiplyingnumbers

in

scientificnota

tion,whatdo youdowiththeexponents?

Add them.

24. Writethequantities3

X 10-

4

cm and3

X

104 km

inordinarynotation.

0.0003

cm;

30

000

km

25. Writeaconversionfactorforcubiccentimeters

andmilliliters.

1 cm

3

/1 mL

26. Whatisdimensionalanalysis?

a method

of

problem solving that focuses on the

units used to describe matter

Chemistry:

Matter

and Change Chapter 2

9

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CHAPTER SOLUTIONS

M A N U A L

27.ThinkingCriticallyWhen subtractingor

addingtwonumbersinscientificnotation,why

dotheexponentsneedtobethesame?

Equal place values should be added to each other.

28. ApplyingConcepts

Youareconverting68

km

tometers.Youransweris

0.068

m.Explainwhy

thisanswerisincorrectandthelikelysource

of

theerror.

Because meters are smaller than kilometers, there

should be more meters than kilometers. The 68 km

was divided by 1000, not multiplied by 1000.

Sedion

2 3

How reliable are

measurements?

pages

36-42

Practice Problems

page

38

Table 2-4

Errors for Data in

Table

23

Student A StudentB StudentC

Trial 1 -0.05 glcm

3

-0.19 glcm

3

+0.11 glcm

3

Trial 2

0.01

glcm

3

0.09

glcm

0.10

glcm

Trial

3

0.02

glcm

0.14

glcm

+0.12

g/cm3

Usedata

from

Table2-4.

Remember

toignore

plus and

minus

signs.

29.

CalculatethepercenterrorsforStudents

B's

trials.

x 100

=

11.9%

x 100

=

5.66%

x 100

=

8.80%

Note: The answers are reported in three

significant figures because student error is

the

difference between the actual value (1.59 g/cm

3

)

and the measured value.

30. CalculatethepercenterrorsforStudent

C's

trials.

~ ~ ~ x

100

=

6.92%

~ ~ ~

x

100

=

6.29%

~ ~ ~

x

100

=

7.55%

Note: The answers are reported in three

significant figures because student error is the

difference between the actual value (1.59 g/cm

3

)

and

the

measured value.

Practice Problems

p ge

39

Determine

the

number

of

significantfigures

in

each

measurement.

31. a. 508.0

L

4

b.

820400.0L

7

c. 1.0200X 10

5

kg

5

d.

807000

kg

3

32. a. 0.049450

s

5

b. 0.000482

mL

3

c. 3.1587X 10-

8

g

5

d. 0.0084

mL

2

10


Solutions Manual

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CHAPTER SOLUTIONS

M NU L

Practice Problems

p ge

4

Roundall numberstofoursignificantfigures.

Writetheanswerstoproblem34

in

scientific

notation.

33. a.

84791

kg

84

790kg

b.

38.5432g

38.54g

c. 256.75em

256.8

em

d. 4.9356m

4.936

m

34.

a. 0.000548

18

g

5.482x10 -

4

g

b. 136758 kg

1.368x 10

5

kg

c. 308659000

mID

3.087

x

10&

mm

d.

2.0145

mL

2.014

mL

Completethefollowingadditionand subtraction

problems.Roundofftheanswerswhennecessary.

35. a.

43.2em

51.0em

48.7em

142.9

em

b. 258.3kg 257.11kg 253kg

768kg

c. 0.0487mg 0.05834mg 0.00483mg

0.1119mg

36. a. 93.26em - 81.14em

12.12

em

b. 5.236em 3.14em

2.10em

c. 4.32X 10

3

em - 1.6 X 103 em

2.7x1

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CHAPTER SOLUTIONS MANUAL

40.

Are the measurements in problem 39 accurate?

Are they precise? Explain your answers.

Answers may vary but might include the

following.

They are

not

precise

for

values

recorded

to

four

significant figures. The

first

and

second values are close enough to the accepted

value to be called accurate.

41. Calculate the percent error fo r each measure-

ment in problem 39.

