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1 Jun 1958

Volume 28, Issue 6, pp. 1007-1264

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Electron Diffraction Study of Lead Tetramethyl

Chi‐hsiang Wong and Verner Schomaker

J. Chem. Phys. 28, 1007 (1958); http://dx.doi.org/10.1063/1.1744334 (3 pages) | Cited 8 times

Online Publication Date: 13 August 2004

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A reinvestigation of Pb(CH3)4 has shown the diffraction pattern to be in agreement with a symmetrical molecular structure and the complex atomic scattering factors of Ibers and Hoerni. The measured interatomic distances are Pb☒C = 2.203±0.010 A and Pb⋅⋅⋅H = 2.79±0.05 A.

Electron Diffraction Study of Trifluoromethyl Iodide

Chi‐hsiang Wong and Verner Schomaker

J. Chem. Phys. 28, 1010 (1958); http://dx.doi.org/10.1063/1.1744335 (4 pages) | Cited 4 times

Online Publication Date: 13 August 2004

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A reinvestigation of CF3I by electron diffraction for this molecule has confirmed the complex atomic scattering factors of Ibers and Hoerni. The structural parameters agree with those reported from earlier, inconclusive determinations.

Dispersion and Absorption of Sound in Ethyl Formate and Study of the Rotational Isomers

Daisaku Tabuchi

J. Chem. Phys. 28, 1014 (1958); http://dx.doi.org/10.1063/1.1744336 (8 pages) | Cited 18 times

Online Publication Date: 13 August 2004

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It was shown by Karpovich that there is the relaxational absorption of sound in liquid ethyl formate and that it results from the rotational isomerism about the C☒O bond. Dispersion of sound velocity is expected from the absorption data, and its existence is confirmed by the present experiments. The sound velocities are measured over the frequency range from 300 kc to 9 mc/sec and at 5°C intervals from 10°C to 40°C by an ultrasonic interferometer. From these experimental results, the energy differences, the equilibrium constant, the rate of isomerization, and the height of the potential barrier hindering the internal rotation are calculated. The value of the energy difference is 2.50 kcal/mole and the height of the potential barrier, referred to the higher energy state is 3.38 kcal/mole. The calculated values of the heat capacity owing to the chemical reaction, the sound velocity at infinite frequency, and the maximum values of the absorption coefficient of sound per wavelength are in good coincidence with the experimental data.

Electronic Structure of Some Diatomic Hydrides

Morris Krauss

J. Chem. Phys. 28, 1021 (1958); http://dx.doi.org/10.1063/1.1744337 (6 pages) | Cited 46 times

Online Publication Date: 13 August 2004

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The self‐consistent field molecular orbital (SCF‐MO) method is applied to the calculation of the ground states of the CH, CH+, NH, OH, and FH molecules. Results are reported for the ionization potentials, excitation energies, binding energies, and dipole moments. The relative behavior of the bonding in these molecules is exhibited by an electron distribution analysis and the importance of s‐p promotion in a single configuration description of these molecules is emphasized.

Kinetics of the Triiodide Equilibrium

Orlo E. Myers

J. Chem. Phys. 28, 1027 (1958); http://dx.doi.org/10.1063/1.1744338 (3 pages) | Cited 12 times

Online Publication Date: 13 August 2004

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The I127 NMR absorption line of iodide ion in aqueous solution is broadened by the presence of iodine molecules. The broadening is consistent with the diminution of phase‐memory time caused by strong quadrupole coupling in triiodide ion, which occurs in dynamic equilibrium. On the basis of a simple bimolecular mechanism, the rate constants for the forward and reverse reactions of the triiodide equilibrium at ca 35°C are (4.1±0.4) × 1010 l/mole‐sec and (7.6±0.8) × 107 sec—1 in the concentration ranges which have been investigated.

Raman Spectroscopy in Liquid Ammonia Solutions. Vibrational Frequencies and Force Constants for Isotopic Species of the Borohydride Ion Having Tetrahedral Symmetry

Allan R. Emery and Robert C. Taylor

J. Chem. Phys. 28, 1029 (1958); http://dx.doi.org/10.1063/1.1744339 (4 pages) | Cited 19 times

Online Publication Date: 13 August 2004

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All fundamentals of the ions 11BH4—, 11BD4—, 10BH4—, and 10BD4— have been observed in the Raman spectra of some alkali metal salts dissolved in liquid NH3 or ND3 at —50°C. A complete assignment of all observed frequencies has been made and force constants have been calculated by the FG method of Wilson.

