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Elementary Physical Chemistry. B y H u g h S. T a y l o r . 22 X 15 crn; p p . i x 531. .Veic I’ork: D. T-an S o e l r a n d Cornpanu, 1.92;. Price S3.75. In the preface the author says: “The present volume attempts the presentation of material suitable for an introductory course in modern physical chemistry. I t is adapted from the two-volume ‘Treatise of Physical Chemistry’ which appeared under the author’s editorship some three years ago. .I need has been felt in several quarters for a single volume of a more elementary nature which should follow the general lines of development in the larger treatise, without, however, its detail. This book is offered in response to such a demand. “Anyone who has ekamined the scope of modern general chemistry cannot but h e struck with the very considerable amount of physical chemistry which finds its place in such a course, often to the detriment of the purely inorganic chemistry. Thp physical chemistry is of course largely descriptive but it is substantially similar in form of presentation to that given in introductory physical chemistry courses a dwadr or so ago. Physical chemistry ought to reap the advantages of that development and is thereiore offered the possibility of substituting for the descriptive, qualitative course B niore rigorous and. theretore, more mathematical discipline. In the present case. it has heen decided to take advantage of this state of affairs and to presume in this outline of phvsical chemistry a knowledge of mathematics which can be obtained in a course covering the elements of the differential and integral calculus. Another and more compelling reason for this decision, however, is the modern trend in physical chemistry-. Any teacher who ~ o u l dadvise his students that he can attain to an understanding of the science as noiv developing xithout the mathematical knowledge required in the present volume is, in the opinion of the author, doing an ill service to his pupils. If one needs conviction on this point let him turn to the current issue of the Journal of the American Chemical Society and find h o x many of the articles in the section of General and Physical Chemistry. for example. in the March issue, can be read intelligently without such mathematical abilit The chapters are entitled: the atomic concept of matter; energy in chemical systems; the gaseous state; the liquid state; the crystalline state; the velocity and mechanism of gaseous reactions; the direction of chemical change; solutions; homogeneous equilibria; heterogeneous equilibria; electrical conductance and ionisation; weak electrolytes; strong electrolytes; photochemistry; colloid chemistry. This book came as a disappointment and a shock to the reviewer: a disappointment because it was not better; z shock because it may be better than the reviewer thinks it is. The treatment seems to the reviewer to be distinctly formal and essentially superficial. If this presentation means real progress, the reviewer is very much of a back numberwhich may very well he true. There is no alternative, hecause there is no possibility of reconciling the author’s general point of view with that of the reviewer. It may he that hoth will go under; but hoth cannot survive. There is nothing personal in this. The author’s point of view is, unfortunately, that of the majority of physical chemists and illustrates the demoralizing effect of the theory of activity, as a t present expounded. The question a t issue is whether we are going to study concentrated solutions and to develop an exact theory, o r whether we are going to stick to ultra-dilute solutions and to play x i t h a n approsimation theory? Do we believe in one hundred percent dissociation of all electrolytes in all aqueous solutions, or don’t \Ye. and why? h few specific illustrations will make t h r situation clearer. On p. 214,the author starts the discussion of the lowering of the partial pressure of a solution hy deducing Henry’s law. So far as we know, Henry’s lam is specific, depending on the nature oi the solvent and of the solute. By an ingenious transformation with the aid oi ideal solutions, the proportionality factor is made to disappear and the author conies out triumphantly with the socalled Raoult Equation (p. -p:p. = x = S!(S, SI,“where .i: will be the mol fraction of the solute present in the solution. The term 1,refers to the mols of solute present, having
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the molecular weight of the solute in the solution, while No is the number of moles of solvent present having the molecular weight of the solvent in the vapor state.” There is of course no proof of this and the author has forgotten that this formula is onIy supposed t o hold for ideal solutions, in which, by definition, the molecular weights of both components are constant throughout and the molecular weight of each is the same in the solution and in the vapor. On p. 243 the author deduces the equation for osmotic pressure on the assumption that Henry’s law holds, which is certainly not exact thermodynamics, unless we mean by exact thermodynamics a calculating machine to which the accuracy of the premises and of the conclusions is immaterial. The reviewer has not been able to find the fairly exact formula for osmotic pressure PV, = (RT/hl)log(p/p‘) where V, is the volume occupied by one gram of the solvent and M is the molecular weight of the vapor of the solvent. H e says definiteiy on p. 2 5 0 that, in the equation PV = RT, V is the volume of solution in which one mol of solute is contained. That has been known for years not to be true. On p. 253 we read: “It was found in the early work on direct measurements of osmotic pressure that results more concordant with experiment are obtained if instead of expressing V in terms of the volume of solution we express it in terms of the volume of solvent (water) a t its maximum density. This variation really amounts to correcting for the volume occupied by the dissolved substance, analogously to the correction made in the case of gaseous pressures for the volume occupied by the molecules themselves.”
