Volume 15, Issue 5, 01 May 1947

The Interpretation of Electron Diffraction Patterns from Hydrocarbon Films
View Description Hide DescriptionThe theoretical expressions previously derived for the scattering of electrons by oriented hydrocarbon chains have been extended and applied to the calculation of characteristic diffraction patterns. These patterns are analyzed to form a basis for obtaining information about the molecular orientation. For the long chain molecules, the azimuthal direction, and the declination from the vertical may be determined independently. The orientation of the hydrocarbon chain about its own axis is less easily established, since it is determined only from the intensity distribution within the separate diffraction orders. When the declination is sufficiently large, randomness in the azimuthal directions is distinguished by the crossed‐line pattern obtained. Randomness in the declination from the vertical may be estimated from the irregular spacing of the intercepts of the crossed lines. Quantitative intensity data would permit a more precise study of the angular distribution of the declination, and also of the orientation of the hydrocarbon chain about its own axis.

The Entropy of Solution of Molecules of Different Size
View Description Hide DescriptionThe entropy of mixing two liquids whose molecules differ in size is expressed in terms which avoid the assumption of a lattice as an artificial frame of reference, and which is not limited to linear polymers. The equation obtained iswhere N _{1} and N _{2} denote number of moles, V the volume of the solution, v_{1} and v_{2} the molal volumes of the pure components and b _{1} and b _{2} the sum of the actual geometrical volumes of 6×10^{23} molecules. With certain simplifying assumptions, equivalent to those used by authors who have analyzed the problem for linear polymers in a lattice frame of reference, the above equation reduces to the form obtained by the latter method. Various methods of obtaining experimental values for b are outlined.

Comments on the ``Hildebrand Rule''
View Description Hide DescriptionAccording to the ``Hildebrand rule,'' normal liquids should have the same entropy of vaporization at temperatures at which their vapors have the same molal volume. Pitzer has shown that liquids which obey the theory of corresponding states should have equal entropies of vaporization at temperatures at which their ratio of vapor volume to liquid volume is the same. He pointed out, however, that this rests upon several assumptions, including, ``potential energy depending only on intermolecular distances and universal shape of potential energy curve.'' In this paper, two pairs of liquids with widely different liquid molal volumes but otherwise closely similar, are compared with the result that the former rule is more closely obeyed, supporting the suggestion that it is an oversimplification to regard the molecular fields of polyatomic molecules as radial from the center of the molecule. The entropy of vaporization of a van der Waals liquid, R[1n(V—b)−1n(v—b)], where V refers to vapor and v to liquid, indicates that equal V and equal v—b should give equal entropy of vaporization. In comparing ethane and diisopropyl, for example, the separation of the methyl groups is more significant than the separation of the molecular centers.

Infra‐Red Spectra of Monomeric Formic Acid and Its Deuterated Forms. I. High Frequency Region
View Description Hide DescriptionThe hydrogen and deuterium stretching vibrations of the molecules HCOOH, HCOOD, DCOOH, and DCOOD have been studied with a high resolution echelette‐grating infrared spectrometer. From the rotational structure of these bands parameters which are functions of the moments of inertia have been calculated. From these parameters, previous data, and assumptions of the hydrogen bond distances and molecular planarity, the following dimensions of the molecule have been derived: O–H, 0.96±0.01A; C–H, 1.08±0.01A; C=O, 1.225±0.02A; C–O, 1.41±0.02A; O–C=O, 125±1°; C–O–H, 107±5°; H–C=O, 122±5°.

Infra‐Red Spectra of Monomeric Formic Acid and Its Deuterated Forms. II. Low Frequency Region (2200–800 cm^{−1})
View Description Hide DescriptionHigh resolution infra‐red studies have been made of monomeric HCOOH, HCOOD, DCOOH, and DCOOD in the region 2200 cm^{−1} to 800 cm^{−1}. Consideration is given to the possibility of the existence of a trans‐form of the molecule. The bands observed are not sufficiently regular in appearance or absorption frequency to permit assignment of vibrational modes without further knowledge of the spectra.

