Physical Chemistry

PHYSICAL CHEMISTRY, "the science that explains on the basis of principles and experiments the physical cause of what occurs through chemical operations in complex bodies." This definition, which was given to it by the first physical chemist M. V. Lomonosov in a course delivered by him in 1751-53, can be retained even at the present time (this course was extracted from the archives of the Academy of Sciences and published only 150 years later by Menshutkin). Various parts of modern physical chemistry were created over the course of centuries thanks to the work of numerous scientists: thus, Lavoisier and Laplace laid the foundation of thermochemistry, Berthollet of chemical statics, Davy, Faraday of electrochemistry, etc. Through the work of Kopp (Korr) and others, a large amount of material was collected establishing the dependence of various physical properties of chemical compounds on their composition and structure. Kirchhoff and Bunsen discovered (in 1857) spectral analysis. The law of conservation of energy, established through the work of R. Mayer, Joule, Helmholtz in the middle of the 19th century, indicated the equivalent relationship between various forms of energy - thermal, mechanical, electrical, chemical, etc. - and thereby contributed to the penetration of physical methods into the investigation of chemical questions. However, the particularly rapid development of physical chemistry as an independent science began in 1887, when van't Hoff and Ostwald founded the journal "Zeitschrift fur physikalische Chemie", which for a long time was the central organ for physical chemistry. Almost simultaneously W. Ostwald published his fundamental course "Lehrbuch der allgemeinen Chemie" (1st volume in 1885, 2nd in 1887), which for the first time gave a complete overview of this new science. Into the laboratory of W. Ostwald at the University of Leipzig, to which he moved in 1887, chemists from all over the world flocked; from it came such luminaries of physical chemistry as Nernst, Bredig, Jones, Le Blanc and many others (Nernst, Bredig, Jones, Le Blanc). Many Russian scientists also studied there, who later propagated physical chemistry in Russia. During this period, the direction of work in physical chemistry was determined by the triumvirate of W. Ostwald, van't Hoff and Arrhenius and was concentrated mainly on the development of questions related to the theory of solutions of van't Hoff and Arrhenius (see Osmotic pressure, Electrolytic dissociation, Solutions). These theories made it possible to establish the connection between the most diverse properties of solutions and thereby served to explain many processes both in technology and in biology. Another branch of physical chemistry, ♦23, which subsequently received strong development, was the doctrine of the rates of chemical reactions (see Chemical kinetics) and of catalysis (see), which gave a theoretical basis for a number of chemical productions. The profound influence on the further development of physical chemistry was exerted by the revolution in the views of physicists and chemists on the structure of matter, which occurred recently as a result of major discoveries of the late 19th and early 20th centuries (the discovery of cathode and X-rays, radioactivity, etc.). Atoms of elements ceased to be indivisible "bricks" of the universe, and penetration into their internal structure, construction of the theory of atomic structure made it possible to explain many of the most difficult questions of chemistry, for example valence, the periodic law (see Periodic system of elements) and others. Progress in the development of physics and chemistry gradually blurs the boundary between these sciences. In the past, in the words of J. J. Thomson, the division of properties into physical and chemical was based on unfamiliarity with the structure of atoms and molecules. Physics could offer no explanation why the properties of an atom of one element differ from those of another. And since chemistry was mainly concerned with the study of this difference between atoms, there was a real difference between these sciences. Meanwhile, in the last quarter of the 19th century, physicists penetrated into this area and achieved such a concept of the atom and molecule which explains how one kind of atom differs from another and how atoms combine with each other to form molecules. Thus the barrier separating chemistry and physics falls. To resolve many questions of physical chemistry it is necessary not only to develop the most subtle techniques of physical methods, but also to create new areas of physics, for example wave mechanics. The close and mutual connection between physics and chemistry has found its vivid expression, among other things, in the fact that along with physical chemistry, the term "chemical physics" has also recently gained recognition. Under this name appeared in 1932 the well-known course by Eucken. At the present time physical chemistry represents an extensive field of knowledge, breaking down into a number of departments, some of which have already grown into entire scientific disciplines. It is enough to name the most important of them: the doctrine of the states of bodies - gaseous, liquid and solid - chemical mechanics; the doctrine of solutions and alloys; the doctrine of the rates of chemical reactions (chemical kinetics) and of chemical equilibrium; electrochemistry, photochemistry, thermochemistry, colloid CHEMISTRY and others.

