E. W. Lund University of Oslo
Oslo, Norway
"Activated Complex"-A
A tribute to Leopold Pfaundler
W h e n reading hundred-year-old papers one is surprised to learn what clear ideas some people had about general aspects of molecular phenomena in spite of a tot,al lack of the detailed information we possess today. 4 man who gave important contributions to the development of physical chemistry, was the Austrian professor of physics, Leopold Pfaundler,' whose papers to a large extent seem to have remained unknown. In the spring of 1867 he wrote an article which treats a chemical reaction in terms of the kinetic theory of heat. He is able to explain the existence of an equilibrium and the observed influence of mass, both, however, only in a qualitative way. As an introduction to Pfaundler's work a short account of the s t a t u of the kinetic theory will be given. By the middle of the 19th century the fundamental ideas of thermodynamics had been formulated and applied to macroscopic physical phenomena, and in 1850 Clausius had expressed the idea that heat is a kind of motion (1). During the following years several people extended t,hese ideas further and tried to explain physical as well as chemical phenomena in terms of molecular movement. I n 1856 IG-onig (92) used the model of a gas consisting of completely elastic spheres in translatory motion with a common constant speed. Due to collisions with the wall of the container the gas exerts a pressure; Kronig derived the expression p = nmvZ/GV, where n is the number of gaseous atoms, each with a mass, m, and a velocity, v , and V is the volume of the container. Kronig added the assumption that the product mu2 or the kinetic energy is equal to the absolute temperature, and found thus his formula to be in correspondence with the gas laws. The publication of this article by Kronig occasioned Clausius in 1857 t,o present ideas about the nature of the motion which he writes he even had before 1850 (3). His 1557 article, which has the title "On the kind of
'
Centenarian?
Leopold Pfaundler was born at Innsbruck on February 14, 1839. He was a student in Munich and in Paris, studying with Wurtz and Regnault in the latter city. He became Professor of Physics at Innsbruok in 1867 and moved to Graa in 1891. BP sides his contributions to kinetic theory he worked extensively in several fields of ohernistry, including organic, and in physics. I t is said that he was deeply interested in the teaching of chemistry and physics. He died at Gree on May 6, 1920.
motion which we call heat," gives that account of molecular motion which is common in today's textbooks. Kronig had limited the treatment to transl* tory motion of molecules with a common constant velocity. Clausius adds other kinds of motion. When two molecules collide it is reasonable to assume the onset of a rotation if by chance the collision is not a central one. Also, it is possible that a molecule which consists of several a t o m is not a rigid body, but that the atoms within certain limits may oscillate with respect to each other. He also remarks that each mass atom may be associated with a quantity of a more subtle substance and that this, without leaving the atom, may be moving in its neighborhood. (A vision of the electron cloud?) The exchange of kinetic energy between the different kinds of motion implies the idea about a distribution of velocities, not a common one as Kronig postulated. Clausius shows mathematically that the kinetic energy of translation is too small to explain the specific heat of gases, a fact which forces him to assume other kinds of motion. He remarks that the additional energy terms are of special importance for gases consisting of complex molecules. Clausius further gives argument for a constant exchange of energy between translation and the kinds of inner motion. This leads to the idea that the amounts of kinetic energy associated with translation on the one side and rotation and vibration on the other, are proportional to one another. Clausius agrees with Kronig that the absolute temperature is proportional to the kinetic energy of translation. Combining these ideas Clausius finds an explanation of the constancy of the specific heat of gases. Clausius also presents the necessary conditions on the molecular level in order that the gas laws shall be obeyed, (1) the space occupied by the molecules must be of negligible dimensions compared with the gas volume, (2) the time of encounter must be negligible compared with the time between two collisions, and (3) the influence of intermolecular forces must be negligible. The last condition must apply for all molecules when they are a t their mean distance and for each molecule during an encounter in such a way that the path on which intermolecular forces are acting is negligible compared to the path on which they are not.