76.49

j;I'I'( -

76.48Jit1f

x

100

001307%

76.49

j;I'I'(

7 6 . 4 9 ; : 4 ~

; r

7

Gr1f

x 100 0.02615%

76.49 :;:9...Gr1f x 100 = 0.1307%

42.

Round 76.51

cm

to two significant figures. Then

round your answer to one significant figure.

77 cm, 80

cm

43. Thinking Critically Which of these measure-

ments was made with the most precise

measuring device: 8.1956 m 8.20 m

or

8.196 m? Explain your answer.

8.1956 m because i t has

the

greatest number of

significant figures

44. Using Numbers Write an expression for the

quantity 506 000 cm in which it is clear that all

the zeros are significant.

5.060 00 x 10

5

cm


Sedion

2.4 Representing Data

p ges

43-45

Problem-Solving Lab

p ge

44

How does speed affect

stopping distance?

1 0 0 r - - - - - ~ - - - - - - ~ - - - - ~

1

8 0 ~ - - - - ~ - - - - - - ~ - - - ~

E

~ ~ t _ _ : F

.......

tl

c

.-

4 0 ~ - - - - ~ - - - - - J - ~ - - - - - i

Q

2 0 ~ - - - - _ ~ - - - - ~ - - - - - 4

2

30

Speed

(mts)

Section 2.4 Assessment

p ge 5

45.

Explain why graphing can be an important tool

for analyzing data.

It provides visual information about relationships

between variables, relative amounts, or parts of a

whole.

46. What type of data can be displayed on a circle

graph? On a bar graph?

parts of a whole; how a quantity varies with a

factor

47. If a linear graph has a negative slope what can

you say about the dependent variable?

It

decreases in value as the independent variable

increases.

48. When can the slope of a graph represent

density?

when

mass is the y value and volume is the

x value

Solutions Manual

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CHAPTER SOLUTIONS M NU LJ

49. Thinking CrHically Why does it make sense

for the line in Figure 2-148 to extend to 0, 0

even though this point was not measured?

Extrapolation

of

measured data extends

the

line

to

this point. The graph shows

that

an object

with

no mass

will

have no volume.

50. Interpreting Graphs Using Figure 2-15,

determine how many months the ozone hole

lasts.

from September to November,

or

approximately

three months

CHEMLAB

pages 46 47

Density

of

Copper

V

4

V

J

3

V

V

10

20 30 40

Volume mL)

Solutions Manual

Chapter ssessment pages 50 52

oncept

apping

51. Use the following terms to complete the concept

map: volume, derived unit, mass, density, base

unit, time, length.

SI units

1 base unit; 2 derived unit; 3 mass; 4. time;

5 length; 6 volume; 7 density

Mastering oncepts

52. Why must a measurement include both a

number and a unit?

2.1)

The number gives you the quantitative value. and

the unit

indicates

what

was measured.

53. Explain why scientists, in partiCUlar need stan

dard units

of

measurement.

2.1)

Scientists f rom

different

countries have differen t

languages and cultures

but

must be able

to

share

and compare data.

54. What role do prefixes play in the metric

system?

2.1)

Prefixes give

the

magnitude

of the

measurement.

55. How many meters are there in one kilometer? In

one decimeter? (2.1)

1000; 0.1

56.

What is the relationship between the 81 unit for

volume and the

81

unit for length?

2.1)

The SI

unit for

volume is

the

cubic meter, m

3

,

which

is

equal to three SI measurements of length

multiplied together.


13

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CHAPTER

0 SOLUTIONS

MANUAL

57. Explain how temperatures on the Celsius and

Kelvin scales are related. 2.1)

The

sizes

of the unitsareequal;C +

273

= K

58. How does scientific notation differ from ordi-

nary notation? 2.2)

Scientificnotationuses anumberbetween1and

10 timesapowerof tento indicatethesizeof

verylarge

or

smallnumbers.

59.

f you move the decimal place to the left to

convert a number into scientific notation, will

the power

of

ten be positive

or

negative? 2.2)

positive

60. When dividing numbers in scientific notation,

what must you do with the exponents? 2.2)

Subtractthem.

61.

When you convert from a small unit to a large

unit, what happens to the number

of

units? 2.2)

It decreases.

