Showing papers in "Journal of Chemical Physics in 1933"
TL;DR: In this paper, the spectral and x-ray properties of water and ionic solutions have been deduced quantitatively in good agreement with experiment using a model of the water molecule derived from spectral and X-ray data.
Abstract: On the basis of the model of the water molecule derived from spectral and x-ray data and a proposed internal structure for water, the following properties of water and ionic solutions have been deduced quantitatively in good agreement with experiment. (1) The crystal structure of ice. (2) The x-ray diffraction curve for water. (3) The total energy of water and ice. (4) The degree of hydration of positive and negative ions in water. (5) The heat of solutions of ions. (6) The mobility of hydrogen and hydroxyl ions in water. And the following inferred in a qualitative way. (7) The density and density changes of water. (8) The explanation of the unique position of water among molecular liquids. (9) The dielectric properties of water and ice. (10) The viscosities of dilute ionic solutions. (11) The viscosities of concentrated acids.
2,835 citations
TL;DR: In this article, the method used by Hylleraas in treating the He atom has been extended to the H2 molecule, which consists of setting up a wave function as a series in the five variables required.
Abstract: The method used by Hylleraas in treating the He atom has been extended to the H2 molecule. The method consists of setting up a wave function as a series in the five variables required, electronic separation being introduced explicitly as one of the variables. The coefficients are then determined so as to produce the lowest energy. The energy found is within 0.03 v.e. of the most probable experimental value, while the form and location of the potential energy curve for various internuclear distances agree with those deduced from spectra to within similar limits. The value of the function is computed for several configurations of the electrons, and compared with other approximations. Application of the method to other problems is discussed. A method is given for the numerical solution of secular equations of high degree.
498 citations
TL;DR: In this article, it was shown that the ultraviolet absorption of NaCl, KCl and KI is in agreement with the dispersion of these salts, and with these assumed absorption curves, the dipole-dipole potential constant for the van der Waals attraction between negative ions can be calculated with considerable accuracy.
Abstract: It is shown that the ultraviolet absorption of NaCl, KCl and KI, which one may estimate from recent experimental work, is in agreement with the dispersion of these salts. With these assumed absorption curves, the dipole‐dipole potential constant for the van der Waals attraction between negative ions can be calculated with considerable accuracy. The constants can be estimated for the other alkali halides. The quadrupole‐dipole constant is also approximated for all alkali halides. The resulting van der Waals potential is much greater than that previously calculated and accounts for the stability of CsCl type lattice for CsCl, CsBr and CsI. The polarizability of a given ion depends on the crystal. It is here assumed that the polarizability varies inversely as the ``main frequency'' in the crystal. This is shown to be in approximate agreement with experiment.
442 citations
TL;DR: In this article, it was shown that the dissociation of certain substituted ethanes into free radicals is due not to weakness of the carbon-carbon bond in the ethane but to the stabilization of the free radicals resulting from resonance among the structures in which the unpaired electron is located on the methyl carbon and those in which it is on other atoms (ortho, para, etc., to the methyl carbons).
Abstract: The secular equations corresponding to the five canonical structures for benzene and the forty-two for naphthalene, considered as six and ten-electron systems, respectively, are set up and solved with certain simplifying assumptions, leading to energy values differing by 1.1055α and 2.0153α, respectively, from those corresponding to unexcited (Kekule-type) structures, α being a single exchange integral involving neighboring carbon atoms. Equating these values to the empirical values of the resonance energy, α is found to be about — 1.5 v.e.It is pointed out that the dissociation of certain substituted ethanes into free radicals is due not to weakness of the carbon-carbon bond in the ethane but to the stabilization of the free radicals resulting from resonance among the structures in which the unpaired electron is located on the methyl carbon and those in which it is on other atoms (ortho, para, etc., to the methyl carbon). The secular equations for a number of such radicals have been solved, neglecting excited structures. The experimentally determined heat of formation of hexaphenylethane from triphenylmethyl, 0.5 v.e., when equated to the calculated value C-C+2.2156α, with C-C = 3.65 v.e., leads to α = — 1.4 v.e. The calculated tendencies towards dissociation are in satisfactory agreement with observation, such features as the smaller dissociating power of β-naphthyl than of α-naphthyl and of biphenylene than of diphenyl being accounted for, so that resonance among the structures considered may be accepted as the principal effect causing the stability of the hydrocarbon free radicals.