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Clausius extends his ideas on the gaseous state to solids and liquids. In the solid state there may be rather complicated types of oscillatory motion. Different parts of the molecule may vibrate with respect to each other and the whole molecule as snch may be in a state of vibration with respect to an equilibrium position or of libration around the center of gravity. In the liquid state the molecules have no equilibrium position. There is a motion tending to separate molecules from each other, but this cannot overcome the mutual attraction. One molecule is, however, not attached to definite neighbors. It leaves these due to attractions from other molecules. During the complicated kind of motion the molecules remain within a certain volume. On the basis of these ideas, which here are summarized briefly, Clausius gives a kinetic theory of evaporation. In liquids the individual molecules may have velocities which deviate from the mean within wide limits. Due to the complexity of movement there may be a favorable coincidence which imparts to a molecule in the surface a translatory energy of such a magnitude that it escapes from its neighbors. A previously evacuated space above the liquid will be more and more filled by such molecules which behave as a gas, colliding with the walls. At that wall given by the liquid surface molecules from the gas will be captured. There will be a state of equilibrium which is not a state of rest involving no evaporation, but a state of simultaneous evaporation and condensation of eqnal magnitude. Clausius extends his argument further and discusses the influence of a foreign gas, as well as internal and external work during evaporation. At the end of this article he takes up the problem of the simple volume ratios during gas reactions. Already Kronig had pointed to a consequence of the kinetio theory, namely that the pressure is proportional to the number of molecules in a certain volume, the temperature being constant. Clausius finds it reasonable t o apply the same idea to the elementary gases, that is, to assume that equal volumes contain the same number of atoms, when pressure and temperature are the same. This idea leads, however, to discrepancies with observed volume ratios. I n order to explain these Clausius arrives at a proposition which he very carefully presents as a hypothesis. He assumes that the force which causes chemical compounds to form and which probably amounts to a sort of polarity of atoms, is active already in elements and that also in this case several atoms are combined in a molecule. The simplest and therefore most probable case of snch a combination would be that two atoms form a molecule. This gives an explanation of the volume ratios. It is surprising to learn that this idea was presented as a bold hypothesis by one of the most outstanding scientists so long after Avogadro's contribution. The most important event within the field of kinetic theory during the following years was the publication by Maxwell in 1859-60 (4) of L'Illustrations of the Dynamical Theory of Gases," in which the famous law of distribution of velocities and other consequences of the kinetic theory were presented. The first who applied the basic ideas of the kinetic theory in chemistry seems to have been Leopold 126 / Journal of Chemical Education
Pfaundler. Ten years after Clausius had published his kinetic theory of evaporation, Pfaundler extended the ideas to chemical reactions. In a paper called "Contribution to Chemical Statics" (5) he first gives a theory of dissociation. Several chemists had explained the observed departure from the laws of gas densities by assuming a partial dissociation. Pfaundler rather ironically remarks that most chemists find the partial dissociation concept to be a satisfactory explanation of the observed irregularities. The partial dissociation is, however, still not explained. Pfaundler puts forward two possible explanations. Either all molecules of a gas have undergone the same change, or the change is different in different molecules, some being completely dissociated, others unchanged. He finds that the second possibility can explain the observed facts. A difficulty is, however, why the same cause (temperature) may give different action. Pfaundler finds an explanation in the previously mentioned paper by Clausius on evaporation and argues that certain kinds of dissociation phenomena could immediately be explained in terms of Clausius' theory. He gives a resume of Clausius' ideas and points to the fact that it is the partial pressure of thevapor which restricts further evaporation. Those who are satisfied with such an explanation may be also satisfied with the explanation of dissociation, namely that it is the partial pressure of the dissociation products which hinders further dissociation. Pfaundler wants, however, to go deeper into the matter and to find out, as Clausius did, the nature of partial pressure. He presents a case which is explainable in terms of Clausius' theory, namely the thermal decomposition of calcium carbonate. He arrives at the conclusion that at a constant temperature there is an equilibrium between ejected and absorbed molecules of carbon dioxide. By lowering the