62.

If

you report two measurements of mass, 7.42 g

and 7.56 g, are the measurements accurate? Are

they precise? Explain your answers. 2.3)

You must

know

the acceptedvalue

to know

if the

measurementsareaccurate.Theyare

fairly

precise

becausethereis

only

0.14gdifferencebetween

the two measurements.

63.

When converting from meters to centimeters,

how do you decide which values to place in the

numerator and denominator of the conversion

factor? 2.2)

Meterswill bein thedenominatorso

that

the

unitswill cancelwhenthestartingvalueis

multipliedby

the

conversionfactor.

64. Why are plus and minus signs ignored in

percent error calculations? 2.3)

You

needto know only thedifferencebetween

themeasuredvalueandthemagnitude

of

the

acceptedvalue.

65.

In

50 540, which zero is significant? What is the

other zero called? 2.3)

the first one;placeholder

66.

Which

of

the following three numbers will

produce the same number when rounded to

three significant figures: 3.456, 3.450, or 3.448?

2.3)

3.450and3.448

67.

When subtracting 61.45 g from 242.6 g, which

factor determines the number of significant

figures in the answer? Explain. 2.3)

the

numberthat has the fewestdigitsto the

right

of the decimalpoint i t

is less

precise.

68.

When mUltiplying 602.4 m by 3.72 m, which

factor determines the number

of

significant

figures in the answer? Explain. 2.3)

3.72;i t has thesmallernumberof significant

figures.

69.

Which

type of

graph would you choose to

depict data on how many households heat with

gas, oil, or electricity? Explain. 2.4)

Abargraphcouldbeusedwith the methodof

heatingonthe x-axisandthe numberof

householdsonthe y-axis. If the dataincludeall

the households

for

aregion,relativenumbers

couldbeconvertedto apercentageandexpressed

as acirclegraph.

70.

Which type of graph would you choose to

depict changes in gasoline consumption over a

period

of

ten years? Explain. 2.4)

line

or

bargraphbecausethey

can

show

how

consumptionvarieswith time

71.

How can you find the slope of a line graph?

2.4)

Choosetwo pointsonthe line.Dividethe

differencein the values

by

the differencein the

xvalues.

Chemistry:MatterandChangeChapter2

SolutionsManual

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CH PTER

0

SOLUTIONS MANUAL

Mastering Problems

Density(2.1)

evell

72.

A5-mLsample

of

waterhasamass

of

5g.

Whatisthedensityof water?

density=

mass

=...!JL = 1g/mL

volume 5mL

evel

2

73. Anobjectwithamassof 7.5graisesthelevel

of

waterinagraduatedcylinderfrom25.1mL

to30.1mL.Whatisthedensityof theobject?

volume=30.1 -

25.1

mL=5.0mL

density

=

mass 7.59 15

I

L

volume = 5.0 mL = . 9m

74.

The

density

of

aluminumis2.7

g/mL What

is

thevolumeof 8.1gof aluminum?

mass 8.1 J.if

I

vo

ume=density

=

2.7.gfmL =3.0mL

ScientificNotation (2.2)

evell

75.

Writethefollowingnumbersinscientific

notation.

a.

0.0045834

mm

4.5834x10-

3

mm

b. 0.03054g

3.054

x 10-

2

9

c.

438904

s

4.38904x10

5

S

d. 7004

300

000 g

7.0043

X

10

9

9

76.

Writethefollowingnumbers

in

ordinary

notation.

a.

8.348

X

106km

8348000 km

b. 3.402X 10

3

g

3402g

SolutionsManual

c.

7.6352

X 10-

3

kg

0.0076352kg

d. 3.02X 10-

5

s

0.0000302

s

evel2

77. Completethefollowingadditionandsubtraction

problemsinscientificnotation.

a.