Molecular Association of Methanol Vapor

Richard G. Inskeep, James M. Kelliher, Paul E. McMahon, and Bruce G. Somers

J. Chem. Phys. 28, 1033 (1958); http://dx.doi.org/10.1063/1.1744340 (4 pages) | Cited 23 times

Online Publication Date: 13 August 2004

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The absorption of infrared radiation by methanol vapor in the region 3200 to 3800 cm‐1 has been studied at 305° and 335°K as a function of vapor density. The results best correlate with the model that methanol vapor is composed of monomer, dimer, and tetramer, with little or no trimer present. The heat of dissociation of the dimer is found to be approximately 3 kcal/mole, and that of the tetramer approximately 17 kcal/mole. The greater stability of the tetramer compared to the dimer is consistent with a cyclic structure for the tetramer.

Viscous Flow of Liquids at Constant Volume and Constant Pressure

J. D. MacKenzie

J. Chem. Phys. 28, 1037 (1958); http://dx.doi.org/10.1063/1.1744341 (3 pages) | Cited 11 times

Online Publication Date: 13 August 2004

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The energy of activation for viscous flow at constant volume, Ev, is dependent on the volume of a liquid. For normal liquids at elevated temperatures, Ev is only a small fraction of the value of the activation energy at constant pressure, Ep. However, for associated liquids, on account of the presence of hydrogen bonds, Ev is almost equivalent to Ep. It is suggested that in highly associated liquids like liquid silica and some molten glasses where flow necessitates the rupture of bonds of even greater energy, the difference between Ev and Ep should be negligible.

Hydrogen Fluoride Polymer Spectrum, Hexamer and Tetramer

D. F. Smith

J. Chem. Phys. 28, 1040 (1958); http://dx.doi.org/10.1063/1.1744342 (17 pages) | Cited 56 times

Online Publication Date: 13 August 2004

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The experimental techniques employed to investigate the polymer absorption are presented.
Experimental results at various pressures at temperatures from —70°C to +73°C are presented. The more important qualitative features noted are: (1) the absorption is strongly dependent upon both the temperature and pressure; (2) in some cases the shape of the bands is dependent upon the pressure; (3) at low temperature only very low pressures of vapor (hence of polymer) are necessary to observe some absorption. The application of Dalton's law, the law of mass action, Lambert's law, and Beer's law, as well as Van't Hoff's equation to the hydrogen fluoride monomer‐polymer system is discussed.
It is then shown that under some special circumstances the absorption varies simply as the fourth power of the pressure, under others as the sixth power of the pressure, but more generally where the absorption is strong as the sum of two terms, one containing the fourth power of the pressure the other the sixth power. The absorption thus corresponds to the overlapping spectra of a tetramer and of a hexamer, which can be separated on the basis of this pressure dependence. From the temperature variation of the absorption, the heats of polymerization are estimated as ΔH4 = —19 kcal/mole and ΔH6 = —40 kcal/mole. In general, the absorption outside the range of monomer absorption is as consistent with a tetramer‐hexamer interpretation for deuterium fluoride as for hydrogen fluoride.

Mean First Passage Time for a Random Walker and Its Application to Chemical Kinetics

Shoon Kyung Kim

J. Chem. Phys. 28, 1057 (1958); http://dx.doi.org/10.1063/1.1744343 (11 pages) | Cited 53 times

Online Publication Date: 13 August 2004

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The mean first passage time for a random walk with reflecting and absorbing barriers is computed by assuming Onsager's reciprocal relation for the transition probabilities. The result, which is valid for an arbitrary dimensional random walk, appears as a quotient of determinants whose elements are the transition probabilities and the initial distribution. For the one‐dimensional case, this result is written as a series which converges rapidly when nearest neighbor transitions predominate; in fact, the series reduces to a closed form for the case when only nearest neighbor transitions are allowed, and always converges for the case when only nearest and next‐nearest transitions are allowed. Montroll and Shuler's computation of the mean first passage time for the case of the truncated harmonic oscillator model of a diatomic molecule is simplified and extended to an arbitrary initial distribution. In addition, the mean first passage time for the case of an‐harmonic oscillator model is computed by using the transition probability obtained recently by Shuler, Bazley, and Montroll. In terms of the mean first passage time, the range of validity of the equilibrium theory in chemical kinetics is discussed.

