Page 39 - Essentials of physical chemistry

1 Ideal and Real Gas Behavior

INTRODUCTION TO THE ‘‘FIRST ENCOUNTER WITH PHYSICAL CHEMISTRY’’

Welcome to ‘‘essential physical chemistry’’! We will explore parts of this field that work out cleanly
in a beautiful way to provide a sense of confidence in your understanding of this interdisciplinary
science. At the end you will hopefully learn to appreciate the beauty of concepts that have been
discovered since the 1600s by intellectual giants and gain a sense of amazement for the far-reaching
effects of those discoveries into all aspects of molecular science. Students who have completed this
course often send this author messages telling how this material has helped them later in biochem-
istry, inorganic chemistry, and physical chemistry laboratory courses. To get the most from this
course it is highly recommended that you personally study the material in Introduction: Mathemat-
ics and Physics Review even if the course lectures start in Chapter 1. It provides a good preparation
for the mathematics and physics concepts we will encounter in the rest of the book. We could
have put review at the end of the book, but many students have reinforced the view of this author
that it needs to be right up front at the beginning and it really makes the understanding of the later
material easier.
Historically, the modern age of science and technology begins roughly in the 1600s and scientific
knowledge has bloomed exponentially since then, although some concepts originated in ancient
Greece and much of clever Roman engineering was lost between 500 and 1600. Thus, we start with
the studies of gases by Sir Robert Boyle (Figure 1.1). We arbitarily assume that applied mathematics
is what distinguishes modern science from medieval engineering so you should be aware that in
every case we will attempt to unify a concept with some equation, often involving calculus. Thus,
you need to pay attention to the worked examples in the chapters, do the assigned problems, and
then try the tests at the end of chapters about where a midterm or final examination usually occurs.
You should pay attention to the time limits given for those tests and practice those problems until
you have that material down cold within the time allowed! Of course, your teacher will give
different questions on the tests in your course but if you can do the sample tests you should be
ready for almost any variation of that type question: What equipment is needed here? You need a
calculator with special functions but a simple $9 solar-powered calculator is adequate if it has
exp(x), sin(x), cos(x), log(x), and ln(x) with at least eight significant figures and scientific exponen-
tial notation. The next requirement is a human brain and an attitude that you can do this (!) provided
you put some time and effort into the work. So let us get started!

PHENOMENOLOGICAL DERIVATION OF THE IDEAL GAS EQUATION

While mathematical theory often runs roughly parallel to physical science, sometimes faster and
other times slower, a key strategy is a process called the ‘‘phenomenological approach.’’ In this
method a process is studied to determine the variables on which it depends and then an equation is
developed, which matches the results of the problem. Often it requires a number of data points to
determine whether the result is linear, quadratic, or some higher order in a given variable but the
case of the ideal gas law is an excellent starting point to illustrate this method and at the same time
enter the important domain of thermodynamics.
Although we could digress to mention early concepts of science by ancient Greek philosophers,
we will begin with the first attempts at quantitative studies that can be related with mathematical

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