6.23 X 10

6

kL +5.34X 10

6

kL

(6.23+5.34) x 1 )6 kL=11.57x 1 )6 kL

=1.157 x 10

7

kL

b. 3.1 X

1Q4

mm

+

4.87 X

lOS mm

(0.31+4.87)

x

10

5

mm

=

5.18

x

10

5

mm

c. 7.21 X 10

3

mg +43.8X 10

2

mg

(7.21+4.38) x10

3

mg =11.59x10

3

mg

=1.159x 10

4

mg

d. 9.15X

10-

4

cm +3.48X

10-

4

cm

(9.15+3.48)

x 10 -

4

em

=12.63

x 10-

4

em

=1.263

x 10 -

3

em

e. 4.68 X 10-

5

cg+3.5 X 10-

6

cg

(4.68+0.35)x

10 -

5

eg =5.03 x

10 -

5

eg

f.

3.57

X

10

2

mL

- 1.43

X

10

2

mL

(3.57- 1.43)

x

10

2

mL=2.14

x 102

mL

g. 9.87

X

1Q4 g 6.2

X

10

3

g

(9.87- 0.62)

x

104 9=9.25

x

104 9

h. 7.52X lOS kg - 5.43 X

lOS kg

(7.52- 5.43)

x

10

5

kg=2.09 X 10

5

kg

i. 6.48X 10-

3

mm -

2.81 X 10-

3

mm

(6.48- 2.81)x10-

3

mm=3.67x10-

3

mm

j. 5.72X

10-

4

dg - 2.3X

10-

5

dg

(5.72- 0.23)

x 10-

4

dg

=5.49 X

10 -

4

dg

78. Completethefollowingmultiplicationanddivi

sionproblemsinscientificnotation.

a. (4.8

X

lOS km)

X

(2.0

X

10

3

km)

(4.8x 2.0) x 10

5

+3 km

2

=9.6x 1 )8 km

2

15

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CHAPTERD SOLUTIONS

MANUAL

b. (3.33X 10 -

4

m)

X (3.00X 10-

5

m)

(3.33 x 3.00)x 10 -

4

+(-5) m

2

=9.99 x

10-

9

m

2

c.

(1.2X 10

6

m)X (1.5X 10-

7

m)

(1.2 x 1.5)x 10

6

+(-7)

m

2

=

1.8x

10 -

1

m

2

d. (8.42X 10

8

kL)+ (4.21 X 10

3

kL)

3

(8.42

+

4.21)x 10

8

-

=2.00

X

10

5

e. (8.4X 10

6

L)

+

(2.4X 10-

3

L)

(8.4+2A x10

6

- -3) =

3.5 x10

9

f. (3.3X

10-

4

mL)+

(1.1 X

10-

6

mL)

(3.3+1.1)x

10-

4

- -6 ) =3.0 x

1 2

ConversionFactors(2.2)

Levell

79.Writetheconversionfactorthatconvertsthe

following.

a. gramstokilograms

1

kg

1000

9

b. kilogramstograms

1000g

c. millimeterstometers

1m

1000mm

d. meterstomillimeters

1000

mm

1m

e.

milliliterstoliters

1L

1000mL

f. centimeterstometers

1m

100cm

evel 2

80. Convertthefollowingmeasurements.

a. 5.70gtomilligrams

1000mg

5.70g x

19

=

5.70

x

1 3 mg

b.

4.37cm tometers

4.37yr x 1 ~ ; m =4.37 X

10-

2

m

c.

783kgtograms

1OO0g

783.kgx 1-"9'"

=

7.83x 10

5

9

d.

45.3mmtometers

45.3.!JH1lx

m O

=4.53 X

10-

2

m

e. 10mtocentimeters

10)ll"x 100

cm

= 1000cm

_

f. 37.5glmLtokgIL

37.5$

1

kg

1000pr['

1rRI:: ' x 1000J.!(x 1L

=

37.59

PercentError (2.3)

Levell

81. Theacceptedlengthof asteelpipeis5.5m.

Calculatethepercenterrorforeachof these

measurements.

a. 5.2m

error

=

5.5m- 5.2m=0.3m

percent

error=

~ : i ' : : - x 100

=

5.5%

b. 5.5

m

error

=

5.5m- 5.5m

=

0m

percent

error

=

5 ~ : . r -

x

100

=

0

c. 5.7m

error

=

5.5m- 5.7m

=

-0.2m

percent

error=

~ : ~ : : : : x 100

=

3.6%

Chemistry:MatterandChangeChapter2

SolutionsManual6

8/11/2019 Unit 2 Text

11/16

CHAPTER SOLUTIONS M NU L

d.

