Chemistry Reference
In-Depth Information
1 yd
Aratio may be changed to an equivalent ratio with different units by apply-
ing the factor label method.
1 ft
EXAMPLE 2.7
1 yd
1 ft
Change 75 mph to feet per second.
1 ft
Solution
1 ft
1 ft
1 ft
Figure 2.3
Number of Square
Feet in a Square Yard
(not actual size) Each side of the
square is 1 yard long or 3 feet long.
The area is the square of these,
or 9 ft
2
.
Miles
hour
Feet
mile
Feet
hour
Hour
minutes
Feet
minute
Minute
seconds
Feet
second
1 yd
2
(
)
(
)
(
)
=
75 miles
1 hour
5280 feet
1 mile
1 hour
60 minutes
1 minute
60 seconds
110 feet
second
Practice Problem 2.7
Calculate the speed in miles per hour of a run-
ner who runs the 100-yd dash in 8.53 s.
Many more examples of the use of the factor label method will be presented
in the sections that follow, where we will work problems involving quantities
that are directly proportional to each other. The method can be expanded to quan-
tities that are equivalent to each other. For example, its use with percentages is
presented in Appendix 1 and with moles of substances in Section 7.3.
The use of percentages as
factor labels is presented in
Appendix 1.
Snapshot Review
❒
In the factor label method, units may be canceled like variables (
x, y
)
in algebra. Placement of the units so that they cancel to give the
desired units is the essence of the method.
ChemSkill Builder 2.5
❒
Some factors are constant, such as the number of cents in a dollar;
others are variable, such as the number of miles traveled by a car per
hour, and these must be given in the statement of a problem.
A. (a) Calculate the number of quarters ($0.25) in $22.75. (b) Calculate the
value in dollars of 144 quarters.
2.2
Exponential Numbers
Objects of scientific interest range from incredibly tiny to almost unimaginably
large. The number of iron atoms that would fit side by side on a line 1 inch
(2.54 cm) in length is about 100 million (Section 13.1). The number that could
