Physical chemistry courses

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. 

But, we expect that the majority of readers will be those with only a rudimentary command of quantum chemistry and chemical bonding theory (e.g., at the level of junior-year physical chemistry course) who wish to learn more about the emerging ab initio and density-functional view of molecular and supramolecular interactions. While this is not a textbook in quantum chemistry per se, we believe that the book can serve as a supplement both in upper-level undergraduate courses and in graduate courses on modern computational chemistry and bonding theory. 

The three laws of thermodynamics provide the theoretical basis required to master nearly all the concepts that are relevant in discussions of molecular energetics. We shall not dwell on those laws, because they are mandatory in any general physical chemistry course [1,8], but we will ponder some of their outcomes. It is also necessary to agree on basic matters, such as units, nomenclature, standard states, thermochemical consistency, uncertainties, and the definition of the most common thermochemical quantities. 

The notion of standard enthalpy of formation of pure substances (AfH°) as well as the use of these quantities to evaluate reaction enthalpies are covered in general physical chemistry courses [1]. Nevertheless, for sake of clarity, let us review this matter by using the example under discussion. The standard enthalpies of formation of C2H5OH(l), CH3COOH(l), and H20(1) at 298.15 K are, by definition, the enthalpies of reactions 2.3,2.4, and 2.5, respectively, where all reactants and products are in their standard states at 298.15 K and the elements are in their most stable physical states at that conventional temperature—the so-called reference states at 298.15 K. 

The course has been taught at the beginning of the third year, at which stage students have completed an elementary course of Organic Chemistry in first year and a mechanistically-oriented intermediate course in second year. Students have also been exposed in their Physical Chemistry courses to elementary spectroscopic theory, but are, in general, unable to relate it to the material presented in this course. 

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. 

These theories may have been covered (or at least mentioned) in your physical chemistry courses in statistical mechanics or kinetic theory of gases, but (mercifully) we will not go through them here because they involve a rather complex notation and are not necessary to describe chemical reactors. If you need reaction rate data very badly for some process, you will probably want to fmd the assistance of a chemist or physicist in calculating reaction rates of elementary reaction steps in order to formulate an accurate description of processes. 

At the same time, as a chemist I was disappointed at the lack of serious chemistry and kinetics in reaction engineering texts. AU beat A B o death without much mention that irreversible isomerization reactions are very uncommon and never very interesting. Levenspiel and its progeny do not handle the series reactions A B C or parallel reactions A B, A —y C sufficiently to show students that these are really the prototypes of aU multiple reaction systems. It is typical to introduce rates and kinetics in a reaction engineering course with a section on analysis of data in which log-log and Anlienius plots are emphasized with the only purpose being the determination of rate expressions for single reactions from batch reactor data. It is typically assumed that ary chemistry and most kinetics come from previous physical chemistry courses. 

This text is focused primarily on chemical reactors, not on chemical kinetics. It is common that undergraduate students have been exposed to kinetics first in a course in physical chemistry, and then they take a chemical engineering kinetics course, followed by a reaction engineering course, with the latter two sometimes combined. At Minnesota we now have three separate courses. However, we find that the physical chemistry course... 

Many physical chemists think that the teaching of physical chemistry is currently experiencing a crisis. First, most students enter a physical chemistry course less prepared, particularly in math, than they did in years past. Second, teachers of physical chemistry face numerous vexing questions, including What do we want to accomplish with the physical chemistry course What topics we present to a diverse audience How much of each subject should we emphasize How can we be certain that the students master the material ... 

An organization scheme for a modern physical chemistry course... 

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. 

Probably an example and problems derived from the carbon dioxide-blood buffer system in humans should be in every physical chemistry course. What a rich, complex example this is from Henry s law for the solubility of carbon dioxide in water (blood) to buffer capacity, that is, the rate of change of the law of mass action with proton concentration. The example can be expanded to include nonideal solutions and activities. How many physical chemistry courses use this wonderful and terribly relevant to life example First-year medical students learn this material. 

Time-related processes truly encompass the real world for how many systems are at equilibrium. It is said that if a human system reaches equilibrium, it is dead. Clearly time-dependent phenomena must be discussed in any physical chemistry course. 

Perhaps the biggest oversight physical chemists make when discussing kinetics is the neglect of volume effects. To be sure any chemical engineer who would forget the influence of volume even in a constantly stirred tank reactor would not be long in the profession. The volume alone can affect the rate of the reaction. How many physical chemistry courses, or text books, point that out ... 

