70
CHAPTER 3
THE METRIC SYSTEM
_ _ 12. a procedure for solving problems that proceeds from a given value to a related
_ _ 13.
__
__
__
__
14.
15.
16.
17.
_ _ 18.
_ _ 19.
_ _ 20.
__
__
__
__
21.
22.
23.
24.
answer by the conversion of units
the volume occupied by a cube 1 cm on a side
a technique for determining volume from the amount of water displaced
the amount of mass in one unit of volume
the ratio of the density of a liquid compared to the density of water at 4 °C
the flow of energy from an object at a higher temperature to an object at a
lower temperature
the average energy of molecules in motion
the basic unit of temperature in the English system
the basic unit of temperature in the metric system
the basic unit of temperature in the SI system
the amount of heat required to raise 1 g of substance 1 °C
the amount of heat required to raise 1 g of water 1 °C
a unit of energy in the SI system
c
Exe r i ses
(m) liter (L) (Sec. 3.1)
meter (m) (Sec. 3.1)
(o) metric system (Sec. 3.1)
(p) reciprocal (Sec. 3.2)
(q) second (s) (Sec. 3.1)
(r) specific gravity (sp gr) (Sec. 3.7)
(s) specific heat (Sec. 3.9)
(t) temperature (Sec. 3.8)
(u) unit analysis method (Sec. 3.3)
(v) unit equation (Sec. 3.2)
(w) unit factor (Sec. 3.2)
(x) volume by displacement
(n)
(Sec. 3.6)
Answers to odd-numbered Exercises are in Appendix I.
12. Write the name of the metric unit indicated by the following
Basic Units and Symbols (Sec. 3.1)
I. Which of the following are basic units in the metric system?
(a) kilometer
(b) gram
(c) liter
(d) millisecond
symbols:
(a) Mm
(c) nL
(b)
(d)
kg
ps
2. Which of the following are basic units in the English system?
Metric Conversion Factors (Sec. 3.2)
foot
(b) ounce
gallon
(d) hour
Write the symbol for the following metric units:
(a) kilometer
(b) gigagram
(c) deciliter
(d) picosecond
4. Write the symbol for the following metric units:
(a) megameter
(b) teragram
(c) centiliter
(d) nanosecond
State the physical quantity expressed by the following metric units:
(a) kilometer
(b) gigagram
(c) deciliter
(d) picosecond
6. State the physical quantity expressed by the following metric units:
(a) megameter
(b) teragram
(c) centiliter
(d) nanosecond
State the physical quantity that is measured using the following instruments:
(a) ruler
(b) platform balance
(c) pipet
(d) stopwatch
8. State the physical quantity that is measured using the following instruments:
(a) micrometer
(b) electronic balance
(c) syringe
(d) atomic clock
State the name and symbol for the metric prefix that represents the following:
Write a unit equation for each of the following metric
equivalents:
(a) mand Tm
(b) g and Gg
(c) Land mL
(d) sand µs
14. Write a unit equation for each of the following metric
equivalents:
(a) m and Mm
(b) g and kg
(c) Land nL
(d) s and ps
1 'i Write two unit factors for each of the following metric
relationships:
(a) m and Tm
(b) g and Gg
(c) Land mL
(d) s and µs
16. Write two unit factors for each of the following metric
relationships:
(a) m and Mm
(b) g and kg
(c) L and nL
(d) s and ps
(a)
(c)
(a) 1 x 1012
(c) 1 x 10-3
(b) 1 x 109
(d) 1 x 10-6
10. State the name and symbol for the metric prefix that repre-
sents the following:
(a) 1 x 106
(c) 1 x 10-9
(b) 1
(d) 1
X
Metric-Metric Conversions (Sec. 3.3)
Perform the following metric-metric conversions:
(a) 1.00 m to km
(b) 100 g to cg
(c) 0.100 L to dL
(d) 0.000 010 s tons
18. Perform the following metric-metric conversions:
(a) 5.00 Mm tom
(b) 50.0 µg tog
(c) 0.500 mL to L
(d) 0.050 ds to s
Perform the following metric-metric conversions:
(a) 6.50 Tm to Mm
(b) 650 Gg to kg
(c) 0.650 cL to dL
(d) 0.000 650 ns to ps
20. Perform the following metric-metric conversions:
(a) 7.50 km to Gm
(b) 750 Mg to Tg
(c) 0.750 pL to µL
(d) 0.000 750 ms tons
103
x 10-12
Write the name of the metric unit indicated by the following symbols:
(a) Tm
(b) Gg
(c) mL
(d) µs
Metric-English Conversions (Sec. 3.4)
State the following metric-English equivalents:
(a) ? cm = 1 in.
