Morton Z. Hoffman and Alfred prock
Boston University Boston, Massachusetts
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Physical Chemistry for Freshmen A rigorous introduction
The trend in freshman chemistry over the last decade has been strongly directed toward increased physical chemistry orientation in the courses. This trend is most clearly evidenced by the changes in the nature of the textbooks used. I n the course a t Boston University discussed in this paper, we have sought to present to selected freshman students a rigorous introduction to physical chemistry. The course is perhaps unique because it was developed outside of the framework of a chemistry curriculum and thus did not have to be concerned with the servicing of future courses or the conforming to accreditation standards. Since that time, however, the course has been made part of the chemistry curriculum thereby introducing a number of problems, some of which can only be solved with the experience of time. In September, 1961, Boston University established a new six-year medical education program whereby selected high school graduates would be admitted to the College of Liberal Arts and permitted, upon the successful completion of the first two years of the program, to enter the Medical School without further application. These students, who had had a t least one year of physics, a year of chemistry, four years of mathematics, high academic standing, and good scores on the Scholastic Aptitude Test, would spend six years including the summers in the program; they would then obtain the BA and MD degrees upon graduation. I n these six years they would fulfill all the liberal arts and medical school requirements so that both disciplines would be represented at least to the same extent as in the normal eight year sequence. I n considering the role of chemistry in this new curriculum, the organizers of the program recognized that the current trend in medicine and biology is toward the molecular biology and biochemical point of view. They also noted that the usual premedical undergraduate physical science courses, consisting mainly of general and organic chemistry with an occasional year of physics, often neglect physical chemistry. To eliminate this deficiency, the planners established a new chemistry course which would introduce the freshmen st,udent in this program to physical chemistry. I n the more than three yean of its operation, 184 students have been admitted to the program. The average SAT scores for the class admitted in Seutember. Presented as part of the Symposium on Teaching of Physical Chemistry before joint sessions of the Divisions of Physical Chemistry and Chemical Education at the 148th National Meetingof the American Chemical Society in Chicago, Illinois, August 31, 1964.
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1964, is 672 (verbal) and 701 (mathematics). Fiftyeight percent of the students were in the top 5y0of their high school graduating class with 87% in the top 10%. Since September, 1963, this course has been open to undergraduate honors students in chemistry who have been selected on the same basis as those in the medical program. I n devising this course and following its evolution, the authors of this paper as the instructors have had two main concerns. The first involved the mathematical abilities of the students. For many of the students, calculus had been introduced in their high school mathematics courses; a few had Advanced Placement in that area. However, no uniformity existed within the class and so no previous calculus background could be presumed. Concurrently with the chemistry course, the medical students would take a year course in physics, the first six weeks of which would be devoted to calculus. The honors students would take a regular calculus course a t the same time. I n considering this in relation to the teaching of physical chemistry, it was noted that very little calculus beyond the basic differentiation and integration procedures need really be used without sacrificing mathematical rigor. We established the policy that if a presentation required mathematical tools beyond the level of the students or if an appropriate simpliied model using their calculus ability could not be devised, then it would he best to exclude such a development from the course material. We have never found need to tell the students that they must accept certain relationships and equations and wait for later courses to make the development clear. The second concern evolved from the first. What topics should he covered in a physical chemistry course for freshmen? Since the course was estahlished within the framework of the medical program, it did not have to prepare the student for any formal course other than the second year organic which in turn would be the basis for the biochemistry course taken a t the medical school. We did not have to be concerned with fitting the course to the needs of further courses in analytical or inorganic chemistry, for example. We could devise a freshman chemistry course for selected students that was self-contained and that had no curriculum restrictions other than the presentation of physical chemistry. I n this connection then, no excuses would have to be made concerning the lack of a comprehensive presentation of descriptive chemistry. Chosen Topics
Rather than presenting a broad survey of the many