What may be a brave new world with which to inform and challenge our students The nanoworld. This is a real and present challenge to provide the best information possible. What this means is that we need to do our best at the time, to incorporate the principles that seem to dictate the behavior of nanomaterials into our physical chemistry courses. (Notice in this discussion other than right now the word nanotechnology will not be mentioned.) Nanoscience and nanochemistry are phrases we should be using to discuss this area. Here again we as chemists are our own worst enemies by not presenting... 

My final remarks are a summary and a challenge. The content of the physical chemistry course cannot be determined by the instructor based on instinct or favorite topics. The subject matter needs to be shaped by the constraints ... 

A possible set of goals for a physical chemistry course might be that the students would be able to ... 

You should evaluate your students preparation for the physical chemistry course. Most people agree that today s students are less well prepared than students of a few decades ago, but the students still come to you with widely varying preparation and abilities both in mathematics and in chemistry. Furthermore, their proposed career paths do not necessarily correlate with their preparation. I found it helpful to pass out a take-home orientation quiz on the first day of class. This quiz contained a few mathematics problems, a few physics and chemistry questions, a request for a list of all of the science and mathematics courses taken, and a request for a statement of the student s proposed career. Analysis of the students responses could be used in planning the course. 

You will have to decide whether to use a mathematical approach or a more conceptual or heuristic approach. The students in the United States of America are now less well prepared in mathematics than were the students of a few decades ago. This provides an incentive to make your physical chemistry course... 

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. 

In this chapter, 1 intend to present the considerations that go into the formulation of physical chemistry courses. They are much the same as go into the formulation of physical chemistry textbooks, of course, for the two modes of delivery go hand in hand. However, I shall do my very best to stand back from my own prejudices and will try to give an even-handed account of a variety of opinions. 

Whereas the American system is horizontal, the British system is vertical. That is, the American system arranges courses in sequence, with what (to be honest) is introductory physical chemistry in the freshman year, then, typically, a physical chemistry course in the junior year. There are modifications of that, of course, but that is the broad picture. By contrast, in the British system, there is not (or at least, until recently, there has not been) a freshman course, on the grounds that high school chemistry is a serious course that in some respects goes beyond an American freshman course. As soon as the college course begins, all three branches are taught in comparable depth and that parallel development continues for all three or four years of the course. 

Apart from the advantages of a T-first approach that I outlined earlier, it seems to me that there is one serious disadvantage of a Q-first approach, which is the unfamiliarity and depth of the mathematics needed to do anything in quantum mechanics. Great care must be taken in a Q-first approach not to overwhelm students at that early stage of their physical chemistry course (or, indeed, at any stage), especially when heavy mathematics is in alliance with bizarre concepts. 

Like group theory, diffraction techniques ebb from and flow into physical chemistry courses. 1 think X-ray diffraction, at least, should be presented because it is so central to molecular biology and the steady state. Moreover, it provides an excellent opportunity for demonstrating the power of Fourier transforms in the understanding of physical phenomena. Indeed, it could be very interesting to develop a Fourier course that embraced diffraction and modem techniques of spectroscopy. 

Much of the research that has been done to date on learning in the domain of thermodynamics has involved the study of populations other than college age physical chemistry students. Thermodynamics is usually first introduced in elementary and introductory physics courses. For this reason, many studies have been conducted from the physics education perspective (56-60). These studies provide insights into the learning of important basic concepts, uncovering misconceptions that students bring into physical chemistry courses. 

Seven separate studies were carried out with chemistry students taking basic physical chemistry courses (777). Students had to solve a novel problem in an open-book, end-of-semester examination. Seven problems were used, mostly taken from the book by Ritchie et al. (108). One of the problems (adapted from Ritchie et al.) is reproduced below ... 

Data were collected from students enrolled in three different courses. Class A was a one-semester introductory quantum mechanics course intended for junior physics majors that typically enrolled about 10 students. Class B was the second-half of a two-semester physical chemistry course for chemistry majors that typically enrolls 30-40 students. The first semester of this course focuses primarily on thermodynamics the second-half spends the first two-thirds of the semester on quantum mechanics and then concludes with a discussion of statistical mechanics. Class C is offered every semester for junior-year chemical engineering majors, and was observed three times Cl, C2, and C3. Cl and C3 were offered during the fall semester, when the mainline population of chemical engineering majors take the course and had enrollments of approximately 70 students. C2 was offered in the spring semester and is frequently taken by students who have done a "co-op" or internship in industry, which requires them to be off-campus for a semester at a time. C2 had an enrollment of around 30 students. The material in Class C is quite similar to the material offered in Class B. The first three-quarters of this class covers quantum mechanics, the remaining time is spent on statistical mechanics. 

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