371 citations
TL;DR: In this article, the condition for the formation of such stable lenses is that the spreading coefficient FS = γ1 − γ2 γ12 shall be negative and the magnitude of the linear tension at the lens boundary is also calculated.
Abstract: A higher hydrocarbon, such as tetradecane, on the surface of water forms a circular lens. The condition for the formation of such stable lenses is that the spreading coefficient FS = γ1 — γ2 — γ12 shall be negative. As the volume of the oil lens is increased, the thickness t at the center slowly approaches a limiting value given by t∞2 = —2Fsρ1/gρ2(ρ1 — ρ2). Equations are given by which FS can be accurately determined from measurements of the radii of large lenses of known volume. The magnitude of the linear tension at the lens boundary is also calculated. Experiments with tetradecane on water at 25°C give FS = —6.2 dynes cm—1 and γ = 26.9. When hydrophilic molecules are introduced into the interface between the lens and the water, they give a spreading force F12 which causes a decrease in — FS and in t. When t<0.1 mm gravitational effects are negligible and the lens degenerates into a duplex film. If such a film is confined by a movable barrier (piston), the force per unit length F exerted on the barrier...
331 citations
TL;DR: The virial theorem can be applied to a molecule, assuming that external forces are applied to keep the nuclei fixed as mentioned in this paper, and the mean electronic kinetic energy is then the negative of the mean total internal energy, plus a term arising from the virial of the external force.
Abstract: The virial theorem can be applied to a molecule, assuming that external forces are applied to keep the nuclei fixed. The mean electronic kinetic energy is then the negative of the mean total internal energy, plus a term arising from the virial of the external force. Since the external force is derivable from the knowledge of the total internal energy as function of nuclear position, this theorem gives a means of finding kinetic and potential energy separately for all configurations of the nuclei, as soon as the total energy is known, from experiment or theory. By using simple forms of curve for total energy, for the diatomic molecule, the kinetic and potential energy are derived and discussed. The curves give direct indication of the formation of the covalent bond, in cases where this occurs, by describing the removal of charge from the atoms to the region between the atoms, with resulting decrease of kinetic energy, increase of potential energy.
329 citations
TL;DR: In this paper, a simple graphical method is developed for calculating the coefficients of the integrals occurring in the matrix elements involved in Slater's treatment of the electronic structure of molecules, based on the discovery by Rumer that the eigenfunctions corresponding to different distributions of valence bonds in a molecule can be represented by plane diagrams which provide information regarding their mutual linear independence.
Abstract: Starting from the discovery by Rumer that the eigen‐functions corresponding to different distributions of valence bonds in a molecule can be represented by plane diagrams which provide information regarding their mutual linear independence, a very simple graphical method is developed for calculating the coefficients of the integrals occurring in the matrix elements involved in Slater's treatment of the electronic structure of molecules.
278 citations
TL;DR: The constants of the empirical repulsion potential assumed by Born and Mayer between two ions, which may be termed the ionic ''radii'' are calculated for the alkali and halide ions from the lattice constants of alkali halides as mentioned in this paper.
Abstract: The constants of the empirical repulsion potential assumed by Born and Mayer between two ions, which may be termed the ionic ``radii,'' are calculated for the alkali and halide ions from the lattice constants of the alkali halides By using 9 such radii the 20 lattice constants can be recalculated nearly within the probable experimental error of their determination The good agreement is regarded as support for the assumptions involved in the calculations
270 citations
TL;DR: In this paper, a simple wave function for the normal state of the hydrogen molecule, in which both the atomic and ionic configurations are taken into account, was set up and treated by a variational method.
Abstract: A simple wave function for the normal state of the hydrogen molecule, in which both the atomic and ionic configurations are taken into account, was set up and treated by a variational method. The dissociation energy was found to be 4.00 v.e. as compared to the experimental value of 4.68 v.e. and Rosen's value of 4.02 v.e. obtained by use of a function involving complicated integrals. It was found that the atomic function occurs with a coefficient 3.9 times that of the ionic function. A similar function with different screening constants for the atomic and ionic parts was also tried. It was found that the best results are obtained when these screening constants are equal. The addition of Rosen's term to the atomic‐ionic function resulted in a value of 4.10 v.e. for the dissociation energy.
