Electrochemistry, Past and Present - American Chemical Society

Chapter 5

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The Contribution of Electrochemistry to the Development of Chemical Kinetics Keith J. Laidler Department of Chemistry, University of Ottawa, Ottawa, Ontario K1N 9B4, Canada Arrhenius's theory of electrolytic dissociation, proposed in 1887, gave the first great impetus to chemical kinetics, and led to an understanding of catalysis by acids and bases. Later the Debye-Hückel theory of strong electrolytes and G.N. Lewis's definition of ionic strength led to a satisfactory interpretation of the kinetic effects of added foreign salts. These effects showed that, when transitionstate theory is applied, the rate of a second-order reaction between A and B must involve a kinetic activity factor yAyB/y≠, where yA and yB are the activity coefficients of the reactants and y≠ is the activity coefficient of the activated complex. The detection of general acid-base catalysis was consistent with the Bronsted-Lowry extended definition of general acids and bases. Electrochemistry and kinetics were born within a few years of each other, and grew up in close association. Unlike their sibling thermodynamics, which had a sickly and confused childhood, theirs was a healthy and vigorous one, largely as a result of the friendly cooperation between them. Most of those who made substantial contributions to either electrochemistry or kinetics made significant contributions to the other; names that come at once to mind are Faraday, Arrhenius, van't Hoff, and Ostwald. The year 1887 is conveniently regarded as the year of birth of physical chemistry, by which is meant that the subject was then first recognized as a separate branch of chemistry. It was in that year that the first journal of physical chemistry, the Zeitschrift für physikalische Chemie, was founded, and that Wilhelm Ostwald (18531932) published the second and final volume of his Lehrbuch der allgemeinen Chemie, the first textbook of physical chemistry. In that same year Ostwald was appointed professor of physical chemistry at Leipzig, and Svante Arrhenius (1859-1927) published his famous theory of electrolytic dissociation. Work in physical chemistry had, of course, been done before 1887, but it was somewhat spasmodic. Faraday's masterly work on ()()97-6156/89/0390-0063$06.00/0 © 1989 American Chemical Society

In Electrochemistry, Past and Present; Stock, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.


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electrolysis (1), carried out in the 1830s, may perhaps be regarded as the first work in electrochemistry. Wilhelmy's work on the rate of inversion of sucrose (2), published in 1850, is perhaps the first work in kinetics although some interesting rate measurements had been made much earlier (3, 4 ) . However, the work that gave the greatest impetus to both electrochemistry and kinetics was done in the early 1880s. It was then that Arrhenius was making the conductance measurements that led to his theory of electrolytic dissociation, and that J.H. van't Hoff (1852-1911) was working at the University of Amsterdam on osmotic pressure and was carrying out investigations in chemical kinetics that led in 1884 to his famous book Etudes de dynamique chimique, the first textbook on kinetics. Also at that time, at the Riga Polytechnic Institute, Ostwald was investigating the behaviour of acids and was studying the acidcatalyzed hydrolysis of various esters. By a happy chance these three men, dubbed by their contemporaries 'Die Ioner' - 'the Ionists' - came together in their endeavours; they corresponded and met over a period of years, and there is no doubt that the friedly relationship that existed between them had a strong influence on the development of both electrochemistry and kinetics. (For more detailed accounts see refs. 5 and 6). Electrolytic Dissociation Ironically, the happy chance was that Arrhenius's dissertation at the University of Uppsala, submitted in 1884, was not well received by the examiners, who gave it such a poor rating that his prospects for an academic career were seriously in jeopardy. Fortunately, instead of accepting defeat and retiring into oblivion, Arrhenius sent copies of his dissertation to several prominent scientists, including Ostwald and van't Hoff. Both of them, while not at once appreciating the significance of what Arrhenius had done, realized that it was probably of great importance and gave him much encouragement, Ostwald, in fact, took the unusual step of travelling to Stockholm to meet Arrhenius and discuss his work, a surprising compliment for a young but already distinguished professor to pay to a younger man who had nearly failed to obtain his degree. Ostwald also offered Arrhenius an appointment at the Riga Polytechnic Institute, but for personal reasons Arrhenius was unable to accept it. Arrhenius had not had much help in carrying out his research, and in writing his dissertation, from the professors at the University of Uppsala. His dissertation was not clearly written, and his interpretations of his results were far from satisfactory; there was no suggestion in it that there can be dissociation into ions. The low rating the dissertation received was not altogether surprising. The discussions with Ostwald were valuable in leading Arrhenius to the idea of dissociation, although Ostwald himself, ever cautious, did not accept the idea until a little later. Before receiving a copy of Arrhenius's dissertation in June, 1984, Ostwald had himself made measurements of the electrical conductances of solutions of a number of acids, and had made kinetic measurements of their catalytic activities. He had observed a marked parallelism between the conductances, measured at a fixed concentration of acid, and the rate constants, and had also noted that the nature of the