topics generally included in the usual third- or fourthyear physical chemistry course, we have chosen to develop a series of selected topics which we believe form the framework of physical chemistry. The depth to which these topics are developed depend, as pointed out, upon the students' mathematical abilities and their desire to comprehend the rationale behind the relationships. Only a few topics are covered in the year; this is compensated by the step-by-step development we have always sought to maintain. Newton's laws of mechanics, the basic relationships of electricity and magnetism, and experimental facts provide the background for all developments. When the students lack the background a t a certain point, a digression is made until the smooth continuity in depth is insured. Six general areas are covered in the lecture part of the course: kinetic theory (10 lectures), structure of the atom (12 lectures), chemical bonding (9 lectures), thermodynamics (30 lectures), chemical kinetics (10
lectures), and quantum chemistry (8 lectures). We begin by getting all the students up to the same chemical level. Although all the students have had at least a year of high school chemistry, their backgrounds are as diverse as the schools from which they come. We begin with a rapid review (3 lectures) of fundamental concepts such as stoichiometry and the solving of related problems. A heavy enlphasis is placed on kinetic theory; this provides an excellent demonstration of scientific reasoning and can be developed to a considerable extent making reasonable mathematical demands of the students. I n the authors' opinion, it is of immense value to show how the picture of the atom emerges as a soft particle having finite size and exhibiting shortrange forces of attraction for other particles. The development of the Maxwell-Boltzmann distribution laws rests upon the barometric forniula, an easily conceived idea.
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The structure of the atom is discussed on a completely experimental basis. The quantitative discussion of the experiments leading to the discovery and characterization of the fundamental particles is based upon an introduction to electricity and magnetism. The development of the Bohr atom includes the electronic spectrum of atomic hydrogen, the Rydberg formula, and the Zeeman effect. The Sommerfeld improvement begins the extension of the quantum number concept which leads to the idea of electron spin. The quantum description of the electron given here is extended a t the end of the year, a deferment made so that the student can have time to acquire more mathematical practice. I n the meantime the semiclassical theory provides all the essential features for the understanding of the periodic table. Bonding between atoms is discussed making use of elementary considerations from electrostatics based on energy, size, and charge. The concept of electronegativity is introduced and developed with the experimental measurement of the dipole moment of heteronuclear diatomic molecules. For this a development of the behavior of the polar molecule in an electrostatic field is presented in terms of two dimensional space; the generalization to three dimensions is easily made. I n this way the students' lack of familiarity withspherical polar coordinates is avoided, and a t the same time the required niatheniatics does not obscure the physical picture. The subject of thermodynamics is developed from the measurable quantities of mass, pressure, volume, and temperature, and the changes that take place in them when certain operations are performed. The functions H, G, and A are introduced as combinations of symbols that arise when the laws of thermodynamics are written to apply to special cases convenient to the experimentalist. Entropy is introduced strictly as an outgrowth of the Carnot cycle. This rigorous development leads to the relationships of equilibrium, electrochemistry, and colligative properties. All equilibrium considerations, including ionic systems, are developed directly from thermodynamics eliminating the unrealistic approach involving the rates of reversible reactions. In the solving of problems, the various cases are not categorized but rather the single method taught is to search for the number of independent equations that equals the number of unknowns. The discussion of chemical kinetics draws strongly upon the previous development of kinetic theory and the concepts of energy. The phenomenological aspects of reaction order serve as the basis of the treatment of kinetics which includes the presentation of activated complex theory, steady-state approximation, and the deduction of merhanisms. laboratory Work
I n the laboratory part of the course, the principal considerations are to develop rapidly the students' techniques, to introduce them to as many physical chemistry experiments as possible, and to confront them with a large number of precise and quantitative exercises. Although the laboratory techniques of most of the students begin a t a fairly rudimentary level (some students have only observed the use of the plae 190 / lournol of Chemicol Educofion