I. Kablukov. Without dwelling in detail on each of these branches, we will consider only the general foundations on which modern physical chemistry is built. The most important of these foundations is undoubtedly the application of the general laws of energetics, the principles of thermodynamics, to chemical processes. The application of thermodynamics determines not only the special field of thermochemistry (entirely based on it), but is also widely used in various fields of physical chemistry. Another no less important foundation is provided by the molecular-kinetic concepts of physical chemistry. These two approaches were initially contrasted with each other as opposite ways of interpreting physicochemical phenomena. However, the research of Boltzmann, which gave a molecular-kinetic interpretation of the principles of thermodynamics, showed the equivalence of both approaches, which do not exclude but mutually complement each other. A natural complement and development of molecular-atomicistic concepts was the doctrine of the atomic structure of electricity, which formed the basis of electrochemistry. If these two directions entirely determined the paths of development of classical physical chemistry, then at present a third, no less important foundation is added to them in the form of atomic physics. Itself still changing its contours and outlines almost every year, intra-atomic physics forces the breaking down and rebuilding of many concepts of classical physical chemistry that seemed immutable. Applications of the first principle of thermodynamics. Unlike pure chemistry, which deals with the transformation of substances, physical chemistry showed the impossibility of studying the transformations of substances in isolation from the energy transformations accompanying them. Therefore, only on the basis of the principles of thermodynamics was it possible to construct the laws of chemical processes. The first principle of thermodynamics, the law of conservation of energy, is expressed by the general equation U=A-Q, where U is the decrease in energy of the system, A is the work produced by it, and Q is the heat absorbed. Thus, the decrease in energy of the system equals the difference between the work produced by it and the heat absorbed by it (or the sum of the work produced and the heat released). The value of U is especially simply measured in the case of a chemical reaction if it is carried out in such a way that it produces no work. Then A = 0 and U = -Q: the decrease in energy of the chemical system equals the heat released by it in the absence of external work. This amount of heat is called the "heat effect" of the chemical reaction. Various calorimeters are used to measure the heat effect. Let us consider, for example, the reaction of displacement of hydrogen from an acid by a metal: Zn + H₂SO₄ = ZnSO₄ + H₂. If this reaction occurs at constant (e.g., atmospheric) pressure, the evolving hydrogen, overcoming the external pressure, produces work equal to the product of pressure and volume increase; part of the reaction energy is expended on this work. Conversely, if the entire reaction is carried out at constant volume, i.e., under conditions excluding the production of mechanical work, then all the disappeared chemical energy will be released as heat, giving a directly measurable heat effect. Obviously, the latter can serve as an exact measure of the change in energy of the system: the decrease in energy of the system in any chemical reaction equals the heat effect of the latter. Taking into account not only changes in chemical composition, but also the inextricably linked energy transformations, it is necessary to include the heat effect U in the equation of the chemical reaction. The reaction under consideration will then be expressed by the equation: Zn + H₂SO₄ = ZnSO₄ + H₂ + 34,782 cal. Chemical reactions can be accompanied by both the release of heat (positive heat effect) and its absorption (negative heat effect). The former are called exothermic, the latter endothermic. If the products of a chemical reaction can be converted back into the original substances, then according to the law of conservation of energy, the heat effects of the forward and reverse reactions must be equal in absolute value but opposite in sign; their algebraic sum must equal zero. It follows directly that the heat effect of a chemical transformation equals the difference in energy of the chemical system in its initial and final states, regardless of the path, through what intermediate reactions, this transformation occurs. Otherwise, by carrying out the forward reaction through one set of intermediate stages and the reverse through another, one could gain or lose energy at will as a result of such a cyclic process. This result, representing