Volume 10, Issue 7, 01 July 1942

Valence and Central Forces in Bent Symmetrical XY_{2} Molecules
View Description Hide DescriptionAppropriate generalized coordinates and potential functions are set up for studying the zero‐ and first‐order vibration problem of the best symmetrical XY_{2} molecular model under the assumption of valence and central forces. The force constants in the quadratic and cubic parts of the potential function of the water vapor molecule are evaluated for these two types of forces by using the data of Darling and Dennison.

Electronic Structure and Stability of Hydrogen Halides and of Complex Ions XO_{4}
View Description Hide Description(1) It is shown that in the hydrogen halide molecules (internuclear distance r _{0}) the proton penetrates the electronic shell of the anion to a depth which for the simplified case of spherical symmetry can be characterized by the condition: The amount of negative charge beyond the sphere of radius r _{0} equals −1e. (2) From the dipole moments μ=xer _{0} of the hydrogen halide molecules it can be concluded: The wave mechanical distribution of the negative charge of the free halide ions is changed by the introduction of the proton in such a way that the center of gravity of an amount of charge equal to —(1−x)e is shifted from the halogen nucleus to the proton. The fraction (1—x) increases with the electronic polarizability of the anion, and would be equal to 1 for an ion of infinitely large polarizability, leading to a completely unpolar type of binding in this case. (3) It is shown that for the complex ions SiO_{4} ^{4—}, PO_{4} ^{3—}, SO_{4} ^{=}, and ClO_{4} ^{−}, the gradation of the X–O distances and of the molar dispersion can be easily understood from the point of view used in 1924 for the case of the molar refraction: These ions represent the result of the polarization of O^{=} by Si^{4+}, P^{5+}, S^{6+}, and Cl^{7+}, and the X–O binding in them shows gradual changes toward the unpolar type. (4) It is pointed out that the relatively unstable HI and ClO_{4} ^{−} approach the unpolar type of binding more closely than any other of the compounds considered here. The generalization of this connection between instability and the degree of deformation of electronic shells explains why compounds like FO_{4} ^{−} and BrO_{4} ^{−} are unknown.

Polarization of Light Scattered by Isotropic Opalescent Media
View Description Hide DescriptionA general study is given of the polarization of light scattered by isotropic media whose elements of heterogeneity are not very small in comparison with the wavelength, (suspensions,colloidal solutions, solutions of large molecules, ...). This includes an extension of a theory by R. S. Krishnan, who, considering certain particular states of polarization of the incident light and applying the law of reciprocity, had proved the equality of two of the four coefficients which are to be considered in these cases. Using Stokes' linear representation of the polarization of light beams, it is shown that the scattering through a given angle and for a given wave‐length is characterized by the 16 coefficients of the linear forms which express the four polarization parameters of the scatteredbeam in terms of the four corresponding parameters of the incident beam and that the law of reciprocity leads to six relations between these sixteen coefficients. For an isotropic asymmetrical medium (having rotatory power), the scattering is thus characterized by ten independent coefficients. In the case of a symmetrical medium, four of these coefficients must be zero, leaving only sixscattering coefficients, and if the scattering particles are spherical, there are two additional relations between these coefficients. The comparison with dipolar scattering by very small elements shows that the best test to prove multipolar scattering is the existence of some ellipticity in the scattered light when the incident beam is linearly polarized in a direction oblique to the scattering plane.

Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops
View Description Hide DescriptionA general treatment of internal rotation is given for molecules whose moments of inertia for over‐all rotation are independent of internal rotational coordinates. Tables are presented for the various thermodynamic functions which are accurate for molecules with one internal rotation and for the potential energy (V/2) (1 — cos nφ). The tables are shown to be a good approximation for molecules with several internal rotational coordinates, provided the potential energy can be expressed as a sum of terms of this type. Methods are suggested for treating problems where cross terms involving more than one internal coordinate are present in the potential energy. The energy level expressions are developed for the more general case with the potential energy expressed by a Fourier series. Although a few specific cases were worked out with different shape potential barriers, it appears that the simple form assumed above will be satisfactory for many purposes.

The Effect of Intermittent Light on a Chain Reaction with Bimolecular and Unimolecular Chain‐Breaking Steps
View Description Hide DescriptionThe effect of intermittent light, as produced by a rotating sector, has been considered for a chain reaction having the following mechanism:It has been shown how to calculate the reaction rate as a function of the sector speed for different values of a certain parameter which depends on the individual rate constants and the light intensity and gives, essentially, the relative importance of the bimolecular and unimolecular chain‐breaking steps. The relationships have been exhibited graphically for the case in which one‐fourth of the sector passes the light beam. These relationships may be reversed, making it possible to obtain the rate constants of the intermediate reactions from measurements with intermittent light.

The Chain Photolysis of Acetaldehyde in Intermittent Light
View Description Hide Description(1) By comparison of the data on the photochemical decomposition and the azomethane‐induced decomposition of acetaldehyde vapor, it has been concluded that the chain‐carrying steps in the two cases are different. For the photolysis the following mechanism is suggested:(There are possibly other chain‐ending steps similar to reaction (3)). (2) Experiments have been performed using intermittent light at 200° and 300°. As a result of these experiments, estimates have been made for the individual rate constants,k _{2}, k _{3}, and k _{4}, and it has been found that the activation energies are 2.6, 11.3, and 7.8 kcal., respectively. (3) It has been found that k _{2} and k _{3} check closely with the collision number multiplied by the appropriate Arrhenius factor. There is little or no evidence of necessity for mutual orientation of the molecules. The significance of this has been discussed. Reaction (4) probably takes place at the walls, and the value of k _{4} is of the same order of magnitude as the fraction of the molecules hitting the walls per second, times the appropriate Arrhenius factor. (4) The extent of and effect of diffusion of radicals beyond the illuminated region have been considered.

