Volume 10, Issue 8, 01 August 1942

Gas Imperfections Determined from the Heat of Vaporization and Vapor Pressure
View Description Hide DescriptionThe imperfections of many gases may be obtained by combining available heats of vaporization and vapor pressure data with the Clausius‐Clapeyron equation. The accuracy of this method in some cases is comparable to that of good direct P.V.T. measurements and therefore may be useful in preliminary investigations. If P is the vapor pressure,T is the absolute temperature, ΔH is the heat of vaporization,V and V_{l} are the molal volumes of the vapor and liquid phases:This equation determines the gas imperfection β. The value of β calculated in this manner is compared with experimental second virial coefficients for H_{2}O, NH_{3}, H_{2}, O_{2}, A, CH_{4}, propane,n‐butane, n‐heptane, ethene, propene, CH_{3}Cl, CCl_{3}F, CH_{3}OH, C_{6}H_{6}, and Hg. Values of β are determined for HI, HBr, HCl, CH_{3}NH_{2}, (CH_{3})_{2}NH, HCN, isobutane, tetramethylmethane, 2,2,4, trimethylpentane, C_{2}N_{2}, COS, PH_{3}, H_{2}S, CH_{3}Br, and C_{2}H_{5}OH. Evidence of hydrogen bondformation is shown for CH_{3}OH, C_{2}H_{5}OH, CH_{3}NH_{2}, and (CH_{3})_{2}NH. It is shown that HI and HCN contain a considerable fraction of instantaneously formed double molecules. The gas imperfection of benzene is perfectly normal. The number of instantaneously formed double molecules is estimated for all of the above molecular species.

The Photolysis of Dimethylhydrazine
View Description Hide DescriptionThe ultraviolet absorptionspectrum of dimethylhydrazine has been shown to exhibit a continuum extending from 2800A to beyond 2000A. Despite the absence of structure the continuum is probably experimental and indicates predissociation. The photolysis using various light sources, at several pressures and wave‐lengths, has been studied. The over‐all quantum yield is 0.3. The principal initial rupture of the molecule involves the scission of a hydrogen atom. Analytically three molecules of the hydrazine give one molecule each of and The low quantum yield is accounted for by addition of hydrogen to the radical produced in the initial split.

The Diffraction of X‐Rays by Liquid Oxygen
View Description Hide DescriptionThe x‐ray diffraction pattern of liquid oxygen at 89°K shows an intense peak at sin θ/λ = 0.157, and very weak peaks at 0.35 and at 0.5; that at 62°K shows an intense peak at 0.159, and weak peaks at 0.35 and at 0.5. The atomic distribution curves have peaks at 1.3A, 2.2A, 3.4A, and 4.2A for 89°K, and at 1.25A, 2.15A, 3.2A, and 4.1A for 62°K. The first peaks are due to the interatomic distance in the diatomic molecule, the second may be due to triatomic oxygen, and the others may be due to higher molecular aggregates.

On the Absorption Spectrum of Some Polymethine Dyes
View Description Hide DescriptionThe energy levels of certain polymethine dyes are calculated approximately. The dyes consist of a chain of conjugated double bonds, with end groups which might or might not differ from each other. Ions and neutral molecules are treated. The calculations are performed both with the valence bond method (resonance between different structures) and the LCAO method, but without antisymmetrization and without taking electronic interaction into account. The effect of chain length and of the nature of the end groups is discussed.

Energy Levels and Color of Polymethine Dyes
View Description Hide DescriptionThe secular determinant for the energy levels of the unsaturation electrons of a polymethine dye is discussed in both HLSP and LCAO approximations. The roots of the secular determinant, which were obtained in the preceding paper by Herzfeld, are applied to a discussion of the longest wave‐length electronic band of symmetrical and unsymmetrical polymethines. The LCAO approximation gives good numerical values for the dependence of both the transition energy and oscillator strength on the length of the polymethine chain in symmetrical dyes, but cannot handle the questions which depend sensitively on a small difference between the groups attached to the two nitrogen atoms at the extreme ends of the chain. Although the HLSP method yields correct qualitative results for symmetrical dyes, it does not give good numerical values. The HLSP method, however, is sensitive to a difference between the two ends of the dye molecule and affords a simple explanation for a number of properties in which unsymmetrical dyes differ from symmetrical ones.

A Practical Method for the Solution of Certain Problems in Quantum Mechanics by Successive Removal of Terms from the Hamiltonian by Contact Transformations of the Dynamical Variables Part I. General Theory
View Description Hide DescriptionProblems in quantum mechanics may be solved by canonical change of the representation in terms of which the dynamical variables are expressed. They may also be solved by contact transformations of the dynamical variables. The usual notation is modified slightly to make it more convenient for developing these two methods. Their parallel development shows their essential equivalence but formal difference.

A Practical Method for the Solution of Certain Problems in Quantum Mechanics by Successive Removal of Terms from the Hamiltonian by Contact Transformations of the Dynamical Variables Part II. Power Series in a Coordinate and Its Conjugate Momentum. The Anharmonic Oscillator by Perturbation Theory
View Description Hide DescriptionThe non‐commutative algebra of polynomials in a coordinate and its conjugate momentum is reduced to common algebra by Weyl's method, and tables are given for facilitating its use. It is shown how the problem of the anharmonic oscillator can be solved by contact transformations, and tables are given for removing terms up to the third degree in its coordinate and momentum and for finding the modified Hamiltonian up to the fourth degree, which is as far as is ordinarily required in molecular theory. To illustrate the power of the method, the energy is computed up to terms of the eighth degree for energy containing terms to that degree (in the coordinate only), obtaining Dunham's result together with the constant terms of that order not given by him.

Statistical Distribution Laws for Rate Processes
View Description Hide DescriptionA re‐examination of the fundamental hypotheses of statistical mechanics shows that the principle of the most probable distribution may be interpreted in such a way as to be applicable as well to systems which are not at equilibrium. The general method of deriving distribution laws for systems not at equilibrium is outlined. The use of this method is illustrated by deriving a general distribution law for systems in which the velocities are required to be non‐Maxwellian. The distribution of velocities of molecules in any group having a specified average velocity is Maxwellian relative to the group average velocity. The average total energy of such a system is shown to be the sum of the kinetic energies of mass motion of the several groups of molecules plus the Maxwellian average energy corresponding to the given volume and temperature.

Statistical Distribution Laws for Rate Processes 2. Non‐Uniform Distributions
View Description Hide DescriptionThe methods developed in the previous paper are used to determine the most general form of statistical distribution law suitable for the treatment of rate processes. The result is particularly applicable to relatively dense systems composed of soft molecules. It is based on the assumptions that each variable whose rate of change is to be measured must be statistically reproducible at all times, and that the molecular motions are not seriously discontinuous. Various special forms of the distribution law result from different ways of expressing the rate variables and experimental conditions. One form is derived for the case in which the rates of change of the average position and kinetic energies of the molecules are to be reproducible. Qualitatively, it agrees with the known frequent behavior of rate experiments, showing frictional dissipation of energy, and the tendency to return to equilibrium. Furthermore, it reduces to the classical distribution law under equilibrium conditions.
 LETTER TO THE EDITOR


The Structure of Substituted Ethylenes and Their Isomerization Polymerization and ``Peroxide Addition'' Reactions
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