the basic law of thermochemistry, was established by Hess in 1840, i.e., before the general law of conservation of energy became known, of which it is a logical consequence. Hess formulated it as the law of constancy of heat sums: whatever the path of chemical transformations, the total sum of all heat effects remains constant. An example can be the formation of a solution of sal ammoniac as a result of the interaction of gaseous ammonia, gaseous hydrogen chloride, and liquid water. In one case, if HCl and NH₃ are allowed to react in the gaseous state and then the resulting NH₄Cl is dissolved in water, and in the other, if HCl and NH₃ are first dissolved separately in water and then combined in the dissolved state, the sum of the heat released at the different stages of both processes turns out to be the same. A more general formulation of the same position can be arrived at if one uses the concept of "heat of formation" of a chemical compound. The heat of formation is understood as the heat effect accompanying the formation of a given compound from its constituent elements. The heat of formation is the basic thermodynamic characteristic of any chemical compound. In the most general form, the basic law of thermochemistry can be expressed as follows: the heat effect of a chemical reaction equals the sum of the heats of formation of the reaction products minus the sum of the heats of formation of the initial substances. In the case of organic compounds, a convenient measure of their chemical energy is the heat of combustion (determined by burning a given substance in an oxygen atmosphere under increased pressure, in the so-called "calorimetric bomb"). According to what has been said, whatever the course of the reactions that organic substances undergo, their heat effect equals the difference in the heats of combustion of the initial substances. This is used, as is known, to determine the energy reserves of food substances. Whatever the paths of the transformation and utilization of nutrients in the organism, all the energy produced by it must exactly equal the caloric reserves supplied by food. The correctness of this proposition, which represents an application of the law of conservation of energy to chemical transformations in a living organism, was experimentally proven by Rubner and Atwater (see Law of conservation of energy and matter, Metabolism). Application of the second and third principles of thermodynamics. The heat effect expresses in thermal units the magnitude of the total change in energy as a result of a chemical reaction. It says nothing about changes in free energy, i.e., about the possibility of using a given reaction to produce work. Meanwhile, the latter quantity has incomparably greater significance for understanding the course of the reaction and for the thermodynamic interpretation of basic chemical concepts: chemical affinity and chemical equilibrium. In order to determine the direction of a reaction on the basis of thermal data, Berthelot put forward as a general principle the proposition that every chemical interaction leads to the formation of those products in which the greatest possible heat effect is obtained. The energy released during the interaction of two substances would then serve as a measure of their chemical affinity, as a measure of the force that causes them to combine with each other. Consideration of any reversible chemical reaction leading to equilibrium between the initial substances and the final products shows the inadequacy of this assumption. Let us have, for example, the reaction A + B ⇌ C + D. According to Berthelot's principle, only the forward, exothermic reaction should proceed. Meanwhile, the final products, taken in the pure state, give the reverse reaction, which proceeds spontaneously (thereby showing affinity between the reacting substances), despite the fact that it is accompanied not by the release but by the absorption of heat. In both cases, through the forward and reverse reactions, the same equilibrium between the reacting substances is achieved. The failure of this attempt is due to the fact that the first principle of thermodynamics (on which the concept of heat effect is based) generally does not allow prediction of the direction of the process. It does not provide, for example, whether heat, when two bodies are in contact, will pass from the hot body to the colder one or vice versa, as long as the total sum of heats remains unchanged. The key to understanding the direction of processes occurring in nature is given by the second principle. It establishes that in any isolated system, only those processes that are accompanied by a decrease in free energy proceed spontaneously. This proposition is fully applicable to chemical processes as well.