Equation of State for Water at High Pressure

L. Knopoff

J. Chem. Phys. 28, 1067 (1958); http://dx.doi.org/10.1063/1.1744344 (3 pages) | Cited 1 time

Online Publication Date: 13 August 2004

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An equation of state for water at high pressures is derived by assuming water to be an amorphous mixture of Thomas‐Fermi‐Dirac oxygen atoms and Wigner‐Huntington hydrogen atoms, the mixture having the correct proportion of atomic constituents. Comparison is made with more intricate models in which interaction of the fields among neighbors is assumed.

Interactions of H— Ions and H Atoms with Ne, A, and H2

Edward A. Mason and Joseph T. Vanderslice

J. Chem. Phys. 28, 1070 (1958); http://dx.doi.org/10.1063/1.1744345 (5 pages) | Cited 25 times

Online Publication Date: 13 August 2004

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Previous work on the systems H—☒He and H☒He serves as a model for the calculation of the interactions of H— ions and H atoms with Ne, A, and H2 from an analysis of beam scattering measurements. It is shown that a mutually consistent interpretation can be developed on the assumption that the forces are repulsive in the region of interest. The H— ion elastic scattering cross sections are used to calculate the interactions of H— with Ne, A, and H2, and the electron detachment cross sections are used to locate the points at which these potential energy curves cross the corresponding curves for H atoms. The crossing points are shown to be consistent with potential energy curves for the interactions of H atoms with Ne, A, and H2 obtained directly or indirectly from independent scattering measurements involving beams of H atoms. The crossing points are used to extend these potential energy curves over a wider range of validity than previously available. Such a mutually consistent picture does not seem to emerge when attractive forces are assumed for the H— interactions.

Relative Detection Efficiency of LiBr and (LiBr)2

P. Kusch

J. Chem. Phys. 28, 1075 (1958); http://dx.doi.org/10.1063/1.1744346 (4 pages) | Cited 10 times

Online Publication Date: 13 August 2004

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The relative efficiency for the production of positive ions when LiBr and (LiBr)2 are incident on a hot oxidized tungsten wire has been determined. It is found that the ratio of the number of ions produced for the molecule (LiBr)2 and the molecule (LiBr) is 2.0±0.1. The result is consistent with the heretofore unverified assumption that has been made in the study of the thermochemistry of the vapors of the alkali halides. Effects arising from the long mean free paths of molecules in ovens used for such studies have been observed and are discussed.

Correlation of Molecular Constants. I. Deduction of Relations

Yatendra Pal Varshni

J. Chem. Phys. 28, 1078 (1958); http://dx.doi.org/10.1063/1.1744347 (3 pages) | Cited 7 times

Online Publication Date: 13 August 2004

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Making certain assumptions regarding constants in Sutherland's potential energy function, a number of relations have been derived between the molecular constants; viz., ke, re, De, ωe, etc. The relations will be examined in succeeding papers.

Correlation of Molecular Constants. II. Relation between Force Constant and Equilibrium Internuclear Distance

Yatendra Pal Varshni

J. Chem. Phys. 28, 1081 (1958); http://dx.doi.org/10.1063/1.1744348 (9 pages) | Cited 16 times

Online Publication Date: 13 August 2004

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A new relation between force constant and equilibrium internuclear distance has been suggested:
math
where d and A are constants for each molecular group. The relation has been examined for a number of molecular groups and found to be satisfactory.

Kinetic Studies of Hydroxyl Radicals in Shock Waves. I. The Decomposition of Water between 2400° and 3200°K