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Development of Chemical Kinetics

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anion had little effect on the rates. On receiving Arrhenius's dissertation Ostwald at once prepared a short paper (7), submitted in July, 1884, in which he described his own kinetic and conductance results and discussed them on the basis of Arrhenius's work, to which he made full acknowledgement. At the time he was not, of course, able to explain the rate-conductance correlation in a very satisfactory way. It is easy today to understand this correlation. Hydrogen ions have much higher mobilities than the anions of the acids, so that the conductance of a solution of an acid provides an approximate measure of the hydrogen ion concentration in the solution; Ostwald was thus really observing a correlation between the rates of the acid-catalyzed reactions and the concentrations of hydrogen ions. The support that van't Hoff provided to the idea of electrolytic dissociation came not from his kinetic work but from his osmotic pressure investigations. The German botanist Wilhelm Pfeffer (1845-1920) had used semipermeable membranes to make numerous osmotic pressure measurements, and van't Hoff noted that for a number of solutions the osmotic pressure II is related to the concentration by an equation of the same form as that for an ideal gas: ΠV = nRT

(1)

Here R is the gas constant and T the absolute temperature; V is the volume and n the molar amount of solute present. Since n/V is the concentration c this equation can be written as Π = cRT

(2)

However, van't Hoff noticed that in the case of certain solutes the osmotic pressure was greater than given by this formula, and for them he introduced a factor i that came to be called the 'van't Hoff factor': Π = icRT

(3)

After reading Arrhenius's dissertation and discussing the matter with him van't Hoff realized that electrolytic dissociation could account for the result, since dissociation leads to an increase in the number of solute species present in the solution. It was in 1885-8 that van't Hoff published his classical papers (8-10) on osmotic pressure. Arrhenius was awarded a travelling fellowship by the University of Uppsala, the authorities having realized belatedly, as a result in particular of the interest shown by Ostwald, that the dissertation could not have been so bad after all. Arrhenius made a very profitable use of his fellowship. He spent some months in 1886 with Ostwald in Riga; later that year and early in 1887 he worked in Würzburg with the German physicist Friedrich Kohlrausch (1840-1910). Later in 1887 he worked with the Austrian physicist Ludwig Boltzmann (1844-1906) at the University of Graz. Early in 1888 he visited van't Hoff in Amsterdam and then went to work again with Ostwald, who by that time had moved to the University of Leipzig. By 1887 Arrhenius had been able, as a result of some of