temperature, one finds that more molecules of carbon dioxide are absorbed. When carbon dioxide molecules are pushed away by an air current, relatively more will be ejected. With respect to a gas dissociation, Pfaundler assumes that a t a given temperature equal amounts of molecules decompose and unite by collision. This explanation requires that at a given instant not all molecules are in the same state of motion. Such a dissimilarity is very probable according to the mechanical theory of heat. Pfaundler then gives the following detailed explanation of the dissociation of a compound AB. As long as dissociation does not take place, all molecules have the composition AB. They have translatory and internal motion. The two kinds of motion are not of eqnal magnitude for all molecules. If they were equal at a certain instant, they would not remain so because of collisions. At a constant temperature the average kinetic energy of internal motion has a certain value which is proportional to the kinetic energy of translation. I n the individual molecules it may be larger or smaller. With increasing temperature the kinetio energy of both kinds of motion is increasing. In the molecules which at the moment have a large internal kinetic energy, the increase may be so large that it results in a complete separation in the components A and B. This separation cannot occur at the same time in all
molecules, but only in those which have a larger internal motion. The separated parts are now free molecules A and B and they perform a translatory motion. I n the meantime another numher of molecules has acquired the maximum of internal motion necessary for dissociation, and thus the number of separated molecules is increasing. The fragments will, however, from time to time meet one another. Not all such encounters will result in a union-only those molecules will combine whose state of motion is such that the resulting aggregate does not have a larger internal motion than it had a t the moment of separation. At a constant temperature the production of free suhmolecules will continue until the numher of reuniting molecules is equal to the numher produced by dissociation, both per unit time. From now on there is a state of equilihrium between dissociation and combination, as long as the temperature is kent constant. With increasing temnerature the numher of dissociating molecules will increase and therefore also the numher of free molecules A and B. This will continue until a new state of equilibrium is established. If a hole is made in the container during the dissociation period both dissociated and undissociated molecules will escape. Because the velocities of molecules are inversely proportional to the square root of their masses, the dissociated parts will diffuse at a higher rate than the undissociated. It is therefore possible to obtain a complete dissociation of a certain mass of suhstance without increase in temperature. The same result is obtainable if one by chemical means can absorb the components or even only one of them (Pfaundler's italics). After giving this theory of dissociation Pfaundler presents in another part of his paper a theory of the eanilibrium state of reci~rocalreactions and an explanation of the mass action. He points to the ohservations that a t a given temperature reactions
- .
A~
AB+C=A+BC
and AB
+ CD = AD + BC
may be caused to proceed in either direction, by increasing or diminishing the amounts of substance on the two sides of the equation. The a5nity of substances is certainly supported by their mass. Quantitative experimental evidence of these effects had been given by Berthelot and PBan de Saint-Gilles in their investigation on formation and decomposition of esters (6). On the foundation laid by Clausius in his theory of state of aggregation and evaporation Pfaundler found it possible to present an explanation also of these phenomena. First he gives a simpler theory. I n a container there are equal numbers of molecules AB and C. With increasing temperature AB will dissociate. If B has an affinity to C, a favorable collision between B and C may result in the formation of a molecule BC. A more probable process is, however, the following. Already before the temperature hrts attained that value which is necessary to cause a dissociation of AB, this may he initiated by the action of the body C. Let us consider a molecule AB, which owing to the temperature has so much internal motion that it is close to dissociation. When this molecule collides with a molecule C,