S. H. Bauer, G. L. Schott, and R. E. Duff

J. Chem. Phys. 28, 1089 (1958); http://dx.doi.org/10.1063/1.1744349 (8 pages) | Cited 20 times

Online Publication Date: 13 August 2004

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The decomposition of water vapor has been studied at temperatures between 2400° and 3200°K generated in plane shock waves by following changes in the concentration of OH with time. Specific radiation absorbimetry permits these measurements to be made with microsecond resolution. The source of OH radiation used was a flash lamp containing water vapor. Measurements were made on the gas behind reflected shock waves in argon at initial pressures near 50 mm Hg and containing the reactant, H2O vapor, in amounts of the order of 1 mole %. The shock tube and associated electronic and optical equipment are described. Problems of purity, chemical analysis, and reduction of data are discussed. Absorption by OH was calibrated with the equilibrium mixtures resulting from the decomposition of H2O and from the reaction of H2 and O2. The rate of formation of OH from H2O is proportional to the H2O concentration and nearly independent of the argon pressure. The effective activation energy is about 50 kcal/mole. Addition of 2% O2 to the mixture approximately doubles the rate of OH formation and preserves the 50 kcal activation energy. Addition of 2% H2 decreases the rate and increases the activation energy to about 80 kcal/mole. Possible reaction mechanisms are considered. The initial rate of appearance of OH cannot be interpreted in terms of the simple dissociation of H2O into H and OH, and it seems necessary to consider a relatively low‐energy path involving H2O2 or the HO2 radical as an intermediate.

Magnetic Properties of Certain Rare Earth Double Nitrates

B. R. Judd and Eugene Wong

J. Chem. Phys. 28, 1097 (1958); http://dx.doi.org/10.1063/1.1744350 (4 pages) | Cited 17 times

Online Publication Date: 13 August 2004

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Paramagnetic resonance experiments have been performed with crystals of diluted erbium magnesium nitrate and diluted holmium magnesium nitrate. Resonance was observed in the first case but not in the second. These experimental results and in addition the Zeeman effects in neodymium magnesium nitrate are interpeted in terms of a crystalline electric field of predominantly icosahedral symmetry.

Free Radical Statistics

Julius L. Jackson and Elliott W. Montroll

J. Chem. Phys. 28, 1101 (1958); http://dx.doi.org/10.1063/1.1744351 (9 pages) | Cited 16 times

Online Publication Date: 13 August 2004

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On the basis of a simplified statistical model, average concentrations of trapped free radicals condensed from a gaseous mixture are calculated. The trapped free radical concentration is obtained as a function of the free radical concentration in the gas and of the number of nearest neighbors in the solid. The mathematical problem presented by the model is solved rigorously in the one‐dimensional case (two nearest neighbors) and approximately for arbitrary numbers of nearest neighbors. Typical calculated percentages of trapped free radicals range from 14% for a simple cubic lattice to 10% for a face‐centered cubic lattice, when the solid is condensed from a completely dissociated gaseous mixture.

Determination of the Electronic Conductivity in Silver Halides by Means of Polarization Measurements

Bernhard Ilschner

J. Chem. Phys. 28, 1109 (1958); http://dx.doi.org/10.1063/1.1744352 (4 pages) | Cited 21 times

Online Publication Date: 13 August 2004

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The current passing through a cell, silver/silver halide/graphite, has been measured as a function of applied potential in the temperature range between 200 and 370°C, for potentials less than 0.5 volt. Under these conditions, the current for steady‐state conditions is mainly electronic. Definite results were obtained for AgBr and AgI, but not for AgCl because of sluggish approach to steady‐state conditions. From an analysis of the current‐potential curves it is concluded that excess electron conduction prevails in AgBr, but hole conduction in AgI.

Interpretation of Infrared Dichroism in Axially Oriented Polymers

R. D. B. Fraser

J. Chem. Phys. 28, 1113 (1958); http://dx.doi.org/10.1063/1.1744353 (3 pages) | Cited 31 times

Online Publication Date: 13 August 2004

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Although the actual distribution of chain directions in a partially oriented polymer cannot be determined from observations of infrared dichroism it is desirable to express the results in terms of a plausible model. A general relation between dichroic ratio and the parameter describing any model distribution is derived and applied to a number of suggested distributions. None are found to give plausible density functions for chain directions and a model based on the orientation of crystallites in a stretched polymer is suggested as a more suitable representation.

Dynamical Stability Criteria for Molecular Motions

Andrew D. Liehr and Harry L. Frisch

J. Chem. Phys. 28, 1116 (1958); http://dx.doi.org/10.1063/1.1744354 (5 pages) | Cited 1 time

Online Publication Date: 13 August 2004

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The Poincaré classification theory of the singularities of the equations of motion of a classical mechanical system are suitably modified to describe the singularities in the motion of an arbitrary quantum‐mechanical system, derivable from a time‐independent Hamiltonian. Dynamical quantum‐mechanical stability criteria are derived starting with the appropriate equations of motion satisfied by the Heisenberg position and momentum matrices of the system. These stability criteria are used to discuss and classify certain singular nuclear motions of molecular systems which are of some interest in the context of prevalent theories of chemical stability and chemical reaction kinetics. In particular we show that the singular nuclear motions of a molecular system whose electronic and nuclear motions can be assumed to be separable, reduce to the rolling motion of dynamically equivalent classical spheres on the electronic potential energy surface.