5.1m

error =

5.5

m - 5.1 m =0.4 m

percent error = x 100 =7.3

Level

2

82. Theaccepteddensityforcopperis8.96glmL.

Calculatethepercenterrorforeachof the

measurements.

a.

8.86glmL

error = 8.96 g/mL - 8.86 g/mL

=

0.10 g/mL

0.10,.gtmt

percent error =8.96,gtmt' x 100 = 1.12

b.8.92g1mL

error =8.96 g/mL - 8.92 g/mL

=

0.04 g/mL

0.04,gtmt' 0

o

446/,

percent error

=

8.96.gJnt( x 10

=.

0

C. 9.00glmL

error = 8.96 g/mL- 9.00 g/mL= -0.04g/mL

0.04.ghYf( 0 0 446

0

/.

percent error

=

8.96 iI it x 1 0=

0

d. 8.98glmL

error

=

8.96 g/mL - 8.98 g/mL

=

0.02 g/mL

0.02 gUnt

percent error =8.96

g.Hn'[

x 100 =0.223

SignificantFigures(2.3)

evell

83. Roundeachnumbertofoursignificantfigures.

a. 431801kg

431800kg

b. 10235.0mg

10240mg

c. 1.0348m

1.035 m

d.

0.004384010

cm

0.004384cm

e. 0.000781

00

mL

0.000 781 0 mL

f.

0.009864

1cg

0.009864cg

Solutions Manual

84. Roundeachfiguretothreesignificantfigures.

a.

0.003210g

0.00321 9

b.

3.8754kg

3.88 kg

c. 219034 m

219000 m

d. 25.38L

25.4 L

e.

0.087

63 cm

0.0876

cm

f. 0.003109mg

0.00311 mg

Level

2

85. Roundtheanswerstoeachof thefollowing

problemstothecorrectnumber

of

significant

figures.

a. 7.31 X 1 4 + 3.23 X 10

3

(7.31 + 0.323) x 10

4

=7.633 x

104

=7.63 x

104

b.

8.54

X

10-

3

-

3.41

X

10-

4

(8.54 - 0.341) x 10-

3

= 8.199

X

10-

3

=8.20 X 10 -

3

c. 4.35dmX 2.34dm X7.35dm

(4.35 x 2.34 x 7.35)

dm

3

=

74.81565 dm

3

= 74.8

dm

3

d. 4.78

cm

+ 3.218

cm

+ 5.82

cm

4.78 + 3.218 + 5.82

cm

=13.818 em = 13.82 em

e. 3.40mg

+

7.34mg

+

6.45mg

3.40

+

7.34

+

6.45 mg= 17.19 mg

f. 45m

X

12m

X

132m

45 x 72 x 132) m

3

=427 680 m

3

=430 000 m

3

g.

38736

kml 78 km

38 736Jot{+ 4784Jot{

=

8.969899 =8.097

Chemistry: Matterand Change Chapter 2

17

8/11/2019 Unit 2 Text

12/16

CH PTER

Representing Data (2.4)

evell

86. Use the accompanying bar graph to answer the

following questions.

a.

Which substance has the greatest density?

mercury

b.

Which substance has the least density?

wood

c. Which substance has a density of

7.87 glcm

3

?

iron

d. Which substance has a density of

11.4 glcm

3

?

lead

Density Comparison

14.0. .---------------

12.01----- - - - - - -

10.0 < ~

8.01--------

6.0 -

4.0

1 :

2.0 1 -

~

~

.,

i

Q

rz} ~

~ . ; > 0 :- h b ~ .sA

~ ,,>,>0; (:) ~ , , ~ t G c . .

Months

SOLUTIONS M NU L

evel 2

87. Graph the following

data

with the volume on

the x-axis and the mass on the y axis. Then

calculate the slope

of

the line.

