Volume 26, Issue 5, 01 May 1957

Effect of Pressure on the Isotope Effect in a Unimolecular Gaseous Reaction : Tritium and Carbon‐13 Effects in the Isomerization of Cyclopropane
View Description Hide DescriptionAs a new means of studying the effect of pressure on unimolecular gaseous reaction kinetics, the tritium isotope effect in the isomerization of cyclopropane to propylene has been measured. At a pressure of 200 mm, the ratio of rate constants for unlabeled and singly‐labeled species is given by k/k′ = (0.86±0.06) exp (385±95/RT). The temperature range was 406–492°C. As the pressure decreases, the isotope effect is lowered and, within experimental error, disappears at 1 mm. Upon the addition of inert gas to cyclopropane at this pressure, the isotope effect is increased to a value corresponding to a higher pressure of reactant. The relation between these results and the calculations of N. B. Slater on the kinetics of this reaction is discussed.
The carbon‐13 isotope effect was measured at 1 atmos and 492°, and was found to be k/k′=1.0072±0.0006. This may be explained on the basis of a change in either a carbon‐carbon or a carbon‐hydrogen bond in the transition state.

Kinetics of the Nitrogen Dioxide Catalyzed Oxidation of Nitric Oxide
View Description Hide DescriptionThe rate constant for the reverse reaction of the rate controlling step (NO+O_{2}+NO_{2}=NO_{2}+NO_{3}) of high pressure nitrogen pentoxide decomposition has been determined to be 6.58×10^{7} cc^{2} mole^{—2} sec^{—1}. This reaction was found to be the rate‐controlling step in the nitrogen dixoide catalyzed oxidation of nitrosyl chloride to nitryl chloride. The equilibrium constant at 25° for the reaction ClNO+NO_{2}=ClNO_{2}+NO as evaluated from the kinetic data was found to be 1×10^{—4}.

Pairing Energies in the Actinide Series
View Description Hide DescriptionThe authors' previous calculations of pairing energies for d^{n} configurations are extended to f^{n} configurations. The ground state of f ^{2}, as in PuF6, is shown to be nondegenerate whether the spins are paired or not. However, detailed calculations show the magnetic properties to favor the view that the spins are in fact paired. This assumption is also found to accord with the observed variation of vibrational frequencies for UF6, NpF6, and PuF6.

Dispersion and Absorption of Sound in Liquids in General Chemical Equilibrium and its Application to Chemical Kinetics
View Description Hide DescriptionIt is shown that there occur dispersion and absorption of sound owing to chemical reaction in a liquid which is in general chemical equilibrium . From the acoustic characteristic equation, the velocity and the absorption coefficient of sound are derived, and the characteristics of the dispersion and absorption curves are examined. The velocity and the absorption coefficient of sound in liquid are derived in terms of the density, the static isothermal compressibility, the thermal expansion coefficient, the partial molar volume, the equilibrium constant, that is, the composition, the reaction heat at constant volume, the molar heat at constant volume, and the rate constant of chemical reaction. By measuring the velocity and the absorption of sound, it is possible to determine the rate constant of chemical reaction, the reaction heat, and the volume change. The application to solutions, especially to electrolyte solutions is shown, and in this case the activity coefficients may be used. As special cases, chemical reactions which are not accompanied by reaction heat or volume change are treated, and the results of Freedman and Manes are compared with the present one, and the differences are pointed out. Several examples of the general formulas are shown. Since it is easy to increase the frequency of sound, the method of measuring the velocity and the absorption coefficient of sound is adequate for determining the rate of a very fast reaction in the equilibrium state.

Carbon Isotope Effect during Oxidation of Carbon Monoxide with Nitrogen Dioxide
View Description Hide DescriptionBy use of naturally occurring C^{12} and C^{13}isotopes in carbon monoxide, the effect of carbon mass on the rate of the reactionhas been studied in a 15–1 Vycor flask, in the temperature range 540–727°K, and at pressures between 1 and 20 mm. The rate constant for the reaction was k=12×10^{12} exp (—31,600/RT) cc mole^{—1} sec^{—1}. The ratio of rate constantsk _{12}/k _{13} was 1.022 at 540°K, 1.019 at 638°K, and 1.016 at 727°K. An activated complex was set up with normal bond distances and normal force constants, and with the reaction coordinate explicitly given in terms of internal coordinates with an interaction term such that the restoring force on an antisymmetric stretching symmetry coordinate is reduced to zero. By means of E. B. Wilson's FGmatrix methods, a vibrational analysis was made of the activated complex, all vibration frequencies were determined for one species, and shifts in frequency due to isotopic substitution were computed by a perturbation method. Similarly, the ratio of effective mass of the reaction coordinate was evaluated, and calculations were checked by the Teller‐Redlich product rule. The isotope rate effect was computed by Bigeleisen's formulation of the activated complex theory. For a set of force constants well within the range of normal values and for normal bond radii, calculated isotope rate ratios at all temperatures are in excellent agreement with observed ones.