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this collaboration, to formulate in an explicit form his famous theory of electrolytic dissociation (11). Shortly afterwards Ostwald published a paper (12) in which, by applying equilibrium theory to the dissociation process, he obtained the relationship between conductivity and concentration that we now refer to as the 'Ostwald dilution law'. From then on progress in both electrochemistry and kinetics proceeded more smoothly and rapidly. The theory of electrolytic dissociation did not, however, at once gain universal assent, and even as late as the 1930s there were a few who did not accept it. Particularly vociferous opponents of the idea were the organic chemist Henry E. Armstrong (1848-1937) and the electrochemist and fruit farmer S.F.U. Pickering (1858-1920), both of them eccentric and controversial individuals. In the 1930s Louis Kahlenberg was giving, at the University of Wisconsin, a course on electrochemistry which took no account of the existence of ions in solution. It is of interest also to note that although Ostwald had played such an important role in the development of the theory of electrolytic dissociation, he believed for most of his career that atoms, molecules and ions were no more than a convenient fiction; he was not convinced of their real existence until 1909, after J.J. Thomson and J. Perrin had carried out their crucial experiments. Strong Electrolytes Arrhenius himself was recalcitrant on one point; he throughout insisted that his interpretation of conductivity in terms of a dissociation equilibrium applies to strong electrolytes as well as to weak ones; for an account of this controversy see ref. 13. Suggestions that strong electrolytes are completely dissociated and that ionic interactions must be invoked to explain the conductivities of their solutions were made by G.N. Lewis (14-16), Niels Bjerrum (17, 18), W. Sutherland (14) and S.R. Milner (20-24). Bjerrum provided spectroscopic evidence for this point of view, and Sutherland and Milner did important work on the theory of ionic interactions. Finally, in 1923, Debye and Hückel (25, 26) developed their comprehensive treatment of strong electrolytes. Arrhenius, however, rejected these ideas and for the most part refused to discuss them. At a meeting of the Faraday Society held in January, 1919, Arrhenius commented that Bjerrum's idea "seems not to agree very well with experiment" (27), and he maintained this position until his death in 1927. Acid-Base Catalysis It was work on catalysis by acids and bases, carried out from about 1890 until well into the present century, that particularly brought electrochemistry and kinetics together and led to great advances in both fields. The interpretation of the kinetics of these catalyzed reactions presented some difficulty. In 1889 Arrhenius suggested (28) that in acid catalysis a free hydrogen ion in solution adds on to a molecule of substrate, the intermediate so formed then undergoing further reaction. This theory, known as the 'hydrion theory', is along the right lines, but it did not lead at once to a quantitative interpretation of the kinetic behaviour. Arrhenius


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realized that certain 'activity' effects had to be taken into account but was not clear as to how this should be done. Later he showed (29) that the kinetics of acid-catalysed reactions could be better understood if one arbitrarily used osmotic pressures instead of concentrations, although the reason for this was not clear. Today we can understand it in terms of activity effects in kinetics. Salt Effects. The solution to the problem came largely from investigations of salt effects in kinetics. The addition of 'foreign salts', which do not have an ion in common with any ion directly involved in the reaction, is often found to have an important kinetic effect. At first the explanations were given in terms of positive or negative catalysis, but this idea proved to be unhelpful. It is best instead to regard salt effects as environmental effects and to explain them in terms of the activity coefficients of the reacting species. As understanding of the thermodynamics of solutions developed, it became clear that equilibrium constants must be expressed as ratios of activities rather than of concentrations. Thus for a general reaction

the equilibrium constant is

where the a's are the thermodynamic activities and the y's the activity coefficients, which multiply concentrations to give activities. The treatment of equilibrium constants in this way was straightfoward, but with rate equations it was not at first clear how to proceed. According to the first proposal made, which came to be called the 'activity-rate theory', the rate of a second-order reaction between A and B should be expressed as

where ko is the rate constant. According to this theory the rate constant simply multiplies the product of the activities of the reactants rather than the product of their concentrations. This idea seems to have originated (30) with the Scottish organic chemist Arthur Lapworth (1872-1941), and it gained support (31-35) from the American electrochemist H.S. Harned (1885-1969) and the British kineticist W.C. McC. Lewis (1885-1956). It soon became apparent, however, that this theory was not consistent with the experimental results. At low concentrations foreign ions always diminish the activity coefficients of ions, a result that is explained by the Debye-Hückel theory (25, 26) in terms of the effect of the ionic atmosphere. The activity-rate theory therefore always predicts a decrease in rate when a foreign


