Equations, physical chemistry course

The first two chapters serve as an introduction to quantum theory. It is assumed that the student has already been exposed to elementary quantum mechanics and to the historical events that led to its development in an undergraduate physical chemistry course or in a course on atomic physics. Accordingly, the historical development of quantum theory is not covered. To serve as a rationale for the postulates of quantum theory, Chapter 1 discusses wave motion and wave packets and then relates particle motion to wave motion. In Chapter 2 the time-dependent and time-independent Schrodinger equations are introduced along with a discussion of wave functions for particles in a potential field. Some instructors may wish to omit the first or both of these chapters or to present abbreviated versions. 

We will consider only the batch reactor in this chapter. This is a type of reactor that does not scale up well at all, and continuous reactors dominate the chemical industry. However, students are usually introduced to reactions and kinetics in physical chemistry courses through the batch reactor (one might conclude fi om chemistry courses that the batch reactor is the only one possible) so we wiU quickly summarize it here. As we vrill see in the next chapter, the equations and their solutions for the batch reactor are in fact identical to the plug flow tubular reactor, which is one of our favorite continuous reactors so we will not need to repeat all these definitions and derivations in the section on the plug flow tubular reactor. 

Equations of state (EOS) offer many rich enhancements to the simple pV = nRT ideal gas law. Obviously, EOS were developed to better calculate p, V, and T, values for real gases. The point here is such equations are excellent vehicles with which to introduce the fact that gases cannot be really treated as point spheres without mutual interactions. Perhaps the best demonstration of the existence of intermolecular forces that can also be quantified is the Joule-Thomson experiment. Too often this experiment is not discussed in the physical chemistry course. It should be. The effect could not exist if intermolecular forces were not real. The practical realization of the effect is the liquefaction of gases, nitrogen and oxygen, especially. 

I review the difficulties and opportunities that we need to consider when developing physical chemistry courses. I begin with a comparison of the structure of courses in the USA and the UK, then turn to the question of the order of the course quantum first or thermodynamics first 1 then consider the impact of biology on our courses and then turn to the role of multimedia and graphics. I conclude with an attempt to identify the key equations of physical chemistry. 

We tell students, particularly in thermodynamics, that they need to be attentive to the conditions under which particular equations are valid. It is equally critical for instructors to consider the conditions in which we are operating The key structural pieces of most physical chemistry courses are the text, the problems we assign, and the time instructors and students have to grapple with the reading and working of problems. 

The Math Concepts course meets two basic needs. It fulfills the ACS requirement for exposure to differential equations and linear algebra and it provides all students taking physical chemistry with the same math background. When the students encounter quantum mechanics in physical chemistry they can concentrate on the chemistry without having to learn the math simultaneously. An added benefit is that we can demand accountability of the students. Because the current Math Concepts course is a pre-requisite for physical chemistry we know that they have had previous exposure to the math because we are directly responsible for that exposure. In all but a very few instances the course is taken in the semester directly preceding the physical chemistry course so the mathematics should be fresh in the students minds. 

To derive equation (13.8), we must make use of the first and second laws, the relationship between internal energy and enthalpy, certain characteristics of ideal gases, and a considerable amount of calculus. The derivation of this equation is typically presented in more advanced physical chemistry courses. 

The prerequisites for the course include two years of chemistry, including organic, analytical, and an introductory inorganic chemistry course, one year of calculus-based physics, three terms of calculus, and introduction to differential equations usually taken concurrently. Most students take the computational laboratory concurrent with the physical chemistry lecture course covering... 

No excuses. Anyone who has passed a course in physical chemistry should be able to crunch this book for numbers and for equations. Engineers can treat it as a handbook with long explanations whose formulae can be plugged into original programs or packaged software (preferably both so as to understand what is being computed). 

In my view, graduate students, especially in physical chemistry or chemical physics, are often misled by typical theoretical courses and research projects. They are likely to think that a blackboard or journal article full of equations is theory. However, usually it is just a treatment that does not invoke ideas outside an already accepted conceptual framework. A genuine theory opens up new perspectives, often by postulating or guessing a short-cut. 

The language we use to describe the forms of matter and the changes in its composition is not limited to use in chemistry courses it appears throughout the scientific world. Chemical symbols, formulas, and equations are used in such diverse areas as agriculture, home economics, engineering, geology, physics, biology, medicine, and dentistry. In this chapter we describe the simplest atomic theory. We shall use it as we represent the chemical formulas of elements and compounds. Later, after additional facts have been introduced, this theory will be expanded. 

The text largely contains fundamental material and focuses on understanding the basic principles rather than learning factual information. Since it is impossible to include all branches of surface science in such an introductory book because of its wide and multidisciplinary scope, a specific and narrow topic, the interfacial interactions between solids and liquids, has been chosen for this book. For this reason, the ionic interactions, charged polymers, electrochemistry, electrokinetics and the colloid and particulate sciences cannot be included. Some fundamental physical chemistry subjects such as basic thermodynamics are covered, and many equations are derived from these basic concepts throughout the book in order to show the links between applied surface equations and the fundamental concepts. This is lacking in most textbooks and applied books in surface chemistry, and for this reason, this book can be used as a textbook for a course of 14-15 weeks. 

At a higher level, such as a Physical or Quantum Chemistry course, a similar discussion can be utilized in a brief background sense. Additionally the relevance of line spectra can be put into context with discussions on the topic of one-electron solutions to the Schrodinger equation, as well as more advanced forays into the electronic structure of multi-electron systems. 

Most of the contents of this book have been taught to PhD students at the University of Grenoble through the course Physics and Physical Chemistry without Equations that started in 2005 at the Doctorate School I-MEP Ingenierie Materiaux Mecanique Energetique Environnement Precedes Production (Engineering, Materials, Mechanics, Energetics, Environment, Processes, Production). 

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