A Calculation of the Energy of Activation for the Racemization of 2,2′‐Dibromo−4,4′‐Dicarboxydiphenyl
View Description Hide DescriptionIn a recent article J. E. Mayer and the author presented a method of calculating the energy of activation for the racemization of optically active diphenyl derivatives from known force constants and from the van der Waals repulsion between ortho substituents. In the present paper, the calculation of this activation energy is carried through in detail for the racemization of 2–2′‐dibromo−4,4′‐dicarboxydiphenyl. The value obtained is 18 kcal./mole. The experimental value is not known, but the free energy of activation for the same process is 19.5 kcal./mole. In the discussion of probable errors, it is shown that the calculated energy of activation is unlikely to be in error by as much as 7 kcal./mole, and that the probable error is only about 4 kcal./mole. The racemization involves distorting the various angles and stretching the various bonds in the molecule, as well as forcing the ortho substituents to approach one another so that the distance between them is less than the sum of their van der Waals radii. In the present treatment, all these deflections and stretchings are computed; that is to say, an accurate model for the activated complex is obtained.

Calculation of Equilibrium Constants for Isotopic Exchange Reactions
View Description Hide DescriptionIt is pointed out that the possibility of chemical separation of isotopes is a quantum effect. This permits a direct calculation of the difference in the free energies of two isotopic molecules. Tables and approximation methods are given which permit a rapid calculation of equilibrium constants if the frequency shifts on isotopic substitution are known. Several applications are discussed.

A Raman Apparatus for Quantitative Polarization Measurements
View Description Hide DescriptionAn apparatus for quantiative measurement of the depolarization factors of Raman lines is described. It is a modification of Edsall and Wilson's method, using polaroid cylinders. Short exposure times result from the use of eight exciting lamps. No apparatus corrections are needed. Alignment is not overly critical. Performance is reported on the Raman lines of CCl_{4}, CHCl_{3}, and C_{6}H_{6}.

Heat‐Capacity Lag Measurements in Various Gases
View Description Hide DescriptionThe impact‐tube method of measuringrelaxation times for the transfer of molecular energy from translational to internal degrees of freedom has been introduced in a previous report. This method has been applied to a series of gases to make measurements of relaxation times which would be difficult to measure quantitatively by sonic methods. Measurements of the relaxation times of the vibrational energy of H_{2}O, N_{2}, N_{2} catalyzed by H_{2}O, and CCl_{2}F_{2} are presented. The existence of a measurable lag in the adjustment of the rotational heat capacity of H_{2} has been confirmed, and measurements of its relaxation time are presented.

A Relation Between Bond Order and Covalent Bond Distance
View Description Hide DescriptionA relation between covalent bond distance and bond order of the form is proposed and tested against the available experimental data. A suitable expression for all covalent bond distances between atoms of the first row of the periodic table of the form is also proposed. The agreement between calculated and observed values is well within the limits of the experimental errors.

The Mechanism of the Luminescence of Solids
View Description Hide DescriptionIn this paper, effort is directed toward explaining various diverse luminescent properties of solids in terms of a simple model of potential energy versus configuration coordinate. Three states of different multiplicities—a normal, metastable and an emitting state—are involved. The luminescent process consists of the excitation of an electron to the metastable level, the activated release of the electron to the emitting level, and a forbidden transition between the emitting and the ground state. With high excitation energy, the metastable state is bypassed. At high temperatures, the electron in the metastable state surmounts a larger potential barrier to undergo radiationless recombination with the activator atom.
Among those significant phenomena that have been measured experimentally and treated quantitatively by calculations based on this model are the temperature dependence of luminescent efficiency and the effect of type and wave‐length of excitation on this temperature dependence; the three types of phosphorescence—spontaneous, metastable, and recombination phosphorescence; the phenomena of two‐stage afterglow and the effect of type of excitation and temperature on the two stages; the relationship between buildup and afterglow kinetics; and the release of electrons from metastable states by thermal energy. The concept of the Absolute Rate theory are used to clear up the essential criteria for the different types of afterglow.
A detailed theoretical analysis of ``glow curves'' is presented and quantitatively applied to improved glow curves obtained at linear rates of heating 100 times slower than those previously reported. The slower rates of heating allow one metastable level to be operative at a time. Both monomolecular and bimolecular mechanisms are treated, and it is concluded that glow curves result from discrete metastable states that are emptied thermally by predominantly monomolecular kinetics. The explicit expressions for the specific rate constants involved in the release of electrons from metastable states are calculated.