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salt is added at low concentrations. However, for some reactions a marked increase in rate is observed. A completely satisfactory solution to the problem did not come until after transition-state theory (36-38) had been formulated in 1935. In terms of that theory, the rate should be expressed not as eq. (5), but as

where y≠ is the activity coefficient of the activated complexes (transition states) formed when A and B come together. However, even before the transition-state theory had been formulated, important steps in the right direction had been taken, mainly through the efforts of three Danish physical chemists, J.N. Bronsted (1870-1947), N.J. Bjerrum (1879-1958) and J.A. Christiansen (18881969). Again there was a valuable contribution of electrochemistry leading to an important fundamental relationship in chemical kinetics. The work of the Danish chemists was based on Lewis and Randall's introduction of the concept of the ionic strength and on the Debye-Hückel theory. Two years before Debye and Hückel had formulated their theory Lewis and Randall (39) had introduced the idea of the ionic strength of a solution, which they defined as

where cj is the concentration of an ion j and zj is its charge number (positive for positive ions, negative for negative ions). The summation in eq. (7) is taken over all of the ions present in the solution. From various lines of evidence Lewis had realized that the effect of dissolved salts on certain properties, such as solubility, is mainly determined by the ionic strength of the solution. This conclusion was later supported when the Debye-Hückel theory was developed. Shortly after that theory was published Bronsted and the American physical chemist V.K. La Mer (1895-1966) applied it to obtain a relationship (40) between the activity coefficient yi of an ion and the ionic strength I. The relationship that they obtained was

where zi is the charge number of the ion i, and the positive quantity B can be expressed in terms of certain properties of the solution such as the dielectic constant. For water at 25°C the constant B has the value of 0.51mol-1/2dm3/2. Equation (8) is obeyed satisfactorily in the limit of very low concentrations and is referred to as the 'Debye-Hdckel limiting law'. Considerable deviations occur at higher concentrations, and modifications to the equation lead to better agreement. Two years before this equation was obtained, Bronsted had made the suggestion (41) that in considering a reaction between two


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species A and B one should focus attention on a critical complex X that is formed during the course of the reaction:

This complex X is the most unstable of the various collision complexes formed and corresponds to what later became called an activated complex, or transition state. On the basis of arguments the validity of which is considered later, Bronsted arrived at the equation

This differs from the activity-rate equation (5) in having the activity coefficient yX, relating to the intermediate X, in the denominator. Bronsted referred to the ratio yAyB/yX as the 'kinetic activity factor'. Later, when equation (8) had been obtained, Bronsted introduced it into eq. (9), as follows (42). From eq. (9)

and the use of eq. (8) for y A , yB and yX leads to

where k ≡ V / [ A ] [ B ] .

Since zX = zA+zB this reduces to

Bronsted and others investigated the effect of ionic strength on the rates of reactions of various ionic types, and found that at sufficiently low ionic strengths plots of log10 k are quite linear, the plots having slopes that are consistent with eq. (12). For reactions between ions of the same sign (zAzB is positive), eq. (12) predicts that increasing the ionic strength increases the rate, and this is found to be true experimentally. If zAzB is negative, however, the rate decreases if the ionic strength is increased, in agreement with eq. (12). The activity-rate equation (5), however, fails for reactions between ions of the same sign, since it leads not to eq. (11) but to an equation with the term z2X missing:

2 2 Since -B (z2A+z2B) is bound to be negative, a plot of log10 k against √I would always be negative, in disagreement with the results for ions of the same sign. The experimental evidence thus favours Bronsted's equations (9) and (12) rather than the activity-rate equation (5). The justification for equations (9) and (12), however, remained a