Interaction between substances capable of reaction occurs only if it leads to a decrease in free energy (and not total energy, as Berthelot thought). The decrease in free energy in turn equals the maximum work that a given process can produce. The greater this work, the stronger the tendency of reacting substances toward chemical interaction. As van't Hoff pointed out, this uniquely determines the magnitude of chemical affinity. The affinity of reacting substances equals the maximum work that, under given conditions, the reaction between them can produce. Affinity becomes equal to zero and all chemical changes cease if the latter cannot produce work. From this follows the thermodynamic condition of chemical equilibrium: in a state of equilibrium, the free energy of a chemical system equals zero. The further from equilibrium, the greater its value. Knowing the free energy of a system in two of its states, one can predict the direction of chemical reaction. In the case of electrical phenomena, the direction of the process is uniquely determined by the electric potential: when two charged bodies come into contact, electricity always passes to the conductor having a lower potential. A similar role is played by the thermodynamic potential of a chemical system—the magnitude of its free energy or chemical affinity. Unfortunately, measuring free energy presents incomparably greater difficulties than calorimetric determination of the thermal effect. The task of its measurement has been successfully resolved only for one extensive group of chemical processes—for reversible oxidation-reduction reactions. The chemical energy of these reactions can be reversibly converted into electrical energy, and consequently the oxidation-reduction potential they give on an indifferent electrode (see Potential) represents a quantitative measure of their free energy and accordingly uniquely determines the direction in which oxidation-reduction reactions proceed. In all other cases, the free energy of chemical processes can be determined only by calculations, for example, from the equilibrium constant of the reaction, if the latter is known. The results obtained by applying the second principle of thermodynamics to the energetics of chemical reactions clearly show the insufficiency of evaluating the latter on the basis of the thermal effect alone. The same must be admitted with regard to the generally accepted evaluation of the energy reserves of food substances by their "caloric value," i.e., by the heat released during their combustion. The maximum work that a chemical reaction can produce equals the decrease in its free energy, whereas the thermal effect measures the decrease in total energy. The use of the latter magnitude would be justified only if the organism worked on the principle of a heat engine, i.e., first burned organic substances and then used the heat released for its working mechanisms. It is well known that the organism works on a completely different principle. It not only lacks devices for creating the large temperature differences necessary for the operation of a "heat engine," but, on the contrary, shows (in warm-blooded animals) a tendency to produce work under strictly isothermal conditions, at constant body temperature. Thus it would seem to completely devalue all the enormous work done up to the present time on caloric research of food, which forms the basis of the usual method of compiling food rations. Fortunately, this natural fear is not justified. The third principle of thermodynamics introduced by Nernst (on the formulation of which it is not possible to dwell here) opened the possibility of calculating the free energy of a chemical compound on the basis of thermochemical data. These calculations showed that precisely for the biologically most important oxidation reactions, the free energy differs very little from the total energy (i.e., from the thermal effect). All chemical reactions proceeding at low temperatures and going practically to completion in one direction are characterized by the fact that their free and total energy are quantities of the same order. Biological oxidation processes are typical representatives of such reactions, most efficient in terms of the possibility of their work utilization. Of no less importance for physical chemistry than the principles of thermodynamics is the molecular-kinetic theory, which is based on the proposition that bodies are built of molecules that are in a state of continuous disordered motion and possess perfect elasticity. Disordered molecular motion depends on the temperature of the body and increases with it; it is therefore defined as the thermal motion of molecules (see Kinetic theory). The calculation of the kinetic energy of a gas establishes a simple dependence between it and temperature: absolute temperature is proportional to the average kinetic energy of the molecules. For compressed gases, significant deviations from the simple Clapeyron equation are observed. However, the kinetic theory successfully overcomes the difficulties arising here by abandoning the simplifying assumptions made for ideal gases. In a compressed gas, one can no longer neglect the volume occupied by its molecules and reducing the space remaining free for their movement. At the same time, one must also take into account the intermolecular forces of attraction, which rapidly increase as the molecules approach. Taking these corrections into account leads to the van der Waals equation (see van der Waals' law). The van der Waals equation turns out to be suitable not only for compressed gases but also for liquids resulting from their condensation. Finally, the phenomena of the transition of a gas into a liquid and back, in particular the doctrine of critical states, find their quantitative expression in the van der Waals equation. If we go from systems with one component (pure liquids and gases) to two-component systems—solutions—we will see here similar relationships. van't Hoff's theory, which is the basis of modern solution theory, proceeds from the analogy existing between dilute solutions and ideal gases. It directly transfers the kinetic theory of gases to solutions and