253 citations
TL;DR: In this paper, a set of bond-energy values for single, double, and triple bonds between atoms, obtained from thermochemical data, such that the total energy of formation from separate atoms of a molecule containing given bonds is equal to the sum of the energies for those bonds.
Abstract: In the first part of this paper there is given a set of bond‐energy values for single, double, and triple bonds between atoms, obtained from thermochemical data, such that the total energy of formation from separate atoms of a molecule containing given bonds is equal to the sum of the energies for those bonds. In the derivation of these values data were used only for molecules for which it is probable that one electronic structure, corresponding to one distribution of valence bonds, represents the normal state to a satisfactory degree of approximation. For other molecules more than one electronic structure of this type contributes essentially to the normal state, the energy of formation of the molecule then being larger than that for any one of the contributing structures. On comparing the energies of formation given by thermochemical data with the values calculated for various structures, it is verified that this difference is always positive or zero (to within the limits of error involved). The difference in energy is interpreted as the resonance energy of the molecule among several electronic structures, and its existence in a given case provides strong evidence that more than one structure is contributing to the normal state of the molecule, the number and importance of the contributing structures being indicated by the magnitude of the resonance energy. In this way the existence of resonance is shown for many molecules, and values found for the resonance energy are tabulated. The substances discussed include carbon dioxide, carbon disulfide, alkyl isocyanates, carboxylic acids and esters, aliphatic amines, carbonic esters, urea and related substances, benzene and benzene derivatives, naphthalene and other condensed ring systems, pyridine and related heterocyclic compounds, biphenyl, fluorene, phenylethylene, dihydronaphthalene, quinone, some ureides and purines, etc.
211 citations
TL;DR: In this article, the authors used the variation method of treating the wave equation for the normal state of He, involving a three-electron bond, leading to the values Z = 1.833, r0 = 0.75A, 0 = approximately 3200 cm(-1), with a maximum 1.4 v.
Abstract: With the use of wave functions constructed from hydrogen-like single-electron functions with an effective nuclear charge Z, the application of the variation method of treating the wave equation for the normal state of He, involving a three-electron bond, leads to the values Z = 1.833, r0 = 1.085A, De = 2.47 v.e., and 0 = approximately 1950 cm(-1). The experimentally determined values (from the He2 spectrum) are r0 = 1.090A, De = 2.5 v.e., and ½ = 1628 cm(-1). A similar discussion of He, with a covalent-plus-ionic wave function, shows that the energy curve has a minimum at r0 = 0.75A, 0 = approximately 3200 cm(-1), with a maximum 1.4 v.e. higher at about 1.1A. This configuration could act as the core for excited states of He and doubly-excited states of He2, some of which would be capable of existence with either one of two moments of inertia, one corresponding to r0 = 0.75A and the other to about the same values of r0 as for the analogous states in excited H or doubly-excited H2.
TL;DR: In this article, a mechanism of diffusion and electrolytic conduction in solids is discussed, which is based on a formal treatment given by Frenkel, and it is assumed that in a crystal in thermal equilibrium some of the atoms or ions are removed from their normal positions in the lattice to irregular ones in the interlattice space.
Abstract: In the present paper a mechanism of diffusion and electrolytic conduction in solids is discussed, which is based on a formal treatment given by Frenkel It is assumed that in a crystal in thermal equilibrium some of the atoms or ions are removed from their normal positions in the lattice to irregular ones in the interlattice space Then diffusion and electrolytic conduction is possible by two processes; first by migration of the ions in the interlattice space, second by migration of the vacant places The number of ions in the interlattice space can be calculated If one considers the influence of polarization the result agrees in the order of magnitude with the observed data It is also shown that the activation energy connected with the processes of movement is of the correct order of magnitude Thus a satisfactory explanation of the exponential factor occuring in the empirical conductivity (or diffusion) formula is obtained The constant factor multiplying the exponential can be explained at once for o
TL;DR: A series of iron oxides with compositions between 76.08 and 76.72 percent Fe, all of them lying within the single phase solid solution area known as Wustite has been prepared and the lattice constants and densities of individual members determined.