Table 2-7

Density Data

Volume

(ml)

Mass (9)

2.0 5.4

4.0 10.8

6.0 16.2

8.0 21.6

10.0 27.0

Density

30.0

25.0

20.0

-

... 15.0

:II

::: 10.0

5.0

1/

/

V

/

/

/

0.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0

Volume(mL)

The graph shows a direct relationship between

mass and volume.

21.6 9 - 10.8 9

slope

=

8.0 mL _ 4.0 mL

=

2.7 g/mL

ixed eview

Sharpen your problem solving skills

by

answering

the following.

88. You

have a 23-g sample

of

ethanol with a

density of 0.7893 glmL. What volume

of

ethanol do you have?

volume

=

d ~ ; ~ ~

=

23..g'x

0 . ~ 8 ~ ~ 1

=

29

mL

89.

Complete the following problems in scientific

notation. Round off to the correct number

of

significant figures.

a. (5.31

X

10-

2

cm)

X

(2.46

X

10

5

cm)

(5.31 x 2.46)

X

10 -

2

+

5

cm

2

= 13.0626 x

1 )3 cm

2

= 1.31 x

1 )4

cm

2

8


Solutions Manual

8/11/2019 Unit 2 Text

13/16

CH PTER

b. (3.78 X 10

3

m)X (7.21 X 10

2

m)

(3.78x 7.21) x 103+2 m

2

=27.2538x 10

5

m

2

2

=2.73 x10

6

m

c.

(8.12

X

10-

3

m)

X

(1.14

X

10-

5

m)

(8.12 x 1.14) x

10 -

3

+(-5)

m

2

=

9.2568 x

10 -

8

m

2

=9.26 x

10-

8

m

2

d.

(5.53

X

10-

6

km)

X

(7.64

X 10

3

km)

(5.53 x 7.64)x

10 -

6

+3 km

2

=42.2492 x

10 -

3

km

2

=

4.22X 10 -

2

km

2

e. (9.33 X lQ4 mm)

-:-

(3.0X

10

2

mm)

(9.33

:

3.0)

x

104-

2

=

3.11

X

10

2

=3.1 x102

f.

(4.42

X

10-

3

kg)

(2.0

X

10

2

kg)

(4.42

:

2.0)

x

10-

3

-

2

=

2.21

X

10 -

5

=

2.2

X

10 -

5

g.

(6.42X 10-

2

g)

-:- (3.21 X 10-

3

g)

(6.42 : 3.21)x10-

2

- ( -3)

=2.00 X 10

1

90. Evaluatethefollowingconversion.Willthe

answerbecorrect?Explain.

rate=

75

m X 60 X 1h.

s

Imm

60mm

rate

=

75m x 6 ~ x 1h x 75 mh

1B 1mm 60

min min

2

No,

the

conversionisnot correctbecause

the

units

of rateshould

be

m/min.Thisexpressionyields

the unitsmh/min

2

Thelastconversionfactor

shouldbe 60min

1h

91.What

mass

of

lead(density

11.4l m

3

would

haveanidenticalvolumeto15.0gof mercury

(density13.6l m

3

?

_ massmercury _

volumemercury -

d

ty - 15.09mercury

ensl

mercury

1cm

3

mercury _110 3

x 13.69mercury - . cm mercury

volume

lead

=

volumemercUry

=

1.10cm

3

1ead

mass

1ead

=

volume

1ead

x densitylead

3

11.49lead

=1.10cm lead x 1cm

3

1ead =12.69lead

SolutionsManual

SOLUTIONS M NU L

92. Threestudentsuseametersticktomeasurea

length

of

wire.Onestudentrecordsameasure-

ment

of

3cm.The secondrecords3.3cm.The

thirdrecords

2.87

cm.Explainwhichanswer

wasrecordedcorrectly.

The

third student

(2.87cm)

is

correct.Ameterstick

hasmarkingsto

the

millimeter,soa third digit

shouldbe estimated.

93.

Expresseachquantityintheunitlistedtoits

right.

a. 3 01 g cg

100cg

3.01,.g'x

=

301 cg

b.

