ELEMENTARY PHYSICAL CHEMISTRY AND MATHEMATICS H. B. WILLIAMS Louisiana State University, Baton Rouge,Louisiana
ACCORDING to chemistry students, elementary physical chemistry is the most difficult subject encountered a t the undergraduate level. From the teaching experience of himself and others, the author suggests certain main factors which contribute toward the frequent failures and consequent reputed difficulty which accompany an elementary physical chemistry course. The essential cause of difficulty lies in the mathematical preparation of the students. Experienced physical chemistry instructors resign themselves t o the necessity of training each new group of students not only in the appreciation of certain mathematical concepts hut even in the use of some of the more simple tools of mathematics. The more common mathematical difficulties are: (1) the use of logarithms, (2) the ability to recognize when integration is necessary, (3) the ability t o recognize conditions under which integration is possible, and (4) the concept of the perfect differential. A few examples should sufficeto indicate the general situation. I t appears that the teaching of logarithms by most mathematics instmctors is concerned principally with methodology. The student is rarely required t o express a logarithm in a usable form, especially in the case of numbers less than unity. To be sure, loglo 0.0045 is 3.653, or even (heaven forbid!) 7.653 - 10, but if the numerical value of the logarithm is desired both forms are useless. Why are students not taught to obtain the usable answer, -2.347, in the above instance? Then, of course, antilogues present the reverse of the same problem.
One simple instance will suffice to demonstrate points (2) and (3) above. Taking the expression dw = pdu, let us ask, when is it desirable to integrate such an expression and under what conditions is it possible to integrate? The student must be taught that it is necessary t o integrate to obtain the total work along a prescribed path. The question of whether or not the expression can be integrated usually leaves the student in a quandary. At this stage in his education he should already know that integration is possible only if p is constant, or is an integrable function of v. This simple analysis of the equation, however, usually escapes the student whose calculus training has consisted of reproducing standard integrations with familiar variables. Such an approach on the part of calculus teachers and their textbooks has taken its toll of otherwise adequate students. The situation cited above is recurrent throughout physical chemistry. As to the fourth and probably greatest difficulty of the physical chemistry student-the perfect differential or its counterpart, the line integral-one feels that the students have never before encountered the concept. Adequate mathematical preparation a t this point would make their grasp of elementary thermodynamics almost automatic once the -~hvsical conceuts were explained. The teacher of physical chemistry should not have to teach elementary mathematics. We are in dire need of mathematics teachers who realize that mathe.. matics is aesigned to be applied. Mathematics for its own sake always leaves the student wanting in his preparation for anything hut more mathematics.