Rate Constants of Second‐Order Reactions from Kinetic Current Measurements
View Description Hide DescriptionKinetic currents have been calculated for the case where the solution contains two electroactive species, one of which may undergo a second order reaction with the reduced form of the other. The results have been applied to the reaction between ferrous versenate and cumene hydroperoxide, assuming the diffusion co‐efficients of all species to be equal. The calculated and observed rate constants are found to differ by 33%, which constitutes reasonable agreement in view of the assumptions made.

Emission Band Spectra of Nitrogen. Kaplan's First and Second Systems
View Description Hide DescriptionSeven bands of Kaplan's first system and eleven bands of Kaplan's second system have been photographed under high resolution. The two systems are definitely and . It is very probable that they are and and that the two lower states belong, along with , to the N_{2} configuration ··· . A clear breaking‐off of the branches coming from the Π^{+} levels of the state above was observed. This is interpreted as an allowed predissociation by a state dissociating to two ^{2}D atoms. Consequently lower limits probably close to the term values for the x, y, w, and a′ states could be determined; this locates the a′ and w states respectively probably about 2.2 and 2.7 ev above state A, in good agreement with theoretical expectations. Perturbation of the remaining Π^{—} levels was also observed. Rotational and vibrational constants and term values of the various states are presented. The transitions a′↔a and w↔a should give rise to bands in the (mostly far) infrared.
It is noted that the constants of both the x and y states are close to those of the N_{2} ^{+} state ··· , and it is proposed that and are respectively derived from the latter by the addition of an electron in a and a ?) Rydberg orbital. It is then proposed that the and p′ states of N_{2}, whose constants are close to those of the ground state ··· of N_{2} ^{+}, are derived from the latter by addition of an electron in the same Rydberg orbital as in the y state. The states p′ and e are the first two members of Worley's first Rydberg series.

Two‐Center Dipole Moment Integrals in Terms of C Functions
View Description Hide DescriptionThe dipole moment integrals for Slater‐type atomic orbitals are conveniently and concisely expressed in terms of the C functions introduced by Ruedenberg, Roothaan, and Jaunzemis in their treatment of the two‐center hybrid integrals. Explicit formulas in terms of both the C functions and the usual A and B functions are given for all such integrals involving orbitals with quantum numbers one and two.

Rate of Recombination of Radicals. III. Rate of Recombination of Ethyl Radicals
View Description Hide DescriptionThe rate constants for the recombination (k _{2}) and the disproportionation (k _{3}) of ethyl radicals have been determined by applying the theory of the rotating sector to the photolysis of diethyl ketone. The values of k _{2} are 1.5±1×10^{13}, 2.0±0.5×10^{13}, and 4.2±0.8×10^{13} cc mole^{—1} sec^{—1}, at 50°C, 100°C, and 150°C, respectively. The ratio k _{3}/k _{2} is taken to be 0.12 from other work. An Arrhenius plot of these results indicate an energy of activation for k _{2} of 2.0±1 kcal/mole. These results are shown to be in agreement with existing theories. A simplified transition state theory calculation of k _{2} is offered, based on the change in the number of degrees of freedom from radicals to activated complex.

Magnetic Susceptibility of Neutron‐Damaged Graphite
View Description Hide DescriptionPrevious work on the magnetic susceptibility of graphite as it is affected by temperature and bromination is extended to include effects of neutron irradiation at about room temperature. Data taken at both room temperature and liquid nitrogen temperature are analyzed and yield consistent values for the number of electrons trapped out by damage defects, thus further establishing the validity of the theory. The trapping rate of electrons, with neutron exposure, is found to be slightly nonlinear and a fair fit of the empirical curve isnumber of trapped electrons per carbon atom=1.4×10^{—4} t ^{2/3},where t is the flux in mwd/ct. This two‐thirds power dependence cannot be taken too literally, since neither the quantity nor quality of the data is sufficiently good. Data are also given for the buildup of paramagnetic centers as damage increases.