the translatory motion of both molecules will be completely or partly transformed to internal motion. The question is now whether the affinity a t this magnitude of internal motion is sufficiently large to keep all three bodies in a union. If this is not the case, the components are again pushed away and a part of the internal motion is transformed into external. How the separation takes place depends evidently on how the internal motion was distributed among the parts. If the internal motion of AB was already rather large before the collision and if it increased even more because of the collision, then a dissociation of the intermediate ABC in A and BC would be more probable than in AB and C. Thus a certain part of all molecules AB which collide with C, will react according to the equation AB C = A BC. Besides molecules AB and C there are now those of A and BC. If even the most favorable coincidence of movements is unable to make the molecule BC dissociate, the reaction will proceed to completion. Above a certain temperature, however, the internal motion in some of the BC molecules may be so large that they will dissociate. If this is the case there will be a mixture of a certain composition which will remain constant a t a fixed temperature. Dissociation reactions will, of course, take place continuously, but they are compensated by an equal number of combinations. Within a certain interval the change of temperature will result in a change in the relative amounts of different molecules. To each temperature corresponds a definite mixture, the composition of which depends on how the different molecules are influenced by the increase in temperature. Pfaundler also discusses the influence on the mixture if more of the gas AB is added. The equilihrium is disturbed; the number of free molecules C is diminished and that of BC is increased. A new equilihrium position is possible with fewer C molecules. The reaction is favored still more when molecules A are removed. In a latter part of his article Pfaundler argues against a theory set forward by Williamson 16 years earlier (7). The latter had developed the idea that there is a continuous exchange of elements in a molecular aggregate. Pfaundler finds his own ideas about a distribution of motion on the individual molecules to give a better physical picture and to be more generally applicable. He discusses diierent types of reaction and shows how his ideas lead to a state of equilibrium and how this state may be changed by removal of reaction products or by change in temperature. Further, he gives a rather detailed treatment of a gas reaction of the type AB CD = AC BD. He discusses diierent limiting cases with respect to amounts of energy associated with the molecules AB and CD at the moment of collision. Large translational and internal motion may result in a separation in four parts A, B, C, and D. Secondly, with small amounts of energy a combined molecule $g may result. Thirdly, the molecules may collide as elastic spheres with no tendency to dissociate. An finally, the molecules may collide under such circumstances that the internal conditions of motion in the instantaneously combined molecule may result in a dissociation along another direction. The system i g may move as such for a while, with some of the original translational motion
+
+
+
+
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transformed into internal. Depending on the values of the different affinities and on the previous state of internal motion of the components AB and CD, the increase in internal motion will result in a dissociation either in the direction filg or The latter direction will be favored if A was in the process of separating from B and C from D just before the collision. On the basis of these ideas Pfaundler found an explanation to the existence of reciprocal reactions. The result of a reaction will depend both on the relative affinities and on the state of motion of the reacting molecules. Pfaundler gives then two examples,
s.
CzH60H
+ H ~ O =I C2H50.S03H+ HzO
and Both reactions have the characteristics of a partial metathesis, and, by removing reaction products or increasing amounts of reactants, a desired result may be achieved. In his concluding remarks Pfaundler gives tribute to Clausius for having forever done away with the assumption of atoms being a t rest. He writes that the success of the mechanical theory of heat surely will invite chemists to apply the extremely fruitful hypotheses of the theory to unravel chemical phenomena so far unexplained.
128 / lournol of Chemical Educafion
This has beer1 a very brief account of Pfaundler's paper, which it is hoped will give the reader some insight into his clear and consequent arguments. Pfaundler was evidently unaware of Guldberg and Waage's paper three years earlier. They had then given the first mathematical formulation of the condition at equilibrium. Their arguments were, however, based on the more vague concept of chemical force. In their first papers they do not talk about motion or energy. They made, however, quantitative experiments and showed that their results, as well as those of others, were in accord with their mathematically formulated equilibrium condition. Pfaundler, on thc other hand, did not support his ideas by experiments and did not give a single mat,hematical formula (as Clausius did). Nevertheless, his ideas were of a realistic physical character and he should certainly be reckoned as a pioneer in describing a chemical reaction between molecules as a dynamical event. Literature Cited (1) CLAUSIUS, R., Ann. Phys. Chem., 79, 368, 500 (1850). (2) K R ~ N I G A,, , Ann. Phys. Chem., 99, 315 (1856). (3) CLAUSIUS,R., Ann. Phys. Chem., 100, 353 (1857). (4) MAXWELL, J. C., Phzl. mag., (41, 19, 19 (1860). L.,Ann. Phys. C h . , 131, 55 (1867). (5) PFAUNDLER, M., AND P ~ A DE N SAINT-GILLES, L., Ann. Chim. (6) BERTRELOT, Phys., 131, 65, 385 (1862); 66, 5 (1862): 68, 225 (1863). (7) WILLIAMSON, A,, Phil. mag., [3], 37, 350 (1850).
