Page 21 - Theory and Problems of BEGINNING CHEMISTRY

CHAPTER 2

Mathematical

Methods

in Chemistry

2.1. INTRODUCTION
Physical sciences, and chemistry in particular, are quantitative. Not only must chemists describe things
qualitatively,butalsotheymustmeasurethemquantitativelyandcomputenumericresultsfromthemeasurements.
The factor-label method is introduced in Sec. 2.2 to aid students in deciding how to do certain calculations. The
metric system (Sec. 2.3) is a system of units designed to make the calculation of measured quantities as easy
as possible. Exponential notation (Sec. 2.4) is designed to enable scientists to work with numbers that range
from incredibly huge to unbelievably tiny. The scientist must report the results of the measurements so that any
reader will have an appreciation of how precisely the measurements were made. This reporting is done by using
the proper number of significant figures (Sec. 2.5). Density calculations are introduced in Sec. 2.6 to enable the
student to use all the techniques described thus far. Temperature scales are presented in Sec. 2.7.
The units of each measurement are as important as the numeric value, and must always be stated with the
number. Moreover, we will use the units to help us in our calculations (Sec. 2.2).

2.2. FACTOR-LABEL METHOD
The units of a measurement are an integral part of the measurement. In many ways, they may be treated
as algebraic quantities, like x and y in mathematical equations. You must always state the units when making
measurements and calculations.
The units are very helpful in suggesting a good approach for solving many problems. For example, by
considering units in a problem, you can easily decide whether to multiply or divide two quantities to arrive at
the answer. The factor-label method, also called dimensional analysis or the factor-unit method, may be used
for quantities that are directly proportional to one another. (When one quantity goes up, the other does so in a
similar manner. For example, when the number of dimes in a piggy bank goes up, so does the amount in dollars.)
Over 75% of the problems in general chemistry can be solved with the factor-label method. Let us look at an
example to introduce the factor-label method.

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