Magnetic Dipole Effects in Ferrites
View Description Hide DescriptionThis paper presents an analysis of the role which classical magnetic dipole‐dipole interactions may play in the physical behavior of ferrites with particular attention to magnetic anisotropy. Included is an evaluation of these effects in magnetite and lithiumferrite where an ordered arrangement of dipoles can exist and a study and calculation of some statistical effects which exist in other ferrites where this ordering is absent. The results obtained from this analysis are then compared with the pertinent experimental data.

Interaction between Sulfur Dioxide and Polar Molecules. I. Systems Containing Aliphatic Alcohols, Ethers, or Benzene in Carbon Tetrachloride
View Description Hide DescriptionThe absorption band of sulfur dioxide near 2800 A in mixed solvents of benzene, aliphatic alcohols, or ethers with carbon tetrachloride is probably in part the result of a donor‐acceptor complex with sulfur dioxide as acceptor.
The characteristic constants for the MeOH, EtOH, n‐PrOH, n‐BuOH, and benzene complexes with sulfur dioxide, and the heats of formation of the benzene and ethanol complexes with sulfur dioxide in carbon tetrachloride have been estimated. The effect of atmospheric water vapor on these systems is also discussed.

Interaction between Sulfur Dioxide and Polar Molecules. II. Systems Containing Ethanol, and Benzene or Hydroquinone
View Description Hide DescriptionThe near ultraviolet absorption for sulfur dioxide in benzene‐ethanol solvent is adequately explained as arising from the superimposed bands for the systems:if it is assumed that in passing from nonpolar to polar solvents there is no change in K _{1}, K _{2}, and in the molar extinction coefficients of the two complexes and of the uncombined sulfur dioxide. Extinction coefficients and equilibrium constants for the benzene complex must be obtained from analysis of solutions with high benzene concentration. It was found that the thermodynamic constants of both complexes, calculated from data for the mixed system, are identical with values obtained for the separate systems with carbon tetrachloride.
A similar analysis of the absorption spectra of hydroquinone‐sulfur dioxide‐ethanol solutions gives a value of 14.0±1.0 kcal per mole for the heat of formation of the hydroquinone‐sulfur dioxide complex in ethanol. The heat of decomposition of the solid hydroquinone‐sulfur dioxide clathrate compound was found, by Wynne‐Jones and Anderson, to be 14.2±0.1 kcal. These results demonstrate the importance of lattices in polar solvents.

Interaction between Sulfur Dioxide and Polar Molecules. III. Water‐Ethanol‐Sulfur Dioxide and Water‐Sulfur Dioxide Systems
View Description Hide DescriptionIt is shown that the temperature dependence of the ultraviolet absorption spectra for water‐sulfur dioxide solutions cannot be explained by the theories of Ley and Konig or Boyd‐Campbell and Maass. Qualitative arguments show that the mechanism, (SO_{2})_{gas}⇀lhdSO_{2}+H_{2}O⇀lhdcomplex⇀lhdH_{2}SO_{3}⇀lhdH^{+}+^{‐}HSO_{3}⇀lhd2H^{+}+^{‐2}SO_{3}, does explain the spectroscopic behavior of dilute sulfur dioxide solutions.
A linear relation is reported between the heat of solution, calculated from vapor pressure data, and the smallest effective molecular diameter of several gases.
Attempts to analyse the absorption spectra of the water‐ethanol‐sulfur dioxide solutions in terms of the separate systems, EtOH+SO_{2}⇀lhdcomplex_{1} and (SO_{2})_{gas}⇀lhdSO_{2}+H_{2}O⇀lhdcomplex_{2}⇀lhdH_{2}SO_{3}⇀lhdH^{+}+^{‐}HSO_{3} are reported. These results are explained by the new liquid lattice theory.