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difficulty for a number of years. Bronsted's original derivation (41) was by no means explicit or convincing. He suggested that the rate should depend in some way on the difference between the chemical potential of X and that of the reactants A and B, and this difference is related to the ratio yAyB/yX; however, it is by no means clear that this ratio should simply multiply the rate expression as in eq. (9). A more satisfactory derivation of eq. (12), although a somewhat complicated one, was suggested by Christiansen (43). His derivation dealt with the frequency of collisions between ions A and B and took account of the electrostatic interactions. By making use of the Debye-Hückel expression for the electric potential as a function of the distance from an ion and making some approximations, Christiansen was able to arrive at eq. (12). He did not obtain eq. (9), since no specific intermediate complex X was postulated in his derivation. Bjerrum's derivation of eq. (9) was based on the idea of an intermediate S and seemed simple and straightforward at first, but on second thoughts it appeared to have a fatal flaw. Bjerrum postulated (44) that an equilibrium is first established between the reactants A and B and a purely physical collision complex S (Stosskomplex):

Bjerrum's complex S is to be distinguished from Bronsted's critical complex X, which is the most unstable of the various complexes found during the course of a reaction and is what we now call an activated complex or transition state. Bjerrum expressed the equilibrium constant for the formation of the complex S as

The concentration of S is thus

He then postulated that the rate is proportional to the concentration of S, so that

which is equivalent to Bronsted's equation (9). There is, however, a difficulty with this derivation. The fact that the equilibrium equation (4) involves activity coefficients requires that the rate constants k1 and k-1 for reaction in forward and reverse directions also involve activity coefficients, since K = k1/k-1. But if the rate constant k-1 for the reverse reaction involves activity coefficients, how can one say that v = k'[s]? It is unreasonable to suppose that the intermediate S follows a



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different type of kinetic equation according to whether it is reverting to reactants or forming products. Bronsted (45) raised this objection to the Bjerrum formulation in 1925, and in an extensive review of salt effects (46) published in 1928 he made only a passing reference to it. The difficulty was further discussed and elaborated by La Mer (47) in a review which appeared in 1932. The answer to the difficulty with Bjerrum's derivation came with the advent of transition-state theory and was first pointed out by R.P. Bell (48). Transition-state theory (36-38) lays emphasis on the activated complexes, which are species that correspond to the col or saddle-point in a potential-energy surface for a reaction. Unlike an ordinary reaction intermediate, such as the Stosskomplex S postulated by Bjerrum, an activated complex has reached a point of no return; it is bound to pass into products and cannot revert to reactants. The process is thus represented as

with a single and not double arrow leading to X . The species X is not in the ordinary sense in equilibrium with A and B; instead it is formed in a state of equilibrium, and is said to be in quasiequilibrium. The concentration of X≠ is therefore correctly given by an equation analogous to eq. (15):

Because X is bound to form products, the rate of their formation is given by transition-state theory as the concentration of X≠ multiplied by a frequency. Thus, if Bjerrum's derivation is modified by replacing the intermediate S by the activated complex X≠, the logical dilemma disappears. Equation (6) is the correct transition-state formula to use, and the ionic-strength effects have been important in leading to this fundamental equation. General Acid-Base Catalysis Another important contribution of electrochemistry to kinetics has been in connection with what is referred to as general acid-base catalysis. It was originally supposed that catalysis by acids and bases is catalysis by hydrogen and hydroxide ions, but evidence was later obtained for catalysis by other acidic species such as undissociated acids and by basic species such as anions. According to the ideas of Bronsted (49) and Lowry (50), an acid is any species that can donate a proton and a base is one that can accept one. Thus CH3COOH and NH+4 are acids, while CH3COO" and NH3 are bases. Conclusive evidence for catalysis by species other than hydrogen or hydroxide ions was first obtained by J.W. Dawson (51-52) of the University of Leeds. His most important work was on the conversion of the keto form of acetone into its enol form, a process that can be studied by measuring the rate of iodination of acetone, the iodine adding rapidly to the enol form. Dawson first showed that undissociated acids bring about acid catalysis and spoke of the 'dual