Hydrogen→Deuterium Exchange Reaction in α‐Keratin

R. D. B. Fraser and T. P. MacRae

J. Chem. Phys. 28, 1120 (1958); http://dx.doi.org/10.1063/1.1744355 (6 pages) | Cited 19 times

Online Publication Date: 13 August 2004

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A quantitative study of the hydrogen→deuterium exchange reaction in α‐keratin by means of infrared spectra showed that after 50 hr at 30°C about 30% of the peptide linkages had not reacted. Observations between 50 and 1000 hr failed to detect any further reaction but elevation of pD or temperature caused additional exchange. Evidence is presented which suggests that the unreactive peptide linkages occur in the organized regions of the structure (microfibrils) and that complete exchange of the replaceable hydrogen atoms in the sidechains takes place.

Application of a High‐Speed Electronic Computer in Diffusion Kinetics

Donald A. Flanders and Hugo Fricke

J. Chem. Phys. 28, 1126 (1958); http://dx.doi.org/10.1063/1.1744356 (4 pages) | Cited 11 times

Online Publication Date: 13 August 2004

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The Argonne electronic computer AVIDAC is applied in the numerical solution of ∂n/∂t = ∇2n−k1n2−k2n, which, with suitable boundary and initial conditions, represents the reaction kinetics of the one‐radical model used earlier by Fricke to describe the track effect in the radiation chemistry of a solution of a single solute. The fractional number of radicals combining with solute molecules is computed in terms of two dimensionless parameters that completely define the problem. Comparison with the formulas derived by using Jaffé's approximation method shows in most cases agreement to within 10% (though in some extreme cases only to within 50% to 80%), which indicates that Jaffé's method should give useful results in developing other aspects of diffusion kinetics.

Theory of Detonations. I. Irreversible Unimolecular Reaction

Joseph O. Hirschfelder and Charles F. Curtiss

J. Chem. Phys. 28, 1130 (1958); http://dx.doi.org/10.1063/1.1744357 (18 pages) | Cited 26 times

Online Publication Date: 13 August 2004

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The composition, temperature, and pressure as functions of distance in a steady‐state, plane gaseous detonation wave are studied. The effects of the coefficients of viscosity, diffusion, and thermal conductivity are included. The basic equations are set up for a gas in which the irreversible unimolecular reaction A→B takes place with the release of energy. The topological nature of the solutions is discussed and some detailed numerical solutions are given. The numerical calculations (obtained by a point‐by‐point integration of the detonation equations) indicate a strong probability that there is a highest ambient pressure above which a steady‐state detonation cannot take place, and indicate a possibility that there is an ambient pressure below which a detonation cannot occur. In the examples considered, there is strong coupling between the reaction zone and the shock zone so that the solutions never come close to the von Neumann ``spike.'' If the Mach number is greater than unity, the solutions have an entirely different nature and exist for only a single ambient pressure rather than for a range of pressures. However, from hydrodynamical considerations, a detonation wave initiated from either a point or a fixed wall can become equivalent to the steady‐state solutions only if the Mach number is greater than or equal to unity.

Theory of Detonations. II. Reversible Unimolecular Reaction

B. Linder, C. F. Curtiss, and J. O. Hirschfelder

J. Chem. Phys. 28, 1147 (1958); http://dx.doi.org/10.1063/1.1744358 (5 pages) | Cited 9 times

Online Publication Date: 13 August 2004

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The effect of a back reaction on the chemical and thermal profiles in a steady‐state plane gaseous detonation wave supported by an exothermic unimolecular reaction is considered. Just as in the irreversible case, considered in the previous paper, the character of the solutions of the detonation equations change when the Mach number becomes greater than unity. However, in agreement with the conclusions of Wood and Kirkwood, for the reversible reaction, this critical Mach number has the value of unity only when it is defined in terms of the equilibrium velocity of sound.
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