interprets osmotic pressure similarly to gas pressure as the result of the impacts of molecules of the dissolved substance against the wall of a semipermeable membrane (see Solutions). A further example of the application of kinetic concepts to a completely different area of physical chemistry can be chemical kinetics and chemical statics (the doctrine of chemical equilibrium). The beginning of the scientific treatment of the kinetics and statics of chemical reactions was laid by the research of Guldberg and Waage, who in 1867 established the law of mass action (see). The starting point is the idea that in the disordered motion of reacting molecules, a certain percentage of their collisions leads to chemical interaction. Therefore, the reaction rate is proportional to the number of molecular collisions. Depending on the number of molecules participating in the reaction, the known equations of chemical kinetics for reaction rates of the first, second, or other order are derived from this basic proposition. In the case of a reversible reaction, the same law of mass action and the same molecular-kinetic concepts make it possible to derive the laws of chemical equilibrium, and the equilibrium itself is dynamic, based not on the cessation of chemical reactions, but on the equal speed of opposite chemical transformations in the forward and reverse directions. Research on the conditions of chemical equilibrium presents an interesting example of the interpretation of the same phenomenon from the point of view of thermodynamics (see above) as well as from the point of view of molecular-kinetic theory. However, the research of Boltzmann showed that the thermodynamic approach to the study of physicochemical phenomena not only does not exclude molecular-kinetic concepts, but on the contrary finds in them a natural explanation. Indeed, according to the kinetic theory of matter, the thermal energy of a substance equals the sum of the kinetic energies of its molecules. It is quite obvious that the disordered molecular motion constituting thermal energy is in no way fundamentally different from ordered motion, in which molecules move with uniform velocity in the same direction, i.e., the entire body moves as a single whole. This explains from the point of view of kinetic theory the equivalence of heat and work postulated by the first principle of thermodynamics. It is clear that external energy can be equally used for moving the entire body as a whole, i.e., for mechanical work, or for the corresponding acceleration of molecular motions, i.e., for heating. From this also follows the inequality established by the second principle between macroscopic (ordered) and molecular (disordered) motions. The former can easily be fully used both for producing work and for heating. This cannot be said of the reverse transformation of disordered, chaotic molecular motions into the work of moving an external load.

According to the second principle of thermodynamics, thermal energy can be converted into mechanical work only by virtue of existing temperature differences within a given system. As these differences equalize, the free energy decreases, becoming zero when a uniform temperature is established throughout the system. From the standpoint of molecular-kinetic concepts, the long-term coexistence within one system of regions having different temperatures would contradict the theory of probability. The exchange of energy between colliding molecules should lead to the equalization of their average kinetic energy. The most probable result of the mass impacts and collisions of molecules is the transition of any ordered motion into the chaotic motion of molecules with the same average speed. Of course, individual molecules can, as a result of molecular impacts, acquire a speed significantly exceeding the average, but the laws of statistics force us to recognize the mass separation of molecules with greater or lesser kinetic energy as an event mathematically improbable. The smoothing out of temperature differences thus means the transition of the system into a more probable state for it. The second principle can be formulated in words: the free energy of a system tends toward a minimum. In the language of the statistical regularities of the molecular-kinetic theory, this means: the system tends to pass into the most probable state for it. From the doctrine of the structure of matter, the molecular-atomistic theory was extended to the doctrine of electricity, thereby for the first time laying the foundation for the concept of the discrete, atomistic structure of energy. The beginning of electrochemistry was laid by the research of Faraday, which led him (in 1833) to the establishment of the fundamental law of electrolysis, according to which the same quantity of electricity liberates from various solutions at the electrode chemically equivalent quantities of different substances. The quantity of electricity necessary to liberate one gram-equivalent of any substance is always the same magnitude. This magnitude, named the 'Faraday' (F), equals 96,490 coulombs. The number of atoms (of a monovalent element) contained in one gram-equivalent is also a constant magnitude, expressed by Avogadro's constant N (6.06×10²³). The ratio of these two magnitudes (F:N) directly determines the magnitude of the electric charge carried and liberated during electrolysis at the electrode by one atom of the dissolved substance. This smallest elementary electric charge maintains the same magnitude, regardless of the chemical nature of the atom carrying it, provided the latter is monovalent. Bivalent atoms carry a double, trivalent atoms a triple charge. Further research, in particular the experiments of Millikan, showed that even outside of solution, for example in a gaseous medium, the electric charge can change only in jumps, by attaching (or losing) a greater or smaller number of such elementary electric charges that play the role of atoms of electricity; these elementary charges were named electrons. The most important stage in the development of electrochemistry was the theory of electrolytic dissociation, according to which atoms and radicals of dissolved substances