As a matter of fact there is no justification for expressing V generally in terms of the volume of solvent (water) a t its maximum density. I t is quite debatable whether “this variation really amounts to correcting for the volume occupies by the dissolved substance.” There is a very important theoretical point involved. Variations from the gas laws are considered to occur when the concentration exceeds molar, p. 221; but this is true only in case we postulate that sugar and water is our standard. With boric acid and boiling water the gas laws hold up to saturation, which suggests that the abnormal behavior of sugar solutions may be due to some other cause. On p. 209 the author points out very properly that liquid water is“an equilibrium of the molec, perhaps others”; but the author does not point ular species Hs0, (HsO),, ( H 2 0 ) ~and out anywhere, so far as the reviewer has seen, that any change in the water equilibrium must affect the application of all laws deduced on the assumption that the water equilibrium is not displaced. Perhaps the author believes that the rapid rate a t which equilibrium is reached precludes the displacement of equilibrium; but that seems impossible. No reference is made to this possibility when discussing the effect of sodium chloride on the inversion of sugar by hydrochloric acid and there is not even a reference to the impossible apparent concentrations of hydrogen ion obtained under these circumstances. We account for the abnormal maximum density of water by postulating different densities for the different modifications of water. We account for the abnormal boiling-point of water on the basis of a difference in the properties of the different modifications. K e account for the abnormal surface tensions of water by a change in the water equilibrium. We know that the color of KO1 is not identical with the color of NzO+ We know that the properties of acetone are not identical with those of diacetone and we know that the properties of SA are not identical with those of Sp, and yet the author does not consider it worth while even to mention that displacement of the water equilbrium might have a n influence in some cases. The author mentions, p. 2 j7, the work of S. U. Pickering, ”who found that if a solution of propyl alcohol and water in a porous cup be surrounded by either the pure alcohol or pure w-ater, there is always a n osmosis of the pure liquid into the cup. This would indicate that the porous cup is not impermeable to any one constituent of the solution but rather to the hydrate formed in solution.” Pickering never showed that the cup was impermeable to the alleged hydrate. All he showed was that the initial flow was predominantly from either pure liquid to the solution in case the solution h a suitable composition. Given time enough and the concentrations on the inside and the outside of the cup would be the same. 0.2
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The author does not say definitely that complete ionization in a crystal connotes complete ionization in aqueous solution; but he implies it, p. 428. “The most recent efforts to explain the deviations from the law of the mass action shown by strong electrolytes have centered around the idea that the theory of partial dissociation is incorrect. h number of lines of evidence have contributed to this idea. By no means the least important evidence came from an entirely unexpected quarter, the analysis of solid salt crystals by the X-ray method of analysis. According to Debye, the intensity of a beam of X-rays reflected from atoms depends upon the number of electrons in the outer shell of these atoms. Upon this basis, in a crystal of sodium fluoride, the intensities should be equal if the lattice points are occupied by ions and unequal if there are atoms present a t such points. The experimental evidence was in favor of ions. Further considerations confirm this view. I t is possible, on the assumptions that ions are present, to calculate the work involved in separating these ions to infinite distance from each other. This energy quantity is known as the lattice energy. The values obtained in such calculations can be used to determine magnitudes which are experimentally verifiable. The agreement obtained between experiment and calculation constitutes a confirmation of the concept of an ion lattice in such solid salts. I t was also shown by the physicist, Rubens, that such solid salts as potassium chloride, when utilized as reflectors for infra-red radiation, selectively reflect light of wave-lengths characteristic of the vibrations of the constituents of the solid salt. These residual rays could only be produced if the vibrators were ions.”