6200m

km

1km

6200.Rfx 1000 =6.2km

c 6.24X 10-

7

g / Lg

10

6

J.Lg

6.24 X

10 -

7

g x

1

=0.624J.Lg

d.

0.2L

0.2J x

1

; 3

= 0.2dm3

e.

0.13callg kcallg

0.13caI1g x ~ ~ c ~ =1.3

X 10 -

4

kcallg

f. 3 21

mL L

Chemistry:Matter andChangeChapter2 9

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14/16

CHAPTER

0

94.

The black hole in the galaxy M82 has a mass

about 500 times the mass

of

our Sun. I t has

about the same volume as Earth s moon. What

is the density

of

this black hole?

masssun =

1.9891

X

10

30

kg

volume

=

21968

X 1010 km

3

moon .

mass

black

hole'"" 500

X

mass

sun

=

500

X

(1.9891

X

1()30 kg) = 9.9455

X

10

32

kg

10

10

km

3

volumeblack

hole

= volume

moon

= 2.1968

X

mass

b1ack

hole

denSltyblack

hole = -v-ol"-u-m-e--

black hole

9.9455 X

1()32 kg

_ 72 3

= 2.1968

X 1010

km3 - 4.5273

X

1u- kg/km

densityblack

hole

=

4.5273

X

77 3 1000 g 1

1H 6)3

1m)3

1u-l.f/km X X

1000

K X

100

cm

=

4.5273

X

1()22+3-9-6

=

4.5273

X

10

10

g/cm

3

95.

The density

of

water is 1 glcm

3

Use your

answer to question 94 to compare the densities

.

of

water and a black hole.

The density of

the

black hole is 4.5273

X

10

10

g/cm

3

(almost

fifty

billion) times greater than

that

of

water.

Thinking ritically

96. Comparing and Contrasting

What advantages

do SI units have over the units in common use

in the United States? Is there any disadvantage

to using SI units?

Answers

will vary

but might

include

that units

based

on powers

of

ten

are easy

to

convert from

one

to

another. Most disadvantages

involve the

initial changing from

another

system to 51

97. Forming a Hypothesis

Why do you think the

SI standard for time was based on the distance

light travels through a vacuum?

There is

no

chance

for matter

to

interfere

with

the

speed measurement

in

a vacuum.

Chemistry:

Matter

and Change Chapter 2

SOLUTIONS

MANUAL

98. Inferring

Explain why the mass

of

an object -

cannot help you identify what material the

object is made from.

Mass itself has

no

meaning without a

measurement

of

its volume. If

the

object is a pure

substance and its

mass

and volume are known,

its

density can help

identify

it.

99. Drawing Conclusions

Why might property

owners hire a surveyor to determine property

boundaries rather than measure the boundaries

themselves?

Surveyors use

equipment that

is

not

affected

by

terrain or

obstacles.

Writing in hemistry

100.

Although the standard kilogram is stored at

constant temperature and humidity, unwanted

matter can build up on its surface. Scientists

have been looking for a more reliable standard

for mass. Research and describe alternative

standards that have been proposed. Find out

why no alternative standard has been chosen

Two

alternative

methods of defining

the

standard kilogram

would

base the unit on

the

Avogadro constant.

which

is

the number of

atoms

in

12 grams of pure carbon-12. One

method

would

depend

in

part on

X-ray

measurements in silicon crystals. Another

method would

depend

on

electrical

measurements

that

determine

the ratio of the

mechanical watt

to the

electrical watt.

At this

time, scientists have

not

gained universal

acceptance

for either

alternative method.

101.

Research and report on some unusual units of

measurement such as bushels, pecks, fIrkins,

and frails.

Student

answers

will

vary. For example, a

firkin

(a small

wooden

tub

used

for

butter

and

lard) is

a unit

of volume

equal

to i

barrel.

102.

Research the range

of

volumes used for pack-

aging liquids sold in supermarkets.

Student

answers

will likely

include

fluid

ounces,

quarts, half-gallons, gallons, liters, and milliliters.

Solutions Manual

0

8/11/2019 Unit 2 Text

15/16

CH PTERD SOLUTIONS

M NU L

103.