Abstract: A series of iron oxides with compositions between 76.08 and 76.72 percent Fe, all of them lying within the single phase solid solution area known as Wustite has been prepared and the lattice constants and densities of the individual members determined. The NaCl structure found by earlier investigators and considered by them to be the structure of FeO has been found throughout this series. Contrary to the earlier results the size of the unit cell decreases as the iron content decreases. The solid solution is of a complex type; an oxygen ion replaces an FeO group with an accompanying increase in valence of 2 Fe++ to 2 Fe+++. The results are discussed from the chemical and structural points of view.
TL;DR: The probability function of Menke has been used as a basis for a statistical treatment of the intermolecular potentials in solutions of symmetrical molecules for which the entropy of mixing is the same as for an ideal solution of the same composition as discussed by the authors.
Abstract: The probability function of Menke has been used as a basis for a statistical treatment of the intermolecular potentials in solutions of symmetrical molecules for which the entropy of mixing is the same as for an ideal solution of the same composition. The resulting expressions enable calculations to be made of the departure of iodine solutions from the ideal solution laws which agree satisfactorily with the observed departures.
TL;DR: In this paper, the authors considered the case where a potential curve giving molecule formation is intersected by a repulsive curve, the curves which cross defining the unperturbed energy levels and wave functions, and found that the discrete lines are not only broadened, but they are shifted in position, slightly distorted in shape, and there is present a series of subsidiary maxima of the absorption coefficient.
Abstract: The calculation of the width and shape of a line which is broadened because of predissociation has been extended so as to include perturbations of intermediate size By ``perturbations of intermediate size'' we mean perturbations which are not so great that lines (of given rotational quantum number) belonging to two adjacent vibrational levels are broadened so as to overlap appreciably; they may be any size up to that limit These calculations have been applied with certain simplifying assumptions to the case where a potential curve giving molecule formation is intersected by a repulsive curve, the curves which cross defining the unperturbed energy levels and wave functions It is found that the discrete lines are not only broadened, but they are shifted in position, slightly distorted in shape, and there is present a series of subsidiary maxima of the absorption coefficient The exact amount of broadening of a line depends very greatly upon its energy relative to the energy at which the potential curves cross, and in general a line which is much broadened will also be much shifted in position In molecules we may expect to have isolated groups of rotational levels in which the central level is sharp, and the rotational levels on either side become more and more diffuse, finally fading out The predissociation phenomena in iodine chloride are discussed on the basis of the above theory In particular, two groups of sharp and diffuse levels, such as described, are considered and are respectively ascribed to the isotopic molecules, ICI35 and ICI37 There is some difficulty in describing the phenomena in iodine chloride quantitatively, but qualitatively the experimental results appear to accord with the theory
TL;DR: In this paper, the summations of state and free energies of the molecules H21, H22 and H1H2 have been calculated at temperatures from 20.4 to 700°K and their dependence on the spin and statistics of H2 discussed and illustrated.
Abstract: The summations of state and free energies of the molecules H21, H22 and H1H2 have been calculated at temperatures from 20.4 to 700°K and their dependence on the spin and statistics of H2 discussed and illustrated. The equilibrium constants of the reaction H21+H22 = 2 H1H2 are found to deviate markedly from the value 4 expected from simple probability considerations. The equilibrium constants of the reactions H21+2 H2Cl⇄H22+2 H1Cl and H21+2 H2I→H22+2 H1I have been calculated and found to be appreciably different from unity, showing that appreciable differences in equilibrium constants of chemical reactions may be expected depending on which isotope of hydrogen enters into the reaction. Small differences in the electrode potentials of the two hydrogen isotopes may be expected but no exact estimates have been made.
TL;DR: The mechanism of the decomposition of a simple linear triatomic molecule formed by the collision of an atom with a diatomic molecule is discussed qualitatively in this paper, and the results are applied to the short-lived molecule HO2 to determine the order of magnitude of its lifetime in a number of different states, although it does not conform strictly to the idealized conditions for which the calculation was made.
Abstract: The mechanism of the decomposition of a molecule formed by the collision between a molecule and another particle is discussed qualitatively. Calculations are then carried through to determine the lifetime of a simple linear triatomic molecule formed by the collision of an atom with a diatomic molecule. The results are applied to the short‐lived molecule HO2 to determine the order of magnitude of its lifetime in a number of different states, although it does not conform strictly to the idealized conditions for which the calculation was made.