The Effect of Electrical Forces on the Stability of Colloidal Sols
View Description Hide DescriptionIt is assumed that the stabilizing potential in a sol is not the potential at a distance t from the surface of the particle, (ζ), but the potential at a distance l, (λ). l is the distance from the solid surface at which a maximum in the potential energy curve determines the rate of coagulation, and λ is a constant for a given sol in states of equal stability. The quantities l—t and λ are evaluated from experimental data.

Variation of Reaction Mechanism with Surface Conditions in the Reduction of Silver Salts by Hydroxylamine
View Description Hide DescriptionSilver bromide oxidizes hydroxylamine at pH 10.2–10.8 to nitrogen and water. Under comparable conditions, silver thiocyanate yields a mixture of nitrogen and nitrous oxide as the gaseous products. By varying the surface conditions of the thiocyanate, the composition of the reaction product may be varied over a wide range. Small additions of bromide or iodide greatly decrease the nitrous oxide yield. With initial partial coverage of the precipitate surface by gelatin, the nitrous oxide yield increases to a maximum. Further gelatin additions progressively decrease the yield. Aging a fresh precipitate increases the nitrous oxide yield. The results are explained by the effects of adsorption upon the relative rates of two competing reaction mechanisms.

Efficiency of the Electrolytic Separation of Chlorine Isotopes
View Description Hide DescriptionThe electrolytic separation coefficient α has been determined for the chlorine isotope separation in the electrolysis of sodium chloride solutions at a platinumanode. Flotation of purified NaCl crystals in ethylene dibromide was employed as the analytical procedure in determining the isotopic composition of samples. Densities of the ethylene dibromide as a function of temperature were separately determined. The electrolytic separation factor for Cl isotopes was found to be 1.0060±0.0005 for the temperature range 25° to 40°C. No significant dependence on either temperature or current density was observed. The coefficient on platinum (1.0060±0.0005) agrees with the value on Acheson graphite (1.0068±0.0014) which may be computed from the data of Yacouban.

The Second Virial Coefficient for Gas Mixtures
View Description Hide DescriptionThe second virial coefficients B for methane, normal butane, and three mixtures of these gases were evaluated from the experimental data, and the interaction term B _{12} computed for methane‐n‐butane from 150° to 300°C. The results were used to study the methods of combination of constants in an equation of state. Computation of B _{12} from a Lennard‐Jones expression similar to that used for a pure gas with σ and θ evaluated as σ_{12}=½(σ_{11}+σ_{22}) and θ_{12}=θ_{11} ^{½}θ_{22} ^{½} where the subscripts 1 and 2 refer to the pure components gave exceptionally good results. This suggested a new method of combination of constants in the equation of state which led to the best results of any method so far used.

Determination of the Lennard‐Jones Parameters from Second Virial Coefficients Tabulation of the Second Virial Coefficient
View Description Hide DescriptionValues of B/(2πNσ^{3}/3) to four decimal places as a function of θ/T are computed from θ/T=0.20 to 1.00 for a Lennard‐Jones (6, 12) potential. The equation B/(2πNσ^{3}/3) = (θ/T)^{¼}[1.064–3.602(θ/T)] computes the tabulated values fairly well. Thus σ and θ can be determined from experimental B values by plotting BT ^{¼} against 1/T and finding the slope and intercept of the best straight line through the points. For methane and n‐butane this method gave parameters that computed B values agreeing with observed values within the experimental uncertainty.

The Electrostatic Influence of Substituents on Reaction Rates III. Solvent Effect
View Description Hide DescriptionThe magnitude of the electrostatic effect of substituents on reaction velocity depends on the solvent in which the reaction is carried out. In order to investigate the influence of solvent, the first and second saponification constants of diethyl malonate and diethyl adipate have been measured, both in water and in 80‐percent alcohol, in solutions of varying ionic strength. The saponification constants have been extrapolated to infinite dilution. The ratio of the first to the second velocity constant at infinite dilution in any one solvent is a measure of the effect of a charged substituent on the rate of saponification. The results obtained in water are compared with those for 80‐percent alcohol, and it has been shown that they are in good qualitative agreement and in fair quantitative agreement with the predictions of the Kirkwood‐Westheimer theory.

Statistical Thermodynamics of Rubber. II
View Description Hide DescriptionThe statistical theory of rubberelasticity is extended by postulating that the total volume of a piece of rubber remains constant during a stretching process. The modified theory is found to be in better agreement with observation than any previous molecular theory. In addition, it is shown theoretically that rubber should obey Hooke's law with respect to shear.
 LETTERS TO THE EDITOR


Atomic Weight Comparisons from Density and X‐Ray Data: Fluorine, Calcium, and Carbon
View Description Hide Description 
Heat of Dissociation of Cyanogen
View Description Hide Description