(b) ? g = llb
(c) ? mL = 1 qt
(d) ? s = 1 sec
EXERCISES
22. State the following metric-English equivalents:
(a) 1 m = ? yd
(b) 1 kg = ? lb
(c) 1 L =?qt
(d) 1 s =?sec
23. Perform the following metric-English conversions:
(a) 86 cm to in.
(b) 36 g to lb
(c) 0.500 qt to mL
(d) 8.00 X 102 sec to s
24. Perform the following metric-English conversions:
(a) 66 in. to cm
(b) 1.01 lb tog
(c) 750 mL to qt
(d) 5.52 x 10-3 s to sec
25. Perform the following metric-English conversions:
(a) 72 in. tom
(b) 175 lb to kg
(c) 0.500 qt to L
(d) 1.05 X 10-4 min to ks
26. Perform the following metric-English conversions:
(a) 800.0 m to yards
(b) 0.375 kg to lb
(c) 1250 mL to gallons
(d) 1.52 x 103 ds to min
27. A Honda Civic gets 13 kilometers per liter in city driving.
What is the mileage in miles per gallon (given that: 1 mi =
1.61 km and 1 gal= 3.784 L)?
28. A Honda Civic gets 16 kilometers per liter in highway driving. What is the mileage in miles per gallon (given that
1 mi = 1.61 km and 1 gal~ 3.784 L)?
Volume by Calculation (Sec. 3.5)
29. A piece of quartz was cut into a rectangular solid measuring 5.00 cm by 5.00 cm by 25.0 mm. What is the volume in
cubic millimeters?
30. A piece of amber was cut into a rectangular solid measuring 5.08 cm by 10.2 cm by 3.05 m. What is the volume in
cubic centimeters?
31. A rectangular solid piece of brass measures 4.95 cm by
2.45 cm and has a volume of 15.3 cm3. What is the thickness
of the brass?
32. A sheet of aluminum foil measures 30.5 cm by 75.0 cm and
has a mass of 9.94 g. What is the thickness of the foil if the
volume is 3.68 cm3?
•· Complete the following volume equivalents:
·· (a) 1 L = ? mL
(b) 1 L = ? cm3
Complete the following volume equivalents:
(a) 1 mL =? cm3
(b) 1 in. 3 =? cm3
• A Dodge Challenger has a 6.10 L engine. Express the volume in cubic inches.
A Chevrolet Camaro has a 378 in. 3 engine. Express the volume in liters.
ume by Displacement (Sec. 3.6)
• The initial water level in a 10-mL graduated cylinder
•. reads 4.5 mL. After a piece of jade is dropped into the
'cylinder, the water level reads 7.5 mL. What is the volume
• of the jade?
•The initial water level in a 10-mL graduated cylinder is
'-5 mL. After a large ruby is added into the cylinder,
water level is 6.0 mL. What is the volume of the
gnesium metal reacts with hydrochloric acid to produce
drogen gas. The gas displaces water into a cylinder, and
level increases from 125 mL to 255 mL. What volume of
drogen is produced by the reaction?
·um metal reacts with water to produce hydrogen gas. If
•gas displaces 212 mL of water into a beaker, how many
. 'c centimeters of hydrogen are produced by the reaction?
71
The Density Concept (Sec. 3.7)
41. State whether the following will sink or float when dropped
into water:
(a) ebony (d = 1.2 g/mL)
(b) bamboo (d = 0.40 g/mL)
42. State whether the following will sink or float when dropped
into water:
(a) paraffin wax (d = 0.90 g/ cm3)
(b) limestone (d = 2.8 g/cm3)
43. Will a balloon filled with the given gas rise in the air or
drop to the ground? (Assume the mass of the balloon is
negligible and the density of air is 1.29 g/L.)