TL;DR: In this paper, the approximate construction of shared electrons in molecules RXn, as linear combinations of atomic orbitals is discussed and illustrated by equations for RX2, RX3, RX4 types.
Abstract: Theory. The approximate construction, for shared electrons in molecules RXn, of molecular orbitals (``orbital'' means one‐electron orbital wave function) as linear combinations of atomic orbitals is discussed and illustrated by equations for RX2, RX3, RX4 types. Properties of bonding, nonbonding, antibonding, also excited, molecular orbitals are described. Valence orbitals include both bonding and nonbonding types. RH3 and H3 orbitals are given as examples. Molecular orbitals constructed from atomic orbitals contain undetermined coefficients and implicit parameters (effective Z's of the atomic orbitals) which make them very flexible. They are useful for a qualitative theory which can be compared with empirical, especially chemical and spectroscopic, data. They also have value in semi‐quantitative calculations (Van Vleck). Applications. Electronic structures, ionization potentials, form and stability (at least some of these properties in each case) of the molecules CH4, NH3, H2O, NH4, CH3, NH2, BeH2, RXn a...
TL;DR: In this paper, the lattice energies and lattice constants of the silver and thallium halides were calculated assuming ionic crystals with a van der Waals potential, which accounts for the low solubilities of the salts.
Abstract: The lattice energies and lattice constants of the silver and thallium halides are calculated assuming ionic crystals with a van der Waals potential. The latter term, which is large, accounts for the low solubilities (high lattice energies) of the salts. The calculations appear to be quantitatively satisfactory for the thallium halides, TlCl, TlBr and TlI, and for the three silver halides AgF, AgCl and AgBr. Definite evidence is found for assuming the existence of a homopolar potential in AgI of about 10 percent of the total lattice energy. One reason for believing this, is the stability of the zincblend instead of the rocksalt lattice, which latter should be stable were the compound purely ionic. There is presumably some homopolar binding in AgBr but it cannot be large. The thallium salts probably are entirely ionic. The theoretically calculated and experimental (chemical) lattice energies are, respectively, in K cal., AgF, 219, 217.7; AgCl, 203, 205.7; AgBr, 197, 201.8; AgI, 190, 199.2; TlCl, 167, 170.1; TlBr, 164, 165.6; TlI, 159, 160.8.
TL;DR: In this article, a method for producing any desired concentration of the isotope of hydrogen, H2, by electrolysis was described, and it was shown that a further reduction of volume to one-half of a cubic centimeter of water remained, this water had specific gravity 1.073.
Abstract: A method is described of producing any desired concentration of the isotope of hydrogen, H2, by electrolysis. Starting with twenty liters of water from an old commercial electrolytic cell and electrolyzing in four stages until only one‐half of a cubic centimeter of water remained, this water had the specific gravity 1.073. Having shown that no large accumulation of the heavy isotopes of oxygen occurs and assuming that the density varies linearly with the fraction of H2, 2/3 of the hydrogen in this water is H2. It is shown that a further reduction of volume to one‐quarter will give 99 percent H2. In our electrolyses the percentage loss of H1 is to the percentage loss of H2 in the ratio of five to one. By two methods we have found 1 in 6500, as a provisional value for the concentration of H2 in ordinary water.
TL;DR: In this paper, a variation function similar to that applied by Rosen to H2 is used in the discussion of the normal state of H2+ in the context of the H2+.
Abstract: A variation function somewhat similar to that applied by Rosen to H2 is used in the discussion of the normal state of H2+.
TL;DR: In this paper, a method of studying the electrical properties of monomolecular films floating upon a liquid has been described, and measurements on the potential jump have been made in order to furnish a comparison with the work of Guyot.
Abstract: A new method of studying the electrical properties of monomolecular films floating upon a liquid has been described. Measurements on the potential jump, dV, because of the presence of monomolecular films of oleic acid, palmitic acid, tricaprylin, and trimyristin on water have been made in order to furnish a comparison with the work of Guyot. Excellent agreement was found in all cases. In addition, Guyot's conclusion was verified that dV for fatty acids depends greatly upon the presence of a trace of sulphuric acid in the water while dV for substances like tricaprylin and trimyristin is but slightly affected by the presence of acid.