capable of conducting an electric current are not only at the moment of its passage but constantly are carriers of elementary electric charges. This theory, formulated by Arrhenius at the time when van't Hoff extended the kinetic theory of gases to solutions, made it possible to eliminate a number of difficulties which the van't Hoff theory encountered in its application to electrolytes. As a result, Arrhenius's concept of the ion as a product of the combination of an atom or chemical radical with one or several elementary charges quickly entered into the common usage of solution theory. During the following two decades, electrochemistry was built on the basis of the concept of the ion as a charged particle possessing all the kinetic properties of a neutral molecule. The osmotic pressure produced by ions along with molecules, the random motion of ions during diffusion, or their directed motion under the action of external electrical forces (electrical conductivity) were easily accommodated within the usual molecular-kinetic concepts. In a similar manner, the laws of chemical interaction between ions in solution were derived from the general law of mass action, from which in particular followed the formulas for the dissociation constant of electrolytes, the change in their degree of dissociation upon dilution (Ostwald's dilution law), the laws of solubility of electrolytes (ionic product of solubility), and so on. A substantial correction to such a mechanical inclusion of the ion within the framework of the molecular-kinetic theory was introduced by the theory of activity, developed mainly by Milner, Bjerrum, Debye, and Hückel, among others. It showed the necessity, in considering the kinetic properties of ions, to take into account the specific characteristics of ions as electrically charged bodies, and to take into account the interionic electrostatic forces acting between them. The modern theory of ionic solutions, without abandoning molecular-kinetic concepts, supplements them with the study of the electrostatic fields inherent in ions. The concept of the corpuscular, atomistic structure of electricity for a long time was not extended to other forms of energy. From the vast amount of new experimental data and theoretical generalizations that initiated the latest physics of the atom, a central place must undoubtedly be given to the doctrine of the discontinuity of light, of the light quantum (see Quantum theory). The quantum theory finds application in explaining the mechanism of photochemical reactions. For a chemical reaction to occur, the expenditure of a certain amount of energy is required. Even in the case when the reaction itself is ultimately accompanied by the liberation of energy, it is first necessary to expend a certain amount of energy to remove atoms from their initial state and make possible their subsequent rearrangement. This energy, absorbed by the molecule for its transition into an active state, for the initiation of its chemical transformation, was named 'activation energy.' According to the molecular-kinetic theory, while the average kinetic energy of molecules grows in proportion to the absolute temperature, the actual kinetic energy of individual molecules fluctuates around this average value in accordance with the laws of statistical distribution. In any given collection of molecules, there are always contained in a certain proportion molecules with the most diverse energy values—up to those corresponding to very high temperatures. Therefore, if a closed system contains molecules capable of chemical interaction, a certain portion of them will, upon collision, possess a sufficient amount of energy to initiate a chemical reaction, an amount exceeding the activation energy. The well-known influence of temperature on the rate of chemical reactions is due to the fact that with increasing temperature the percentage of molecules whose energy exceeds this threshold increases. In the case of a photochemical reaction, a molecule that has absorbed a light quantum immediately, in a jump, raises its energy level and as a result becomes activated. The magnitude of the quantum energy plays a characteristic role in this process. It has the smallest value for the red end of the spectrum and increases as the length of the light wave decreases, as one moves toward the violet and especially toward ultraviolet radiation. It is well known that it is in this sequence that the chemical activity of light rays increases. In a number of cases, it is possible to directly specify the region of the spectrum, starting from which light quanta have sufficient energy for the activation of a given photochemical reaction. According to the 'law of equivalence' formulated by Einstein, each absorbed quantum corresponds (is equivalent to) the occurrence of one elementary chemical reaction, one elementary molecular transformation. However, in practice, this law, which has the significance of a basic postulate of photochemistry, in many cases cannot be subjected to exact proof, since the elementary chemical process in many cases is complicated by subsequent secondary reactions (similar to how in electrolysis subsequent secondary reactions at the electrodes often distort the direct results of the fundamental electrochemical law of Faraday). In particular, in the so-called 'chain reactions,' the elementary photochemical process can serve as the initial link of a chain of further transformations that proceed without the absorption of light. The latest development of physics has led to a deep penetration into the structure of the atom and molecule and to the physical interpretation of the basic chemical processes and properties of matter—an interpretation that gradually blurs the boundary between physics and chemistry. The modern theory of the atom became possible only as a result of the extension of atomistic concepts, briefly outlined above, from the doctrine of matter to electricity and to radiant energy. Attempts to construct a model of the atom as a system of moving electric charges remained unsuccessful until Niels Bohr in 1913 brought it into agreement with the quantum theory of the emission and absorption of light.