(a) helium (d = 0.178 g/L)
(b) laughing gas (d = 1.96 g/L)
44. Will a balloon filled with the given gas rise in the air or
drop to the ground? (Assume the mass of the balloon is
negligible and the density of air is 1.29 g/L.)
(a) argon (d = 1.78 g/L)
(b) ammonia (d = 0.759 g/L)
45. Calculate the volume in milliliters for each of the following liquids:
(a) 25.0 g of ether (d = 0.714 g/mL)
(b) 15.0 g of acetone (d = 0.792 g/mL)
46. Calculate the mass in grams for each of the following liquids:
(a) 250 mL of gasoline (d = 0.69 g/mL)
(b) 150 mL of methanol (d = 0.79 g/mL)
47. Calculate the mass in grams for each of the following solids:
(a) 7.50 cm3 of rock salt (d = 2.18 g/ cm3)
(b) 455 cm3 of borax (d = 1.715 g/cm3)
48. Calculate the volume in milliliters for each of the following solids:
(a) 1.00 kg of iron (d = 7.87 g/ cm3)
(b) 1.00 kg of titanium (d = 4.51 g/cm3)
49. Calculate the density in grams per milliliter for each of the
following:
(a) 25.0 mL of ethyl alcohol having a mass of 19.7 g
(b) 11.6 g marble whose volume is found by displacement
tobe4.1 mL
50. Calculate the density in grams per milliliter for each of
the following:
(a) 10.0 g of ether having a volume of 14.0 mL
(b) 131.5 g bronze rectangular solid measuring 3.55 cm x
2.50 cm x 1.75 cm
Temperature (Sec. 3.8)
51. State the freezing point of water on the following temperature scales:
(a) Fahrenheit
(b) Kelvin
(c) Celsius
52. State the boiling point of water on the following temperature scales:
{a) Fahrenheit
(b) Kelvin
(c) Celsius
53. Express the following Fahrenheit temperatures in
degrees Celsius:
(a) 100 °F
(b) -215 °F
54. Express the following Celsius temperatures in
degrees Fahrenheit:
(a) 19 °C
(b) -175 °C
55. Express the following Celsius temperatures in Kelvin units:
(a) 495 °C
(b) -185 °C
56. Express the following Kelvin temperatures in degrees Celsius:
(a) 273 K
(b) 100 K
•
72
CHAPTER 3
THE METRIC SYSTEM
Heat and Specific Heat (Sec. 3.9)
Distinguish between the terms "temperature" and "heat."
58. State the metric value for the specific heat of water.
A beaker containing 250 g of water is heated from 23 °C to
100 °C. What is the heat gain in calories?
60. A pool containing 2.5 x 108 g of water cools from 25.0 °C to
17.0 °C. What is the heat loss in kilocalories?
Calculate the heat required to raise 25.0 g of iron
[0.108 calj(g X C)] from 25.0 °C to 50.0 °C.
62. Calculate the heat released as 35.5 g of copper
[0.0920 cal/(g x °C)] cools from 50.0 °C to 45.0 °C.
Find the specific heat of platinum if 35.7 cal is lost as 75.0 g
of the metal cools from 43.9 °C to 28.9 °C.
64. Find the specific heat of gold if 25.0 cal is required to heat
30.0 g of gold from 27.7 °C to 54.9 °C.
0
Genera~
Exercises
If a computer hard disk has a capacity of 1.5 terabytes (TB),
what is the storage capi;l-city in megabytes (MB)?
-4111 Computer Hard Disk Some
computer hard disks have a
storage capacity greater than
1000 gigabytes (GB). That is,
some new hard disks can store
terabytes (TB) of information.
66. If a CD can store 650 megabytes (MB) of data, and a
computer hard disk has a capacity of 350 gigabytes (GB),
how many CDs of information can be loaded onto the
hard disk?
.._ Computer Compact Disk
Compact disks (CDs) have
generally replaced floppy
disks for data backup and can
store about 500 times the
amount of information.