“If, therefore, in the solid state, such substances as potassium chloride are wholly ionic, it may be assumed that in solution, with the ions separated by solvent molecules, complete dissociation is probable,” p. 429. If this were a necessary consequence, as many people seem to think, it would apply to all solvents, which nobody has yet been willing to advocate. Thirty-six years ago Nernst pointed out that a high dissociating power for a liquid was equivalent to a high solubility coefficient for the ions. The converse is also true. Complete dissociation a t all concentrations for potassium chloride means that the molecule of potassium chloride, which can exist as vapor, is absolutely insoluble in liquid water. When discussing Henry’s law, Taylor says, p. 290, that “Nernst shows that we cannot logically think of a substance as distributed between two phases if its molecular condition in the two phases is different.” Assuming this statement to be true, it follows that hydrochloric acid which exists as a molecule in vapor must therefore exist to some extent in the undissociated form in water. This amount may be very small; but if there can be some, there is no theoretical reason why there should not be more. Xernst’s approximation formula for concentration cells is referred to, p, 439; but the reviewer has found no reference to the exact theory of Helmholtz. Incidentally, the author mis-spells cation and cathode, and also Grotthuss. The Grotthuss-Draper law is given, p. 473, in the perfectlj proper form that “only the rays that are absorbed are effective in producing chemical change;” but there is no reference to the further work of Grotthuss on photochemical depolarizers. Instead, we have the perfectly true but not very helpful statement that “not all absorbed radiation results in chemical change. The numerous investigations of spectroscopy demonstrate the occurrence of absorption of light in many cases entirely unrtssociated with chemical change. I n such case, the light sufiers a transformation into one or other forms of radiant energy or into change in the energy content of the molecules, which change, however, need not result in chemical reaction. Photochemical change is, therefore, one possible resultant of the absorption of radiation. Furthermore, as will be more fully discussed in the sections dealing with photosensitization, it is not necessary that the reacting species absorb the radiation. Photo-reactions may result from the absorption of light by one of the non-reactive constituents of the system.” 4 t the meeting of the Piational Colloid Symposium held at the University of Michigan last June, the reviewer felt, and said, that the European viewpoint, as exemplified by Kruyt, was five to ten years behind that in America. After reading the pages on lyophile colloid solutions, pp. 517-518,the reviewer feels almost like apologizing to hlr. Kruyt.
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Changing to a less important point, that of order, it seems a pity to take up reaction velocity before equilibrium relations. I n his capacity as a possible back number the reviewer still holds to what he wrote thirty years ago about Ostwald’sgreat text-book. “At first sight i t seems natural to begin with the approaches to equilibrium and then to study the phenomena of equlibrium. Guldberg and Waage started from the kinetic theory of gases and deduced an expression for the velocity of reaction. According to this view there could be equilibrium only when the rate of formation of one system was equal to the rate of deeompositon of the same system, and it was therefore natural to broach the subjectofchemical affinity by a discussion of velocities. On the other hand we do begin our studies of chemistry, either as individuals or as a race, by examining cases of equilibrium. Most chemists never get beyond a study of qualitative equilibrium and the physical chemist passes in the laboratory from qualitative to quantitative equilibrium and then to a study of the laws describing the phenomena of change. There seems to be no good reason why the teaching of the text-book should reverse the teaching of the laboratory. It is urged by some that we must consider equilibrium as a dynamic phenomenon, involving the balancing of two velocities; but this is not true. There is no balancing of velocities when a voltaic cell is opposed by an electromotive force equal to its own, and yet there is equilibrium. This conception is a relic of the kinetic theory of gases and it is surpsising to find Ostwald, of all people, adopting it. For our purposes, it is better to start from the theorem of Wenzel, 1777, quoted by Ostwald, p. 40, that the strength of the chemical action is proportional t o the concentration of the reacting substances. That is the most general and the most accurate statement of the mass law which can be made today.” Gibbs did not deduce his criteria of equilibria from a balancing of reaction velocities. The decisive point, so far as the reviewer is concerned, is that we can deduce the form of the equilibrium equation without a knowledge of the intermediate stages, whereas the form of the reaction velocity equation depends entirely on the question whether there are or are not intermediate reactions and on the relative speeds of these intermediate reactions. The author is enthusiastic over the theory of activity. When discussing the electromotive forces of amalgam concentration cells, p. 439, he says that “it is apparent; from a comparison between the calculated and experimental results, that, a t low concentrations of amalgam, the agreement is fair, but that, in the more concentrated solutions, there is a very great discrepancy between experiment and the requirements of theory based on the laws of ideal solutions. I t is evident therefore that for a general treatment of solutions some alternative method of theoretical approach is required. This need has been met in the use of the activity function introduced into thermodynamic chemistry by G. K.Lewis.’’ There is not a word to show thst there are any objections to this theory, which means that no criticisms have been made which seem to the author worth mentioning. Evidently, the walls of Jericho did not fall down at the first blast of the trumpet. “The incompatibility between the postulates of Arrhenius concerning the degree of dissociation of strong electrolytes and the evidence for complete ionization of such electrolytes have led to a number of efforts which, starting from the assumption of complete ionization, would obtain expressions in agreement with the results of experimental measurement of the thermodynamic properties of such solutions. Of these efforts the most notably successful is that of Debye and Huckel. These authors assume that, in dilute solution, the departure from validity of the laws of dilute solutions found with btrong electrolytes, is to be ascribed to the ionization. They point out that, in a solution of a non-electrolyte, the relation between the partial free energy and the concentration is given by the expression F = R T In c Const. They suggest that, for a solution of an electrolyte, the free energy is given by the expression F = R T In c Fe Const., where, in addition to the terms normally obtained with a nonelectrolyte, there is a n additional term, F,, associated with the electrical free energy, the energy effect due to electrical forces between the ions. These forces act in such a way that in the neighborhood of any ion. there will be more ions of unlike sign than of like sign. Consequently, a
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dilution of the solution involves, in the separation of the ions, a n amount of work done against this electrical attraction and, therefore, a corresponding increase in the energy content of the solution,” p. 445. What Debye and Hiickel have done is to assume that the formula with which they started was absolutely accurate except for disturbances due to the electrical changes of the ions. They have then adjusted their assumptions perfectly frankly so as to make their calculations agree with the facts. There is no possible objection to this; but agreement between the observed and the calculated results does not prove the accuracy of the assumptions any more than it did in Loeb’s work on the proteins. If we have a n effect due to an ion which is not a function solely of its electrical charge, this introduces another term and the calculations must be revised because the agreement between the observed and the calculated data is then fictitious. Similarly any error in the original formula vitiates all that follows. This is not the place to discuss the validity of the thermodynamical formulas from which Debye and Huckel start, though the reviewer has very definite opinions on this point. I t seems t3 the reviewer, however, that the existence of a Hofmeister series in true solution is satisfactory evidence of the existence of a specific factor which is a function of the nature of the ion and not solely of its electrical charge. If, for instance, iodine ion displaces the water equilibrium differently from chlorine ion, all the calculations of Debye and Hiickel will have to be revised. This does not mean that their work goes into the discard. Xobody questions the possibility or the probability of disturbances due to electrical charges. The whole question is whether one hundred percent or less of the variations is due to this cause. It ayould be an excellent thing if the physical chemists of the world would get together in a co-operative effort to develop a satisfactory theory of concentrated solutions, perhaps under the auspices of the National Research Council; but that time seems still far distant. It is to be hoped, however, that the tide has turned and that this book represents high-water mark for the theory of activity which has threatened to engulf us. Wilder D. Bancrojt
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Kinetic Theory of Gases. By Leonard B. Loeb. 25 X 16 cm; p p . xci 656. A‘eu York: McGraw-Hill Book Company, 1927. Price: 86.60. I n the preface the author says: “The last thirty years have seen the beginning and development of a new period in physics and chemistry, namely the atomic period. I n contrast to the period preceding it where nature’s proceases were described in terms of continua, recent developments have emphasized the discrete structure of the submicroscopic universe. Thus, today one hears of the atoms of matter, the atoms of electricity, and even the atoms of energy, the quanta. Accordingly the modern physical sciences are demanding and constantly using atomic terminology, concepts, and methods of analysis. It is therefore important t h a t the physicist and chemist have available a fairly complete understanding of these methods. “Of all atomic concepts, the atomic theory of matter is the oldest and perhaps the most complete. I n particular because of its relative simplicity the problem of the atomic nature of gases, in the form of the kinetic theory of gases has attained the highest degree of perfection in this field. I t s admirable methods of analysis are therefore indispensable