Dependence of Bond Order and of Bond Energy Upon Bond Length
View Description Hide DescriptionA simple inverse square relation of the form,(where N is the bond order, R is the bond length, and a and b are constants characteristic of any given pair of atoms) has been found to agree satisfactorily with the available values for bond orders. For CC bondsa and b are found to have the values 6.80 and −1.71, respectively; for CN they are 6.48 and −2.00; for CO they are 5.75 and −1.85. The available data on bond energies suggest a relation of the same form,between bond energy E and bond length R, where l and m represent the characteristic constants of a given atomic pair.

The Effect of High Mechanical Stress on Certain Solid Explosives
View Description Hide DescriptionEleven different solid explosives have been subjected at room temperature to stresses of the order of those which prevail in the detonating front. Two types of stress were applied. The first consisted of a hydrostatic pressure of 50,000 kg/cm^{2}, on which was superposed a shearing stress sufficient to produce shearing deformations of the order of 60 radians. The second type consisted of a hydrostatic pressure of 100,000 kg/cm^{2}, with a comparatively small superposed shearing deformation. Seven of the eleven explosives survived stress of the first type without detonation. Only four of the explosives were subjected to the second type of stress; three of these survived without detonation. It is probable that in those cases where detonation occurred secondary effects were responsible, such as striking of sparks by fractured fragments of steel. The general conclusion is drawn that stresses of these magnitudes, without the cooperation of high temperature, cannot be counted on to produce detonation.
Incidentally it was found that yellow ammonium picrate is transformed irreversibly to the red form by the first type of stress. Values were obtained for the plastic flow stress as a function of hydrostatic pressure. The strength increases approximately linearly with pressure.

On the Behavior of Pure Substances Near the Critical Point
View Description Hide DescriptionIt has been suggested several times that the phenomena of condensation could be understood by considering the vapor as a system in which molecules are associating into clusters, these obeying the ordinary laws of equilibrium. One can also consider the liquid as a system in which bubbles of vapor are forming. The present paper attempts to apply these ideas to phenomena occurring in the neighborhood of the critical point. Only thermodynamic methods are used, in conjunction with some general assumptions concerning the properties of the molecules involved. Some aspects of the surface tension of the liquid near the critical point have been considered in some detail. The highest temperature T_{m} at which a meniscus can exist is assumed to be the temperature at which the surface tension vanishes at the same time that the condition for equilibrium between liquid and vapor phases is fulfilled. It is concluded that the pressure‐volume isotherm at T_{m} has a finite horizontal region, corresponding to the squeezing out of surface when the surface tension is zero. The slope of the isotherm at T_{m} in the vapor region outside the horizontal portion is closely related to the slope in the liquid region just to the other side of the horizontal part; these slopes approach zero as the flat part is approached. Above T_{m} there is still a process which may be called condensation, but no horizontal part to the isotherms. This is in contradiction to conclusions reached by Mayer and Harrison on the basis of their statistical theory of condensation, but is apparently not in real contradiction to the theory.

The Effect of Pressure on Surface Tension
View Description Hide DescriptionThe thermodynamic formula for the change of surface tension with pressure is interpreted for a one‐component system and for a two‐component system consisting of an inert gas over a liquid. In the latter case the effect of pressure on surface tension can be attributed in part to absorption of gas at the surface of the liquid and in part to an intrinsic decrease in density of the liquid in the neighborhood of the surface. The equations are interpreted in terms of the Gibbs adsorption isotherm. The adsorption of gas at the liquid surface has been estimated in several cases from data in the literature.
 LETTERS TO THE EDITOR


Chemisorption of Gases
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Errata: On the Dissociation Energies of CO, N_{2}, NO, and CN
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Molecular Association in Hydrogen Fluoride Vapor
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The Mechanism of Nitrogen Pentoxide Decomposition
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The Detection of Radioactive Persulfate Fragments in Emulsion Polymerized Styrene
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