H. FALKENHAGEN, Elektrolyte. S. Hirzel, Leipzig 1932, p. 346.

H. FALKENHAGEN, Electrolytes.

The theory of solutions, which was a field whose foundations were laid by the founders of classical physical chemistry—van ’t Hoff, Arrhenius, and Ostwald—is at present, in the part concerning dilute solutions, being transformed into an exact physical theory. Such major physicists as Debye, with a whole host of collaborators and pupils, are participating in the development of this theory; methods such as integral equations, accessible perhaps only to physicists, are being brought into play. Falkenhagen’s book is, above all, an exposition of the questions resolved by Debye’s theory during the nine years of its existence; it is not a book on electrolytes in general, and still less a book on solutions; strictly speaking, it is a book on the theory of dilute solutions of strong electrolytes. This, however, is by no means a defect; the author himself took part in the development of the theory and, together with Debye, predicted the phenomenon of the dependence of the electrical conductivity and dielectric constant of electrolyte solutions on the frequency of the current used to measure them, and in work carried out with Dole gave the theory of their viscosity. The reader therefore feels that the author is master of this field, and not a painstaking reviewer of other people’s work.

At present the theory of strong electrolytes, whose foundations were laid in 1923 by Debye and Hückel, has developed so far that one senses a

the necessity of presenting it synthetically, in a purely deductive form. Such a presentation would make it possible to assess the exact limits of applicability of each approximation, to clarify in greater detail the physical meaning of such basic concepts as the activity coefficient, and to raise the question of the possibility of extending the theory to concentrated solutions. The author, however, proposes a path toward such a synthetic presentation of the theory analogous to its historical development. He begins with the basic definitions (Chapter 1), expounds the thermodynamics of ideal solutions (Chapter 2), then in the third chapter presents the classical theory of electrolytic dissociation and its application to weak electrolytes. In Chapter 4 he shows the inadequacy of the classical theory for explaining the equilibrium states of solutions of strong electrolytes and sets forth the foundations of their empirical thermodynamics, as given by Lewis and his collaborators. Chapter 5 contains a very old presentation of the experimental material on the electrical conductivity of solutions both under ordinary conditions (low voltages, low frequencies) and under those conditions (high voltages or high frequencies) in which new phenomena are observed. Along the way the impossibility of explaining this material by means of the classical theory becomes clear. After a brief survey of the first attempts to explain the deviations of strong electrolytes from the simple laws of ideal solutions, in Chapter 6 the author goes directly from the theories of Ghosh to a presentation of the foundations of Debye’s theory and its applications, which occupy more than two thirds of the book. Apparently wishing to make his book accessible to physical chemists, among whom interest in the questions discussed is much more developed than among pure physicists, Falkenhagen refrains from a systematic exposition of the most difficult mathematical questions of the theory, such as the theory of the Wien effect, the theory of viscosity, and the determination of the successive approximations to the fundamental equation of the theory, carried out by the method of integral equations by La Mer, Zand, and Gronwall. As a result the physicist-reader remains dissatisfied and, after reading Falkenhagen’s book, does not receive a complete acquaintance with the theory sufficient for undertaking independent work in this field. On the other hand, this simplified exposition is not so easy as to be accessible even to an average physical chemist, especially of the older generation. This remark also applies to the last (twelfth) chapter, which contains an account of the work of Fowler and Kramer, who attempted to give a statistical interpretation of Debye’s theory. Chapter 11 is devoted to more concentrated solutions. It contains an exposition of Bjerrum’s “association theory,” of experimental work on heats of dilution and of their theoretical treatment both according to Debye’s theory and according to Nernst’s theory, and of interesting methods for determining the degree of dissociation proposed by Onsager, Nernst, Davies, and Bjerrum, as well as the results of studying solutions by optical methods, including the Raman effect and Brønsted’s theories of ion interaction.

The author completely excludes a whole series of questions, apparently because an exact theory of them does not yet exist, although many of them are of great interest. Above all, he does not touch at all upon the fundamental question of the theory of solutions—the question of solubility, as well as another fundamental question of the theory of electrolytes: the question of the nature of strong electrolytes and the causes of electrolytic dissociation.

The questions of electrolyte diffusion and of the origin of diffusion potentials are not treated, which is apparently explained by the absence of a theory of these phenomena from the point of view of Debye–Onsager’s ideas. At the time the book was written, however, this question had in general form been solved by Onsager, who gave a general theory of the viscosity, electrical conductivity, and diffusion of mixtures of any number of electrolytes.

The phase potentials, surface tension of electrolyte solutions, and their influence on the surface tension of systems containing no electrolyte are not mentioned even once. Excluded from consideration are the phenomena of anomalous electrical conductivity, as well as all theoretical and experimental works connected with the question of the influence of electrolytes on the kinetics of reactions in solutions. The interesting work of Born on the connection between mobil—

...and the radius of the ions; but six whole pages are devoted to Nernst’s theory of heats of dilution, the value of which may well be doubted.

Despite these shortcomings and a certain paucity of ideas and broad generalizations (apart, of course, from those expressed by other authors), Falkenhagen’s book can be recommended to anyone who wishes to become acquainted with the present state of the theory of strong electrolytes. The book has recently appeared in an English edition, which, unfortunately, was not available to us.

Vl. Semenchenko