not only for prospective physicists, but for both chemists and physicists engaged in experimental or teaching work. “When attempting to teach a course on the kinetic theory of gases, at the University of Chicago, in the summer of 1922, the writer discovered t h a t there was in print but one text in the English language on modern kinetic theory. This text was far beyond the scope of the average American college student including even the first-year graduate students. The lack of facility in foreign languages among the students precluded references to texts in foreign languages. Finally, in his own field of work, which depends on the kinetic theory, the writer and his students have been much hampered by lack of a handy reference book containing a collection of the classical and more moden aspects of the kinetic theory. This book was written in an attempt to meet this situation.” The chapters are entitled: historical; the mechanical picture of a perfect gas; the mean free path; the distribution of molecular velocities; the more accurate equation of state, or
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van der Waals’ equation; transfer of momentum, of energy, and of mass through a gas; the laws of rarefied gases and surface phenomena; the reality of molecular motions; specific heats and kinetic theory; contributions of kinetic theory to electrical and magnetic properties of molecules; application of the kinetic theory to the conductivity of electricity in gases. If “a” is the constant of a n equation giving the number of electrons which escape molecular encounters in going z ern in the gas, “it is seen that in order of magnitude the values of a t the higher speeds are nearly the same as those for ”a” computed from kinetic theory. For still higher speeds, “a” decreases rapidly as the velocity increases. This is easily explained, since it is only for lower speeds t t a t the collisions of electrons with molecules are elastic and they are deflected by the surfaces of the molecules. .it higher speeds the electrons begin to shoot through the molecules. The behavior at the lower velocities is nearly normal for all but the inert gases. At speeds near those exciting characteristic resonance effects in the electrons of the atoms or molecules themselves, the bombarding electrons, especially in the inert gases, seem to be much more readily deflected than otherwise. Thus the effective ares of the molecules are increased and the mean free paths fall to lower values. At still lower speeds the atoms of argon, neon, krypton, and xenon appear to become more transparent to electrons than the kinetic theory demands. I n fact, the area for argon drops to one-fifteenth its kinetic-theory value a t the lowest velocities, or the mean free path is multiplied by about I j. The meaning of this is obscure, and is characteristic of the peculiar symmetry of the inert gas atoms. The other gases appear to show nearly normal free paths as the velocity decreases. “On thz whole. then, the electron free paths lead to a brilliant confirmation of the distribution law and agree surprisingly well in magnitude with those computed from molecular free paths and the kinetic theory.” p. 51. “A theoretical study of the behavior of electron atmospheres has shown that these are in all respects analogous to gaseous atmospheres. They differ from them chiefly in the smaller masses of the electrons and their mutual repulsion due to their charges. For the great attenuation of the atmospheres in a number of experiments the distances between individual electrons becomes so great that the potential energy of the forces of repulsion are negligible compared with the kinetic energies possessed by the electrons a t those temperatures. Thus the electrons sensibly obey the laws of a perfect gas, i.e., pi’ = R T , or p = ,YkT, where ,V is the number of electrons per cm3, k is the gas constant per electron or per molecule, and T the absolute temperature. Hence it would not be surprising to find that in such an atmosphere the average kinetic energy of one electron is3 k T / z andthat theenergies are distributed according to the Maxwell distribution law. “Now it was a t one time believed that these electron atmospheres existed even in the interiors of metals, and that thus the electrons might be in thermal equilibrium R-ith the atoms of the metal. Thus on heating a metal, if the Maxwell distribution law held inside the metal, electrons emitted because of their heat motions would, by See. 43, be expected t o show this same distribution outside. This assumption, according to Richardson, may be applicable even if the electrons are emitted from the surface and flow away constantly without attaining a steady state. Whether the hlaxwellian distribution exists in the dense electron atmospheres assumed inside the metal surfaces, or even whether such atmospheres exist a t all (a point which is a t present open to a reasonable doubt), the fact remains that Richardson has predicted that the electron streams emitted from the surfaces of incandescent metals have the energies corresponding to electrons in thermal equlibrium with the surface, and that their energies are distributed according to Maxwell’s distribution law. Such a definite prediction deserves experimental test. If it is found to correspond to facts, then it is a fact of great importance whether the initial assumptions of Richardson (which he has in part modified) are correct or not, for no matter what the mechanism is, one would have definite proof that electrons emitted by a hot body are: ( I ) in temperature equilibrium with it according to the law of equipartition and of Maxwell, and ( 2 ) that the electrons have a distribution of velocities predicted by Maxwell’s law. Thus one would have a directly measurable quantitative verification of a Maxwellian distribution of velocities existing in the heat motions of particles of matter. This point must be stressed, for except
