Mathematics for General Chemistry

A Scientific Notation and Experimental Error A.2 B SI Units, Unit Conversions, Physics for General Chemistry A.9 C Mathematics for General Chemistry A.21 D Standard Chemical Thermodynamic Properties A.37 E Standard Reaction Potentials at 25°C A.45 F Physical Properties of the Elements A.47 G Solutions to the Odd-Numbered Problems A.57... 

Appendix 3 contains a mathematical review touching on just about all the mathematics you need for general chemistry. Exponential notation and logarithms (natural and base 10) are emphasized. 

Mathematics is an essential tool in chemistry. This appendix reviews some of the most important mathematical techniques for general chemistry. 

The term theoretical chemistry may be defined as the mathematical description of chemistry. The term computational chemistry is generally used when a mathematical method is sufficiently well developed that it can be automated for implementation on a computer. Note that the words exact and perfect do not appear in these definitions. Very few aspects of chemistry can be computed exactly, but almost every aspect of chemistry has been described in a qualitative or approximately quantitative computational scheme. The biggest mistake a computational chemist can make is to assume that any computed number is exact. However, just as not all spectra are perfectly resolved, often a qualitative or approximate computation can give useful insight into chemistry if the researcher understands what it does and does not predict. 

This short book is intended for students who lack confidence and/or competency in the essential mathematical skills necessary to survive in general chemistry. Each chapter focuses on a specific type of skill and has worked-out examples to show how these skills translate to chemical problem solving. 

You ve probably already heard a lot about your general chemistry course. Many think it is more difficult than other courses. There may be some justification for that opinion. Besides having its very own specialized vocabulary, chemistry is a quantitative science, which means that you need mathematics as a tool to help you understand the concepts. As a result, you will probably receive a lot of advice from your instructor, teaching assistant, and fellow students about how to study chemistry. We hesitate to add our advice experience as teachers and parents has taught us that students do surprisingly well without it We would, however, like to acquaint you with some of the learning tools in this text. They are described in the pages that follow. 

Instructors can cover as much of the Fundamentals as they wish, whenever they wish skip it all or assign it for independent study. Students can also turn to the Appendixes for help with mathematics, units, conversion factors, and the correct use—within the normal practice of general chemistry, at least—of significant figures. 

This book is mainly intended as a supplement for the mathematically sophisticated topics in an advanced freshman chemistry course. My intent is not to force-feed math and physics into the chemistry curriculum. It is to reintroduce just enough to make important results understandable (or, in the case of quantum mechanics, surprising). We have tried to produce a high-quality yet affordable volume, which can be used in conjunction with any general chemistry book. This lets the instructor choose whichever general chemistry book covers basic concepts and descriptive chemistry in a way which seems most appropriate for the students. The book might also be used for the introductory portions of a junior-level course for students who have not taken multivariate calculus, or who do not need the level of rigor associated with the common one-year junior level physical chemistry sequence for example, an introduction to biophysical chemistry or materials science should build on a foundation which is essentially at this level. 

The book grew out of supplementary lecture notes from the five years I taught advanced general chemistry at Princeton University. Placement into this course is based almost exclusively on math SAT scores—no prior knowledge of chemistry is assumed. Most of the students become science or engineering majors, and they have a broad range of interests, but the strongest common denominator is interest in and aptitude for mathematics. 

The Journal of Chemical Physics, founded in 1933, would welcome papers perhaps too mathematical for the Journal of Physical Chemistry, or too chemical for the Physical Review." [3] Barriol considered himself, while being student at the Ecole Normale Superieure, not to be at the top level of mathematics - the way of working of my mind was of another type" [4] - but he was also too mathematical to be a chemist and he was too chemical to be a physicist. From the beginning, he was interested in entities generally called molecules by chemists, their movements and their properties. For Barriol, their dielectric properties were of the highest value when one wanted to have a look into the microstructure of matter. 

You probably remember the solution to these problems from general chemistry. The 2s and the three 2p AOs are mathematically combined in a kind of averaging process to produce four equivalent hybridized AOs. Because they result from combining one s orbital and three p orbitals, the new AOs are said to be sp3 hybridized. The hybrid AOs are ideal for bonding. They are all equivalent, and they have tetrahedral geometry. In addition, each has a large lobe of the orbital pointed in the direction where the other atom of the bond will be and only a small lobe on the other side of the carbon. This directionality of the hybrid AO allows for maximum overlap when it interacts with another AO to fonn a MO. The hybridization process and the sp3 hybrid AOs are shown in Figure 3.6. 

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