form balance), exposure to experiments involving complicated instruments and skills and a high degree of demanded precision rapidly shapes their control of laboratory situations. After several preliminary weeks devoted to becoming acquainted with the analytical balance, burets, and volumetric glassware, the students go on to perform those experiments considered to he classics of physical chemistry as well as others specially devised for the course or adapted from descriptions presented in THIS JOURNAL.' An attempt has been made to maintain a close correlation between lecture and laboratory topics while a t the same time we have recognized that some subjects may lend themselves better to one part of the course than the other. The students take their data in duplicate, one set going to the instructor a t the end of the laboratory period. Revision of data is not tolerated and so the students quickly learn to organize their data page and maintain the highest intellectual honesty. Their laboratory reports contain error analyses and comparison of results with the "accepted" literature values. With the almost individual attention the instructors and graduate teaching assistants can give to the small sections (no more than 16 students), the presentation of challenging physical chemistry experiments to the freshmen has been, in our opinion, very successful. Evaluation
Because of the dual nature of the students in the course, any evaluation must be carried out on two levels. Our over-all view is that the acceptance level of the m e terial is quite high. From examinations and discussions with the students, we believe that they do gain an understanding of the physical chemistry quantitative approach as well as the ability to solve problems. While much of this success is no doubt due to the students' intelligence, some success can be attributed to the close contact we have always sought to maintain with the students. We meet the students in recitation classes, laboratory, office hours, and, a t the beginning of the semester, orientation discussions for the purpose of establishing good study habits and attitudes. As with all specially developed courses, we faced the inevitable problem of finding suitable textbooks for both the lecture and laboratory aspects of the course. During the first three years of the course we have used a t various times "Principles of Chemistry, Sixth Edition'' by Hildebrand and Powell, "Principles of Chemistry" by Hiller and Herber, and "Physical Chemistry, Second Edition" by Daniels and Alherty. The physical chemistry oriented general chemistry books were unsuitable because of the greater depth of the fewer overall topics we wished to cover. The third- and fourthyear physical chemistry books assumed a chemical sophistication that could not he expected of freshman students. The same problem existed with regard to a laboratory manual. This year the students are using textbook and lahoratory material which we have written for the c ~ u r s e . ~
' A complete listing of the experiments used will be provided interested readers on request to the authors. For information concerning the publication of this material, write: College Division, McGraw-Hill Book Co., 330 West 42nd Street, New York, N. Y. 10036.
From the point of view of the medical program, the course and the material presented appear to be successful. The first group of students are in their second year a t the medical school. The evaluation of the course, however, is more critical for the honors chemistry majors. It is no longer a question of whether a year of physical chemistry can be presented to freshmen. The problem is, having done so, what revisions must be made in the rest of the chemistry curriculum, particularly in any further physical chemistry course. Should these honors students now proceed through the regular sequence to the junior-year physical chemistry course and hear a repetition of much that they have already heard as freshmen? On the other hand, they are not well enough prepared for the more advanced physical chemistry senior courses, and in the over-all picture, how can the advantage these students possess in their knowledge of the foundations of physical chemistry and their relative ignorance of qualitative descriptive chemistry be reconciled? We believe that the answer lies in the reconsideration of the whole honors chemistry curriculum taking into account the content of this freshmen course. The descriptive inorganic aspects of chemistry can be
presented in a later coulse utilizing the students' backgrounds in handing, equilibrium, electrochemical potentials, and kinetics. The repetition of ionic equilibrium in quantitative analysis may be avoided. Further, on the junior level with an even deeper mathematics background the student may now take a physical chemistry course that will take him up to a point where he may begin graduate level courses in his senior year. All this must he considered within the framework of ACS requirements and available faculty. The question might be raised as to whether an approach such as ours is suitable for all freshman chemistry students. We commend the general trend to physical chemistry for freshmen. On the other hand, we believe that our approach has been successful for us because of the selected nature of the students. We do not feel that it would necessarily be appropriate to have this course as the only chemistry exposure for a nonchemistry major. However, it is possible that in the not too distant future, when high school graduates will all have had an introduction to calculus and a solid exposure to chemistry and physics, all chemistry and science majors can be exposed to a rigorous introduction to physical chemistry in their freshman year.
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