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for the two other proofs which are given in this chapter, both of which depend on the constants deducible from the Maxwell law, no direct verification of the distribution exists. Outside of these three experimental verifications, the distribution law is unproved experimentally, for it only appears in constants of the kinetic theory whose value is the subject of dispute owing to uncertainties in averaging. Thus the experimental verification of such constants up to the present furnishes no certain proof of the validity of the present law, and all available evidence is of value,” p. 105. “In a recent paper Jones has eliminated a number of the errors inherent in Schottky’s work and succeeded in obtaining values of R which deviated less than 15 per cent from the true value of R between temperatures of 1450’ and zooo°K. The deviations were nearly equally great on both sides of the true value and the average deviation was about j per cent. Very recently the experiments of Jones were extended by Germer, using a straight tungsten filament and a cylindrical electrode. He also used a device for heating his filament and measuring the thermionic currents when the heating current was off. Measurements were made a t eight different temperatures from r#oD to z47s0K. Correcting for the contact difference of potential between the filament and the grid, it was found that a t each temperature (except a t very low voltages where the space charge effect limited the current) the current varied with the soltage in just the manner calculated on the assumption that the electrons leave the filament uVith velocity components distributed according to Maxwell’s law for a n electron atmosphere in temperature equilibrium with the hot filament. At z475’K the assumed Maxwellian distribution was verified u p to a retarding potential so great that only one electron in 1010 emitted electrons was able to reach. the collector. This accurate extension of the previous measurments verified the law over a large range of temperatures, and over a remarkable range of velocities. It constitutes probably the best quantitative verification of the law, in that it verifies it over so great a range of velocities. Thust the fact must be accepted that-no matter whether the theoretical assumptions are correct-(r) the electrons are emitted from a hot metal with the mean energy which the Maxwell distribution law would lead one to expect; and ( 2 ) the velocities are distributed among the electrons in accord with the Maxwellian law to within one per cent. Thus the Maxwellian law has been obtained and verified quite definitely in one case, oiz., that of the velocities of electrons which are purely of thermal origin,” p. I IO. “It is of interest to note in passing that the development of Boyle’s law is a beautiful illustration of the progressive advance of physical science. First there is the discovery of a general regularity or law of nature through crude quantitative measurement. Th1a is followed by a stimulating “explanation” in terms of a mechanical analogy. Then, as the result of more accurate measurements, what might he called second-order deviations come to light. Following these appears a brilliant ertension of the mechanical theory to include the deviations. It is to be noted that such a change in the theory is not reuolutionary in any sense. Kothing is upset and no errors have been made. The further investigation merely indicates the limitations of the fundamental assumptions. Such limitations being discovered, a further extension is possible, and the accuracy of the theory is extended perhaps to another significant figure. Following this improvement still more precise measurement again reveals deficiencies which require extension of the theory. Thus the knowledge and comprehension of the phenomenon can continue indefinitely, new improvements in technique making further experiment possible, new extensions in mathematical treatment alsc making perfection of the theory possible. It might seem &s if this process would go on nd infinitum. Unfortunately, as accuracy advances progress becomes increasingly difficult, owing to t he increase in mathematical complexity. Thus it soon becomes almost impossible to handle some of the resulting involved expressions. A simple example of this also appears in the practical application of the equation of state. To this day most engineers are, for simplicty, forced to assume the Boyle’s law equation, since the comp1:cations introduced by the more accurate van der Waals’ equation already begin to increase the complexity of their calculations more than the increase in accuracy would warrant. “The van der Waals’ equation, accordingly, besides Surnishing an admirable second approximation to the true behavior of gases, can be of value in indicating the manner of ad--