Findoutwhattheacceptablelimits

of

errorare

forsomemanufacturedproducts

or

forthe

dosesof medicinegivenatahospital.

Student

answers

willvary.Fordefinitive

information

on the

subject,encourage students

to contact

the

U.S. NationalInstitute

of

Standards

and

Technology(NIST),

manufacturers.

pharmacists,or hospitalpharmacies.

Cumulative Review

Refresh your understanding

of

previous chapters by

answering the following.

104. You

recordthefollowinginyourlabbook:A

liquidisthickandhasadensity of 4.58glmL.

Whichdataisqualitative?Whichisquantita-

tive?(Chapter1)

Thick is qualitative;a density

of

4.58g/mL is

quantitative.

Standardized Test Pradice

Chapter

p ge 53

Use the questions

nd

the test taking tip to prepare

for your standardized test.

1.

Whichof thefollowingisNOTanSIbaseunit?

a. second(s)

b. kilogram(kg)

c. degreesCelsius

("C)

d. meter(m)

c

2. Whichof thefollowingvaluesisNOT equiva-

lenttotheothers?

a.

500meters

b.

0.5kilometers

c. 5000centimeters

d.

5X lOllnanometers

c

3.

Thecorrectrepresentation of 702.0gusing

scientificnotationis

a. 7.02 X 10

3

g

b.

70.20X

101

g

c.

7.020X 10

2

g

d.

70.20

X

10

2

g

c

4. Threestudentsmeasuredthelengthof astamp

whoseacceptedlengthis2.71cm.Basedonthe

tablebelow,whichstatementistrue?

a. Student2isbothpreciseandaccurate.

b.

Student

1

ismoreaccuratethanStudent3.

c. Student2islessprecisethanStudent

1.

d. Student3isbothpreciseandaccurate.

a

Measured

Valuesfor a

Stamp s

length

Student1 Student2

StudentJ

Trial1 2.60

em

2.70

em

2.75em

Trial2 2.72em 2.69em

2.74

em

Trial3 2.65

em

2.71

em

2.64em

Average

2.66em 2.70em 2.71 em

5.

Chemistsfoundthatacomplexreaction

occurredinthreesteps.Thefirststeptakes

2.5731 X 10

2

S

tocomplete,thesecondstep

takes3.60X10-

1

s,andthethirdsteptakes

7.482 X

1 1 s.

Thetotalamount

of

timeelapsed

duringthereactionis

.

a. 3.68 X

101

s

b. 7.78X

1 1

s

c. 1.37 X

101

s

d.

3.3249 X 10

2

s

d

6. Howmanysignificantfiguresarethere in a

distancemeasurement

of

20.070km?

a. 2

b.

3

c.

4

d. 5

d

SolutionsManual

Chemistry:

Matter

andChangeChapter2 21

8/11/2019 Unit 2 Text

16/16

CH PTERD

InterpretingGraphs

Usethegraphtoanswerthe

followingquestions.

Age

of

Icelayers inVostokIceSheet

70000

65000

60000

55000

QI

0000

QI

5000

40000

"5

QI

35000

30000

25000

20000

/

/

/

lL

iI""

/

ill

500 550600 650700750 800850 9009501000

Depthof icelayerbelow surface(m)

7.Usingthegraph,astudentreportedtheage of

anicelayerat705

mas

4.250X 1 )4 years.The

acceptedvaluefortheageof thisicelayeris

4.268 X I)4 years.Thepercenterror

of

the

student'svalueis

a. 0.4217%

b.

99.58%

c. 0.4235%

d.

1.800%

a

SOLUTIONS

M NU L

8. Theslopeof thegraphisabout

a.

80

years/m

b.

80m/year

c. 0.015years/m

d. 1500m/year

a

9.Whatageisanicelayerfoundatadepth

of

l000m?

a. 6.75

X

1 )4 years

b. 7.00 X 1)4 years

c. 6.25

X 1)4 years

d. 6.5

X

1 )4 years

d

Chemistry:Matter

and

Change Chapter2 Solutions

Manual

2

unit 2 text

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