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CHAPTER

2

Scientific Measurements

Section 2.1 Uncertainty in Measurements 2. (a) (c)

Unit meter liter

Quantity length volume

Unit (b) gram (d) second

Quantity mass time

4.

(c) 15.50 cm and (d) 20.05 cm each have an uncertainty of ± 0.05 cm.

6.

(c) 75.518 g is the only mass with an uncertainty of ± 0.001 g.

8.

(d) 25.50 mL is the only reading with an uncertainty of ± 0.05 mL.

Section 2.2 Significant Digits 10. (a) (b) (c) (d)

Measurement 0.05 g 0.10 g 25.0 g 10.10 g

Significant Digits 1 significant digit 2 significant digits 3 significant digits 4 significant digits

(a) (b) (c) (d)

Measurement 0.5 s 0.50 s 0.500 s 500 s

Significant Digits 1 significant digit 2 significant digits 3 significant digits 1 significant digit

Measurement 1.2  100 g 4.50  101 g 5.02  10–1 g 1  10–2 g Rounding Off Nonsignificant Digits

Significant Digits 2 significant digits 3 significant digits 3 significant digits 1 significant digit

12.

14. (a) (b) (c) (d) Section 2.3

Scientific Measurements     3


16. (a) (b) (c) (d)

Example 20.155 0.204 500 2055 0.2065

Rounded Off 20.2 0.205 2060 0.207

(a) (b) (c) (d)

Example 4.123  105 4.456  1010 4.000  10–7 4.075  10–12

Rounded Off 4.12  105 4.46  1010 4.00  10–7 4.08  10–12

18.

Section 2.4 Adding and Subtracting Measurements 20.

(a) (b)

0.55 cm + 36.15 cm +17.3 cm = 54.00 cm 4.0 cm + 16.3 cm + 0.95 cm = 21.25 cm

rounds to 54.0 cm rounds to 21.3 cm

22.

(a) (b)

22.10 cm – 10.5 cm = 11.60 cm 10.0 cm – 0.15 cm = 9.85 cm

rounds to 11.6 cm rounds to 9.9 cm

Section 2.5 Multiplying and Dividing Measurements 24.

(a) (b) (c) (d)

26.

(a) (b) (c) (d)

5.1 cm  1.25 cm  0.5 cm = 3.1875 cm3 5.15 cm  2.55 cm  1.1 cm = 14.44575 cm3 12.0 cm2  1.00 cm = 12.0 cm3 22.1 cm2  0.75 cm = 16.575 cm3 = = = =

8.84 g/mL 3.04878 g/mL 4.262 g/mL 9.1235 g/mL

rounds to 8.8 g/mL rounds to 3.0 g/mL rounds to 4.26 g/mL rounds to 9.124 g/mL

Section 2.6 Exponential Numbers 28.

(a) (b)

30.

(a)

4     Chapter 2

3   3   3   3 = 34 



rounds to 3 cm3 rounds to 14 cm3 rounds to 12.0 cm3 rounds to 17 cm3

4

= () = 3–4

10 10 10 10 10 10 = 106


Full file at http://testbank360.eu/solution-manual-introductory-chemistry-5th-editioncorwin (b) 32.



= ()

4

= 10–4

(a) (b)

Number 1 1012 1 10–22

Scientific Notation 1,000,000,000,000 0.000 000 000 000 000 000 000 1

(a) (b)

Number 100,000,000,000,000,000 0.000 000 000 000 001

Scientific Notation 1 1017 1 10–15

(a) (b)

Scientific Notation 1 100 1 10–10

Number 1 0.000 000 000 1

34.

36.

Section 2.7 Scientific Notation  38. (a) (b) (c) (d)

Number 1,010,000,000,000,000 0.000 000 000 000 456 94,500,000,000,000,000 0.000 000 000 000 000 019 50

40.

2.69 1023 radon atoms

42.

3.44  10–22 g/lead atom

Scientific Notation 1.01  1015 4.56  10–13 9.45  1016 1.950  10–17

Section 2.8 Unit Equations and Unit Factors 44. (a) (b)

46. (a) (b)

Unit Equation 1 quart = 2 pints 1 century = 100 years

Unit Factors and and

48. (a) 1 kilogram = 1000 grams is an exact equivalent. (b) 1 kilogram = 2.20 pounds is an approximate equivalent because it relates two different systems of measurement (English and metric).

Scientific Measurements     5


50. (a) 1 month = 4 weeks is an approximate equivalent because the number of days in a month varies. (b) 1 hour = 60 minutes is an exact equivalent. 52. (a) 1 kilogram = 1000 grams has an infinite number of significant digits because it is an exact equivalent. (b) 1 kilogram = 2.20 pounds has three significant digits because it is an approximate equivalent. 54. (a) 1 month = 4 weeks has only one significant digit because it is an approximate equivalent. (b) 1 hour = 60 minutes has an infinite number of significant digits because it is an exact equivalent. Section 2.9 Unit Analysis Problem Solving 56.

12 inches 

58.

325 milligrams 

60.

15 teaspoons

62.

12.0 weeks 

= 84.0 days

64.

50.0 troy ounces

66.

1.00 year 

3.0  102 centimeters

=

=

5.01 grains

= 5.0 tablespoons

= 1560 grams 

 

Section 2.10 The Percent Concept 68.

225 mL oxygen

70.

 100%

6     Chapter 2



= 1080 mL air

= 12.0% of gasohol is ethanol

= 9.46  1017 cm


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72.

0.375 g table salt

= 0.147 g sodium

74.

3.87  1021 kg total

76.

Total quantity = 2.554 g copper and zinc Quantity of zinc = 2.490 g Quantity of copper = 2.554 g – 2.490 g = 0.064 g

= 2.10  1021 kg Titania

 100% = 2.5% copper

Percent of copper:

General Exercises 78.

1.000  103 mL (±1 mL)

80.

3.00  108 meters per second The velocity must be expressed in scientific notation because the rounded value, 300,000,000 meters per second, has only one significant digit.

82.

Remaining length: 255 cm – 2(25.0 cm) = 205 cm

84. (a) (b) 86.

Exponential Number 0.170  102 0.00350  10–1

Scientific Notation 1.70  101 3.50  10–4

Mass of a neutron = 1.6749  10–24 g Mass of a proton = 1.6726  10–24 g Mass difference: (1.6749  10–24 g) – (1.6726  10–24 g) = 2.3  10–27 g

88.

Total distance =

+

Total distance: 2.39  105 miles + 4.84  107 miles

= 4.86  107 miles

Scientific Measurements     7


90.

4.1 billion years = 4.1  109 years 4.1  109 years 

 100% =

92.

AB–:

94.

1 troy pound

8     Chapter 2

= 2.2  1015 minutes 0.498% AB– type = 373 grams (gold)


Solution manual introductory chemistry 5th edition corwin