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theory' of acid catalysis, by which he meant acid catalysis by both hydrogen ions and by undissociated acids. Evidence for general base catalysis was later obtained by Bronsted and Pedersen (53) for the decomposition of nitramide. Somewhat later Bronsted and Guggenheim (54), simultaneously with Lowry and Smith (55), showed that the mutarotation of glucose was subject to general catalysis both by acids and by bases; in other words, there was catalysis by hydrogen and hydroxide ions, by undissociated acids, by the anions of acids, and by species such as NH+4. Both Bronsted and Lowry realized the significance of these facts when they suggested their extended definition of acids and bases. Dawson's term 'dual theory' of catalysis had to be changed to 'multiple theory'. Concluding Remarks At the outset it was said that both kinetics and electrochemistry, unlike thermodynamics, had a healthy and vigorous childhood. At the same time it should be recognized that at first investigators in physical chemistry tended to be treated as pariahs by the majority of chemists. Van't Hoff suffered a period of unemployment at the beginning of his career, and Ostwald at first had to work as a schoolteacher with no facilities for research. Van't Hoff's theory of the tetrahedral carbon atom was derided by the organic chemist Hermann Kolbe (1818-1884). Ostwald's important early work in physical chemistry was not at all appreciated by many chemists, who complained that Ostwald was not a true chemist since he had discovered no new compounds; to this Ostwald cheerfully retorted that the number of compounds that he had discovered was minus one, since he had shown by physical methods that an alleged new compound was identical with a substance that was already well known. Such hostility to physical chemistry carried well into the present century. In the 1920s W.H. Perkin, Jr., the professor of organic chemistry at Oxford, enjoyed commenting that physical chemistry was all very well, but of course it does not apply to organic compounds, which constitute the vast majority of all chemical compounds! This attitude of Perkin created some discomfort for N.V. Sidgwick, a member of his department. Fortunately these attitudes survive no longer. Physical chemistry is regarded as respectable, and even sometimes useful, by the vast majority of chemists. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9.

Faraday, M. Phil. Trans. Roy. Soc. 1834, 124, 77-122. Wilhemy, L. Pogg. Ann. 1850, 81, 413-433,499-526. Wenzel, C.F. Lehre von der Verwandschaft der Körper; Dresden, 1777. Thenard, J. Ann. Chim. Phys. 1818, 9, 314-317. Root-Bernstein, R.S. "The Ionists: Founding Physical Chemistry, 1872-1890", Ph.D. Thesis, Princeton University, 1980. Laidler, K.J. "Chemical Kinetics and the Origins of Physical Chemistry", Arch. Hist. Exact Sci. 1985, 32., 43-75. Ostwald, W. J. Prakt. Chem. 1884, [2], 30, 93-95. van't Hoff, J.H. Arch. Neerlandaises 1885, 20, 239-302. van't Hoff, J.H. Z. Physick. Chem. 1887, 1, 481-508. A



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10. 11. 12. 13. 14. 15. 16. 17.

18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53.