TL;DR: In this article, the quantum-mechanical treatment previously applied to benzene, naphthalene, and the hydrocarbon free radicals is used in the calculation of extra resonance energy of conjugation in systems of double bonds.
Abstract: The quantum‐mechanical treatment previously applied to benzene, naphthalene, and the hydrocarbon free radicals is used in the calculation of extra resonance energy of conjugation in systems of double bonds, the dihydronaphthalenes and dihydroanthracenes, phenylethylene, stilbene, isostilbene, triphenylethylene, tetraphenylethylene, biphenyl, o, m, and p‐diphenylbenzene, and 1,3,5‐triphenylbenzene. The calculated values, which are in approximate agreement with empirical values from thermochemical data, are used in the discussion of chemical properties and in the formulation of rules regarding conjugation in overlapping systems.
TL;DR: In this paper, the surface potential of a gaseous film with homo-heteropolar molecules is determined by a single smooth curve for the relation between surface potential and molecular area.
Abstract: Simultaneous measurements of film pressure and surface potential have been carried out by the use of an apparatus designed in such a way that the potential may be determined for any location on the surface of the film. At film pressures above that of the gaseous films, organic substances with homo‐heteropolar molecules give a single smooth curve for the relation between surface potential and molecular area. At areas sufficiently great to reduce the pressure to that of the gaseous film the surface potential becomes variable and remains variable until the area becomes so great that the continents and islands of condensed film evaporate in the two‐dimensional system to give a gaseous film alone. For example with films of myristic acid at 17° the surface potential is represented by a single curve below a molecular area of about 50 sq. A, and by any value below 170 mv at higher areas, at which islands in the film persist. The areas above which the surface potentials become variable, due to the effects of islan...
TL;DR: In this paper, the vibrational potential of polyatomic molecules is discussed in the light of the theory of directed valence Andrews' assumptions of ''valence forces'' are seen to be rather special, but at the same time are fairly good approximations under certain conditions.
Abstract: The vibrational potential of polyatomic molecules is discussed in the light of the theory of directed valence Andrews' assumptions of ``valence forces'' are seen to be rather special, but at the same time are fairly good approximations under certain conditions The normal vibrations of three body systems are calculated for the potential function V=12[k1(Δr1)2+k2(Δr2)2+k3(r102+r202)(Δγ)2] with r1, r2 radial coordinates and γ an angular one The potential terms proportional to Δr1Δr2, etc, are treated as perturbations These calculations are applied to the ethyl halide and ethyl alcohol molecules by considering the CH3, CH2 and OH groups as dynamic units Force constants were determined which gave approximately the experimental frequencies The calculation of the normal modes of vibration illustrate the approximate validity of the designation of the modes of vibration of unsymmetrical three body systems as two independent radial motions and an angular motion
TL;DR: In this article, the existence of finite entropies at the absolute zero is established thermodynamically, and the requisite interpretation of statistical ideas to secure concordance with this result is discussed.
Abstract: With the object of testing experimentally the third law of thermodynamics as applied to crystalline solutions, the chief thermodynamic properties of such a solution of silver bromide and silver chloride have been studied. Measurements described and recorded include: the free energy of formation, obtained from measurements of the e.m.f. of appropriate silver‐silver halide electrodes against hydrogen; the heat of formation, from measurements of heat absorbed in dissolving the various phases in a thiosulfate solution; the specific heats between 15°K and 298°K of the pure constituents and the solid solution. The entropy of silver bromide and of silver chloride is calculated from the specific heat curves. The entropy change in the formation of the solid solution at 298°K is calculated from the experimental data and is found to agree with the result calculated statistically. The latter is identical in form and magnitude with the entropy as calculated thermodynamically for an ideal solution, though the heat content and free energy show that the solution is far from perfect. From the specific heat curves it appears that the entropy of mixing persists essentially unchanged in magnitude to the lowest temperature of the measurements, and presumably to the absolute zero. The existence of finite entropies, or entropy differences, at the absolute zero is regarded as established thermodynamically, and the requisite interpretation of statistical ideas to secure concordance with this result is discussed. Finally, although the existence of a valid but limited third law is accepted, and a concise general statement of it suggested, it is pointed out that the ``principle of the unattainability of the absolute zero'' must be regarded as extra‐thermodynamic in character.