Page 25 - Essentials of physical chemistry

Introduction: Mathematics

and Physics Review

Welcome to ‘‘Essentials of Physical Chemistry’’! We really have a challenge here! According to the
new requirements of the American Chemical Society, only one semester of physical chemistry is
required for the BS in chemistry, although a second semester is an acceptable elective. Within
chemistry education there has long been a division between students who shy away from mathemat-
ics and those who appreciate the quantitative nature of the bridge between chemistry and physics.
This is not only unfortunate in closing doors to students who might go further in research but is an
unnecessary result of a long tradition of physical chemists reveling in esoteric difficulties. Our
position here is that physical chemistry faculty should strive more to popularize the field of physical
chemistry without degrading the level of treatment by using enthusiastic joyful teaching methods!
There are many applications of physical chemistry where the mathematical modeling has been
developed to a point where clean solutions are available and can be compared to experimental results
with a sense of wonder at the level of understanding they give to the molecular world that is truly
amazing! Here we attempt to provide mnemonics and other analogies to bring chemical principles in
focus with calculus-level treatment for the ‘‘essential’’ topics in physical chemistry in one semester,
along with enough material to continue further treatment of other topics in an elective semester. It is a
‘‘Mission Impossible’’ to present essential topics in physical chemistry in one semester, so our
attitude is ‘‘Just the facts, Jack!’’ If there are four ways to explain something, we will use only one
way that we think makes the point, but we will fill in most of the mathematical steps to make that one
way as clear as possible. This leads to abbreviated treatments but with sufficient mathematical depth
that interested students will still be able to advance to further topics with a good foundation.
Although we need to treat a broader range of topics today, we aim to reach the level of clarity for
undergraduates as given in what we consider a pedagogical masterpiece by G. S. Rushbrooke as
Introduction to Statistical Mechanics, Oxford Press, London, 1962; just the necessary facts, key
equations, and only a few problems at the end of each chapter. Our hope is that any student who
follows the text with pencil and paper will do well on the Graduate Record Examination or other
advanced courses. We cannot cover every topic in one semester but we can give a good foundation
with active student participation. After the absolutely essential topics in the first semester, we
include further topics for an elective second semester that fill in what should be normally included in
a two-semester treatment of physical chemistry, in greater detail at a more leisurely pace. However,
we still have to pack some spectroscopy into the first semester because a student may not elect the
second semester and yet modern topics are heavily dependent on spectroscopy! Did I say we have a
challenge? By the way, some sensitive souls have told me that I should not use capital letters to
emphasize words since in this age of texting that denotes shouting, BUT in my lectures I routinely
emphasize some words more loudly than others to wake up the back row of the class! Thus no
offense is intended, it is just a style mechanism to maintain class attention!

REVIEW OF NECESSARY MATHEMATICS AND PHYSICS
If you have flipped through some pages of this text you may be concerned about the amount and level
of mathematics herein. You need to give the text a chance since it is based on over 30 years of
teaching students just like yourself who may have sold your calculus text and wondered why you had
to take any calculus at all. There is a high probability that you have recently passed a course or two in
organic chemistry, which involved little mathematics but massive amounts of learning. The approach

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