Page 23 - Theory and Problems of BEGINNING CHEMISTRY

12 MATHEMATICAL METHODS IN CHEMISTRY [CHAP. 2

Better, however, is to do both multiplications in the same step:
60 min 60 s

2.50 h = 9000 s
1h 1 min
EXAMPLE 2.3. Calculate the speed in feet per second of a jogger running 7.50 miles per hour (mi/h).

7.50 mi 5280 ft 39 600 ft
Ans. =
1h 1mi 1h
39 600 ft 1h 660 ft
=
1h 60 min 1 min

660 ft 1 min 11.0ft
=
1 min 60 s 1s
Alternatively,

7.50 mi 5280 ft 1h 1 min 11.0ft
=
1h 1mi 60 min 60 s 1s
It is usually more reassuring, at least at the beginning, to do such a problem one step at a time. But if you
look at the combined solution, you can see that it is easier to do the whole thing at once. With an electronic
calculator, we need to press the equals = key only once, and not round until the final answer (Sec. 2.5).
We will expand our use of the factor-label method in later sections.

2.3. METRIC SYSTEM
Scientists measure many different quantities—length, volume, mass (weight), electric current, voltage,
resistance, temperature, pressure, force, magnetic field intensity, radioactivity, and many others. The metric
system and its recent extension, Syst` eme International d’Unit´ es (SI), were devised to make measurements and
calculations as simple as possible. In this section, length, area, volume, and mass will be introduced. Temperature
will be introduced in Sec. 2.7 and used extensively in Chap. 12. The quantities to be discussed here are presented
in Table 2-1. Their units, abbreviations of the quantities and units, and the legal standards for the quantities are
also included.
Table 2-1 Metric Units for Basic Quantities

Fundamental Abbreviation
Quantity Abbreviation Unit of Unit Standard Comment

Length or distance l meter m meter
d
Area A meter 2 m 2 meter 2
Volume V meter 3 m 3 meter 3 SI unit
or liter L older metric unit
3
1m = 1000 L
Mass m gram g kilogram 1 kg = 1000 g

Length (Distance)
The unit of length, or distance, is the meter. Originally conceived of as one ten-millionth of the distance
from the north pole to the equator through Paris, the meter is more accurately defined as the distance between
two scratches on a platinum-iridium bar kept in Paris. The U.S. standard is the distance between two scratches
on a similar bar kept at the National Institute of Standards and Technology. The meter is about 10% greater than
the yard—39.37 in. to be more precise.
Larger and smaller distances may be measured with units formed by the addition of prefixes to the word
meter. The important metric prefixes are listed in Table 2-2. The most commonly used prefixes are kilo, milli,