How many significant digits are in the following unit factors?
(b) 1lb/454 g
(a) 1 m/10 dm
(c) 1 L/1000 mL
(d) 1 qt/946 mL
68. Which of the following are exact equivalent relationships?
(a) 1m=10 dm
(b) llb = 454 g
(c) 1L=1000 mL
(d) 1 qt= 946 mL
An automobile airbag inflates to 50.0 Lin 35 ms. What is the
time of inflation in microseconds?
70. An automobile antilock brake system (ABS) operates the
brakes at 30 pulses per second. How many times do the
brakes pulse in 1.00 ds?
A light year is the distance light travels in 1.00 year. Given
the velocity of light, 1.86 X 105 mi/s, how many miles does
light travel in a light year?
72. A parsec is the distance light travels in 3.26 years. Given the
velocity of light, 3.00 X 108 m/s, how many kilometers does
light travel in a parsec?
Olympic athletes compete in a 1500-meter event but not in a
mile event. Which race is shorter: 1500 meters or 1 mile?
74. An oxygen molecule travels 975 mi/hat room temperature.
What is the velocity in meters per second?
How many 325 mg tablets can be produced from 2.50 kg of
powdered aspirin?
76. How many molecules of water are in one drop if there are
3.34 x 1022 molecules in 1.00 g (given that 1 mL = 20 drops)?
A basketball court measures 94.0 feet by 50.0 feet. Calculate
the playing area in square meters (given that 1yd=0.914 m)?
78. A football field measures 100.0 yards by 160.0 feet.
Calculate the playing area in square yards.
What is the density of a metal sample if a 37.51 g sample
added into a graduated cylinder increased the liquid level
from 50.0 mL to 57.5 mL?
80. What is the mass of 275 L of seawater if the density is
1.025 g/ cm3?
What is the specific gravity of gasohol if the density is
0.801 g/mL?
82. What is the density of jet fuel if the specific gravity is 0.775?
Express the density of water in the English units of pounds
per cubic foot.
84. Express the density of water in the English units of pounds
per gallon.
The space shuttle uses liquefied hydrogen at a temperature
of -422 °F. What is the equivalent Kelvin temperature?
86. The temperature in the Mojave Desert in California has
reached 324 K. What is the equivalent Fahrenheit temperature?
A red-hot fireplace poker is plunged into 3500 g of water at
22 °C. If the water temperature rises to 51 °C, how many
kilocalories of heat are lost by the poker?
88. A 10.0 g sample of metal at 19.0 °C is dropped into 75.0 g of
water at 80.0 °C. If the resulting temperature is 78.3 °C,
what is the metal? (Hint: Refer to Table 3.5.)
Calculate the mass of titanium [0.125 cal/(g X C)] that
requires 75.6 cal to heat the metal from 20.7 °C to 31.4 °C.
90. Calculate the mass of lead [0.0308 calj(g X 0 C)] that
releases 52.5 cal as the metal cools from 35.7 °C to 25.1 °C.
What is the temperature change when 10.5 g of silver
[0.0566 cal/(g X 0 C)] absorbs 35.2 cal of heat?
92. What is the temperature change when 8.92 g of sodium
[0.293 cal/(g X 0 C)] loses 750 cal of heat energy?
A 10.0 g sample of copper [0.0920 calj(g X 0 C)] gains
27.8 cal of heat. If the initial temperature is 22.7 °C, what is
the final temperature?
94. A 15.5 g sample of titanium [0.125 cal/(g X C)] loses
32.9 cal of heat. If the initial temperature is 28.9 °C, what is
the final temperature?
The density of mercury is 13.6 g/ mL. Express the density in
SI units (kg/m3).
96. The specific heat of mercury is 0.0331 cal/(g x °C). Express
the specific heat in SI units JI (kg x K).
The radius (r) of the international prototype kilogram cylin·
der is 1.95 cm. Assuming the density of the kilogram is
·
21.50 g/ cm3, calculate its height (h). The volume of a cylin· ·
der equals 1Tr2h, where 1T is the constant 3.14.
0
0