"Quantization" of possible electron orbits made it possible to develop a theory of atomic structure that expresses both its chemical and electrical properties, as well as its optical characteristics and the nature of the light spectrum it produces. In recent years, alongside the development of such a corpuscular theory of the atom, another interpretation has also become possible, which also has its roots in the properties of radiant energy. The concept of the quantum nature of emitted and absorbed light necessarily leads to the conclusion that the propagation of light also has a quantum nature, that a light ray represents a flow of light quanta, light particles ("photons"). Optics, however, cannot abandon the wave theory of light, which explains the phenomena of light propagation (in particular, diffraction, interference, etc.) much better, although it is poorly suited for describing the processes of light emission and absorption. However, an analysis of the corpuscular and wave interpretations of light phenomena shows that it is possible to use the equations provided by either of them, passing from one system of equations to another by means of a certain system of transformations. In a similar way, the corpuscular model of the atom can also be expressed by means of the equations of wave mechanics. Such a "wave theory" of matter, while not differing in clarity from the quantum-mechanical interpretation, in many cases has advantages over the latter in the mathematical analysis of phenomena. Physical chemistry and biology. From the very first steps in the development of physical chemistry as an independent science, it became obvious what enormous significance it has for biological disciplines. In many cases, biologists, developing questions not yet studied by contemporary physical chemistry, contributed to its development through their own research. It is sufficient to mention here the osmotic studies of Pfeffer and de Vries, Nageli's research on the structure of colloidal micelles (carried out before the emergence of colloid chemistry), Loeb's work on the application of Donnan's principle to the theory of colloidal phenomena, etc. Of the large number of scientists who applied physical chemistry to the study of biological questions, J. Loeb must undoubtedly be placed in the first place, who laid the foundation for the physico-chemical analysis of life processes as an independent scientific direction. The most important branch of physical chemistry, which first found wide application in biology, was the doctrine of solutions (see), including the theory of electrolytic dissociation (see Ions, Electrolytic dissociation). As early as 1902-1904, Hamburger's comprehensive course appeared: "Osmotic Pressure and Ion Theory in the Medical Sciences," summarizing the first results achieved here. Subsequently, the development of physico-chemical biology found its most complete and systematic expression in the classical manual by Hober: "Physical Chemistry of the Cell and the Tissues" (1st ed. in 1902, 6th ed. in 1926). Colloid chemistry, which studies the colloidal state in which both the protoplasm itself and its main component, protein bodies, are found, has also acquired no less importance. Similarly, other branches of physical chemistry are finding increasingly greater application in the study of life processes. The physical chemistry of the living organism successfully solves tasks that are inaccessible to either purely physical or chemical research. This depends primarily on the very nature of life processes, in which the chemical transformations occurring in the organism have mainly energetic significance, serving as a source for the release of various kinds of energy. Conversely, physical effects are perceived by the organism only after their preliminary transformation into chemical changes, for example, into changes in ionic concentration (see, for example, Ionic theory of excitation), which then cause further (in particular, colloidal) changes. Thus, physical and chemical changes never occur in the living organism in isolation, but always in close connection and interaction with each other, i.e., in the form of physico-chemical processes. The enormous and rapidly growing significance of the physico-chemical direction in biology is also due to methodological reasons. Biological physical chemistry uses mainly physical (especially electrometric) research methods—methods that allow the study of the living cell and are not associated with operations that kill protoplasm, as inevitably happens in chemical analysis. Therefore, physical chemistry easily overcomes the main danger facing purely chemical research—the danger of transferring to the living cell data obtained from the cellular corpse."