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vance of scientific thought. From what has preceded, it is seen that, while it has its limitations, it is perhaps the most serviceable equation, for, owing to its still considerable simplicity, it makes it possible to deduce the values of the constants involved [e.g., the size of the molecules and the constant of attraction) to the first order of approximation. With the more accurate modifications the increasing complexity of the quantities render such evaluations more difficult, and the loss of generality in application renders correlation between the constants of the equation obtained from a variety of phenomena impossible. Thus by its means, as will be seen in this chaper, the molecular constants a and b can be determined and can be found to agree from three apparently independent sets of data, to wit: ( I ) deviation from the gas laws, ( 2 ) critical constants, (3) the Joule-Thomson eff e c t , " ~ 1. 2 1 . "Jellinek shows that each of the isotherms of Andrews can be fitted closely except in the unstable region) by van der Waals' equation if the proper constants are chosen. Good agreements can be obtained at the following temperatures for the values of a and b given: Temperatures b = 0.0023, a = 0.008497 curves fit for a curves fit for b 6 5T. 0.008497 o 0023 64 0°C. 0.007529 I 0 0 0°C. 0.006798 o 0032 Thus the equation fits for either b constant and a varied, or a constant and b varied. From 6.5" to 100' the a values vary 20 per cent when b is constant, and for a constant the b values may vary by 30 to 40 per cent in this same range. Jellinek says that the use of a variable a seems more adequate for this reason as well as from the indications of the data on the variation of B , the pressure coefficient, with temperature. On the other hand, van der Waals' theory demands that b vary with the volumes when these become small and a might be expected to vary with volume also. So that variations in both a and b with volume and temperature are to expected, a varying less with volume than b and b less with temperature than a," p. 159. "In studying the evaporation processes of metals from filaments, as well as certain chemical effects caused by them, Langmuir had arrived independently a t a somewhat different view of such phenomena. He believed that for the cases observed by Wood of what the latter termed diffuse reflection, one had no reflection in the real sense. but an actual case of condensation and reevaporation. At first sight it might be thought that the distinction between a diffuse reflmsction and a condensation and reevaporation was rather a hair-splitting one, for in any cse the condensed layer of atoms postulat,ed by Langmuir cannot be a p preciable in thickness. Thus the atoms must condense and reevaporate very rapidly. I n fact, it is conceivable that the time of impacts with the surface, resultingin diffuse reflection, is quite the same as the time which the condensedatomsspendon the surface. If this were true, the two processes would appear to be indistinguishable in the limit, and perhaps they are so. This is only a n appearance'in the general case and the difference in point of view is an important one near the critical temperature which can be tested experimentally. If reflection takes place a t a given temperature, and if there is a critical temperature of condensation, the condensation may occur sharply at the critical temperature and urd2 not depend o n the density of the stream of impinging atoms. On the other hand, on Langmuir's condensation and reevaporation theory, condensation and evaporation will depend very markedly on the density of the atomic stream, for the rate of evaporation depends on the temperature, while the rate of condensation depends on the density of the atoms near the surface. For low stream densities where evaporation is rapid compared to condensation, the two phenomena may appear to be the same and in the limit may be so. Near the condensation temperature a considerable increase in the density of the stream of atoms could cause an accumulation of atoms on t h t surface which would disappear on reducing the stream density, provided a condensing layer did not fully form. S o change would occur on reflection, for the number of reflected atoms would be equal to the number of the impinging ones. Long since Langmuir's article came out, Chariton and Semenow, by a very ingenious scheme, have actually shown that the condensation on a surface with a temperature gradient down
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its length occurs a t lower temperatures where the density of the atom stream is reduced. The evidence is not accurately quantitative and one may question it on other grounds. I-ntil it is more definitely proved, it must not be accepted as final. I t , however, points strongly t o the correctness of Langmuir's point of view," p. 309. "Langmuir studies the amount uf reflection from surfaces by a study of the rate of chemical reactions. If one calculate from the rate of a surface catalysis the ratio of the number of molecules which react to the number of molecules striking the surface a fraction e is obtained. He assumes that the molecules that react must stick. This I - e is the reflectivity, or a t least the upper limit for it. The values of e found in some reactions are interesting. hut it would seem hardly convincing as regards reflectivity, for in a reaction of Nz with CuO giving atomic nitrogen the value of e = 0.002 was found. This probably indicates that the reaction did not occur for every niolecule which was not specularly reflected, for it is quite likely from slip measurements that E for S zon CuO is as high as 98 per cent or even more. aud not 0.002. Again. it is possible t h a t the value of 6 in a reaction may be very much higher than the value of a . the accommodation coefficient. This is the case for H Zmolecules striking a filament of tungsten a t 2joocI