Microwave Spectrum and Barrier to Internal Rotation in CH_{3}BF_{2}
View Description Hide DescriptionThe microwave spectrum of CH_{3}BF_{2} has been observed in the frequency range 12–33 kmc. The identifiable lines are explained in terms of a model consisting of a symmetric top (CH_{3}) rotating with respect to an asymmetric framework (BF_{2}) with the top axis coinciding with the (least) principal inertial axis of the molecule. The value of the barrier to internal rotation was determined to be 13.77±0.03 cal. Three moments of inertia were also obtained from the analysis: A = 10586.73 (BF_{2} group only), B = 8329.01, C = 4650.52 Mc. These are insufficient to determine the molecular structure, but are consistent with the structure reported from electron diffraction.Stark effect measurements yield a dipole moment of 1.67±0.02 D.

Anomalous Centrifugal Distortion Coefficients in Linear Polyatomic Molecules
View Description Hide DescriptionThe theory of the effect of resonance, in particular Fermi resonance and l‐type resonance, on the effective centrifugal distortion coefficient of a molecule for a given vibration state is developed. The theory is applied to certain cases where l‐type resonance occurs and to certain cases where both l‐type resonance and Fermi resonance occur. No instances appear to have been investigated where Fermi resonance occurs without l‐type resonance being present. The agreement between the theory and the experimental results appears to be satisfactory to the approximation of the theory.

Relationship of the Second Virial Coefficient to Polymer Chain Dimensions and Interaction Parameters
View Description Hide DescriptionA useful approximation has been found for the excluded volume integral for the interaction of a pair of polymer molecules, represented by Gaussian distributions of chain segments about their respective centers of gravity. By means of this approximation, the theoretical expression for the second virial coefficient in the expansion of the osmotic pressure is represented over the entire range of polymer‐solvent interaction by X _{1} and X _{2} are related to the thermodynamic interaction parameters χ_{1} and χ_{2}, respectively, in the semiempirical expression for the solventchemical potential μ_{1}—μ_{1} ^{0}=RT[ln(1—v _{2})+(1–1/x)v _{2}+χ_{1} v _{2} ^{2}+ χ_{2} v _{2} ^{3}+···] where v _{2} is the volume fraction of polymer and x the ratio of molar volumes of polymer and solvent. Inclusion of the higher term χ_{2} v _{2} ^{3} (and X _{2}) constitutes a refinement over the treatment previously published. It is shown that the influence of X _{2} may be appreciable for low molecular weights and in poor solvents; its effect vanishes as the molecular weight becomes large. However, if X _{2}≠0, the temperature at which A _{2} for a given polymer‐solvent pair becomes zero will, in general, depend upon the molecular weight. The similar influence of this term on the expression for the intramolecular expansion factor is smaller, although not necessarily negligible.
Interaction parameters (χ_{1}) are calculated from second virial coefficients for a number of polymer‐solvent systems, and these are compared with the χ_{1} values obtained from intrinsic viscosities (intramolecular theory). The good agreement obtained offers strong evidence for the general validity of the intermolecular (A _{2}) and intramolecular theories.
A _{2} increases slightly more rapidly with decrease in M than theory predicts. On the whole, however, the consistency of results is gratifyingly good.
The intrinsic viscosity increases linearly with A _{2} M in poor solvents. This relation must be replaced by one of approximate direct proportionality in good solvents.

Calculation of the Surface Energies of Alkali Halide Crystals
View Description Hide DescriptionRapidly converging lattice sums for the electrostatic and van der Waals contributions to the surface energy of a generalized sodium chloride crystal have been derived. As special cases numerical values of these sums for the {100} and {110} faces of a NaCl‐type crystal and for the {110} face of a CsCl‐type crystal were computed. Surface energies for {100} faces of NaCl‐type alkali halides and for {110} faces of both NaCl‐and CsCl‐type alkali halides have been calculated.

Madelung Constants of Some Cubic Crystals
View Description Hide DescriptionA simple method for evaluating the Madelung constant of a CsCl‐type crystal is described. The Madelung constants of CaF_{2}‐type and ZnS‐type lattices are computed to ten decimal places from linear relations between the Madelung constants of these and NaCl‐ and CsCl‐type crystals.

Raman Spectrum of Triethylborane
View Description Hide DescriptionFrequency shifts and polarization data are reported for the Raman spectrum of liquid triethylborane, B(C_{2}H_{5})_{3}. By comparison with the spectra of trimethylborane and ethane, tentative assignments are made for most of the observed bands.