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translation of the latter paper, by J. Walker, appears in The Foundations of the Theory of Dilute Solutions; Alembic Club, London, 1929; no. 19, pp. 5-42. van't Hoff, J.H. Phil. Mag. 1888, 26, 81-105. Arrhenius, S. Z. Physik. Chem. 1887, 1, 631-648. Ostwald, W. Z. Physik. Chem. 1888, 2, 36-37. Wolfenden, J.H. Ambix, 1972, 19, 175-196. Lewis, G.N. Z. Physik. Chem., 1908, 61, 129-165. Lewis, G.N. Z. Physik. Chem., 1910, 70, 212-219. Lewis, G.N. J. Am. Chem. Soc., 1912, 34, 1631-1644. Bjerrum, N. Proc. Seventh Int. Congress on Applied Chemistry, 1909, 55, (1909); a translation of this paper is included in Niels Bjerrum, Selected Papers; Copenhagen, 1949, p. 56. Bjerrum, N. Seventh Int. Congr. Appl. Chem., 1909, 9, 58-60. Sutherland; Phil. Mag., 1902, 3, 161-177; 1906, 12, 1-20; 1907, 14, 1-35. Milner, S.R. Phil. Mag., 1912, 23, 551-578. Milner, S.R. Phil. Mag., 1913, 25, 742-751. Milner, S.R. Phil. Mag., 1918, 35, 214-220. Milner, S.R. Phil. Mag., 1918, 35, 352-364. Milner, S.R. Trans. Faraday Soc., 1919, 15, 148-151. Debye, P.J.W.; Hückel, E. Physikal. Z., 1923, 24, 185-206. Debye, P.J.W.; Hückel, E. Physikal. Z. , 1923, 24, 305-325. Arrhenius, S.A. Trans. Faraday Soc., 15, 10-17. Arrhenius, S.A. Z. Physik. Chem., 1889, 4, 226-248. Arrhenius, S.A. Z. Physik. Chem., 1899, 28, 319-335. Lapworth, A. J. Chem. Soc., 1908, 93, 2187-2203. Jones, W.J.; Lapworth, A.; Lingford, H.M. J. Chem. Soc., 1913, 103, 252-263. Harned, H.S. J. Am. Chem. Soc., 1918, 40, 1461-1481. Harned, H.S.; Pfenstiel, R. J. Am. Chem. S o c . 1922, 44, 21932205. Jones, C.M.; Lewis, W.C.McC. J. Chem. Soc. 1920, 117, 1120-1133. Moran, T.; Lewis, W.C.McC. J. Chem. S o c . 1922, 121, 1613-1624. Eyring, H. J. Chem. Phys. 1935, 3, 107-115. Evans, M.G. ; Polanyi, M. Trans. Faraday Soc., 1935, 31, 875-895. Evans, M.G.; Polanyi, M. Trans. Faraday Soc., 1937, 33, 448-452. Lewis, G.N.; Randall, M. J. Am. Chem. Soc., 1921, 43, 1112-1154. Brosted, J.N.; La Mer, V.K. J. Am. Chem. S o c . 1924, 46, 555573. Bronsted, J.N. Z. Physik. Chem. 1922, 102, 169-207. Bronsted, J.N. Z. Physik. Chem. 1925, 115, 337-364. Christiansen, J.A. Z. Physik. Chem. 1924, 113, 35-52. Bjerrum, N. Z. Physik. Chem. 1924, 108, 82-100. Bronsted, J.N. Z. Physik. Chem. 1925, 115, 337-364. Bronsted, J.N. Chem. Revs., 1928, 10, 179-212. La Mer, V.K. Chem. Revs., 1932, 10, 179-212. Bell, R.P. Acid-Base Catalysis; Clarendon Press, Oxford, 1941; pp. 28-31. Bronsted, J.N. R e c . trav. chim., 1923, 42, 718-728. Lowry, T.M. J. Soc. Chem. Ind., 1923, 42, 43-47. Dawson, J.W.; Powis, F. J. Chem. Soc. 1913, 103, 2135-2146. Dawson, J.W. ; Carter, J.S. J. Chem. Soc., 1926, 2282-2296. Bronsted, J.N.; Pederson, K.J. Z. Physik. Chem., 1924, 108, 185-235.


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5 4 . B r o n s t e d , J . N . ; Guggenheim, E.A. J . Am. Chem. S o c . 1 9 2 7 , 4 9 , 2554-2584. 5 5 . Lowry, T . M . ; S m i t h , G . F . J . Chem. S o c . 1 9 2 7 , 1 3 0 , 2 5 3 9 - 2 5 5 4 .


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