Volume 20, Issue 1, 01 January 1952

The Microwave Spectrum of a Slightly Aspherical Top—The Structure and Dipole Moment of Sulfuryl Fluoride
View Description Hide DescriptionThe microwave spectrum of the slightly aspherical rotor, sulfuryl fluoride, has been investigated. Seven lines were found in the twenty to thirty thousand megacycle region. Six of these lines were assigned to J=1→2 and 2→3 rotational transitions of the molecule S^{32}O_{2}F_{2} and the other to the 1_{11}→2_{12} transition of S^{34}O_{2}F_{2}. These lines can be fitted to within the limits of experimental error (0.002 percent) with the following reciprocal moments of inertia:
Structural parameters were determined from these moments and the assumption of C _{2v } symmetry. The latter was confirmed by intensity measurements.The S–O distance differs by −0.06A from the published electron diffraction value.
Measurements on stark lobes of the three 1→2 transitions of S^{32}O_{2}F_{2} gave a quantitative check of the assignment and a value of 0.228 Debye units for the dipole moment.

Diffusion through an Interface—Binary System
View Description Hide DescriptionDiffusion measurements have been made between saturated layers in the system SO_{2}—n‐heptane, using S^{35} tagged SO_{2} as a radioactive tracer. The results are evaluated in terms of the interfacial transfer coefficient α introduced in a previous paper. The resistance in the interface is significant compared with the resistance to ordinary diffusion, even within 4°C of the critical solution temperature.

Diffusion through an Interface—Ternary Systems
View Description Hide DescriptionDiffusion measurements have been made at 22°C and at 40°C in the system phenol‐H_{2}SO_{4}‐water, using S^{35} tagged H_{2}SO_{4} as a radioactive tracer. Measurements made through the interface indicate that a significant resistance resides in the interface at both temperatures, and that the solution chemistry of the system must be quite complex. The relation of the results to practical mass transfer problems is briefly discussed.

Diffusion in Indium Near the Melting Point
View Description Hide DescriptionDiffusion coefficients for the systems Tl^{204}–In and In^{114}–In have been measured in the solid state and in the neighborhood of the melting point. The measurements were made in both polycrystalline masses and in single crystals. For the polycrystalline samples a rapid, but not discontinuous, rise in the diffusion co‐efficient occurred about 0.5°C below the melting point. For the Tl^{204}–In system in a single crystal the rise in D occurs just below the melting point. This indicates grain boundary melting in the polycrystalline sample. For the In^{114}–In diffusion in a single crystal the rapid rise still occurred well below the melting point, indicating that increasing lattice disorder also contributes to the increase in D.

Transition Probabilities. II. Calculation of Semi‐Theoretical f‐Numbers for Hydrogen Using the Dipole Velocity Operator
View Description Hide DescriptionThe computations of Mulliken and Rieke using the LCAO MO and the AO methods for transition probabilities of the Lyman (^{1}Σ_{ g } ^{+}—^{1}Σ_{ u } ^{+}) and Werner (^{1}Σ_{ g } ^{+}—^{1}π_{ u }) transitions in hydrogen have been repeated using the alternative velocity form of the transition moment operator. It is found that, for an effective Z value of 1.2 for the 1s AO (the variation value) and a suitable Rydberg form for the excited state, the transition probabilities calculated from these two operators agree well. In addition there is quite good agreement between the AO and MO methods in each instance and between the calculated and experimental value for the sum of the strengths of the Lyman and Werner transitions.

Kinetics of Decomposition of Nitric Oxide at Elevated Temperatures. I. Rate Measurements in a Quartz Vessel
View Description Hide DescriptionThe rate of thermal decomposition of nitric oxide has been measured in a quartz vessel from 872 to 1275°K. The reaction follows a second‐order rate law over the range of temperatures studied. Variations in the surface‐to‐volume ratio of the reaction vessel indicate the predominance of a heterogeneous mechanism at temperatures below 1000°K, whereas at higher temperatures a homogeneous mechanism prevails. The experimental data are interpreted on the basis of the relative contribution of the heterogeneous and homogeneous mechanisms to the over‐all kinetics. Such an analysis explains the variation in effective activation energy with temperature from a value of 21.4 kcal below 1000°K to 82 kcal above 1600°K. An intermediate temperature region exists in which both mechanisms contribute an important part to the over‐all rate.

Decomposition of Di‐t‐butyl Peroxide and Kinetics of the Gas Phase Reaction of t‐butoxy Radicals in the Presence of Ethylenimine
View Description Hide DescriptionThe reaction of di‐t‐butyl peroxide with ethylenimine has been studied between 129° and 154°C. The t‐butoxy radicals formed by the rupture of the O–O bond of the peroxide,are postulated to enter into the following reactions:The rate constant for the unimolecular decomposition of the peroxide into t‐butoxy radicals is found to be in the range k _{1}=6×10^{14} e ^{−36,000/RT } to k _{1}=6×10^{16} e ^{−40,000/RT } sec^{−1}. The activation energiesE _{4}—E _{3}/2=4.8 kcal/mole and E _{2}—E _{5}=12 kcal/mole are calculated from the kinetic data. The complete rate expression for the capture of imine H atom by CH_{3} radical,is obtained by using Gomer and Kistiakowsky's values for k _{3}=4.5×10^{13} (moles/cc)^{−1} sec^{−1} and E _{3}=0. The activation energy for the thermal decomposition of t‐butoxy radical is about 17 kcal/mole if E _{4} and E _{5} of similar type H capture mechanisms are assumed equal.

Bond Orbitals and Bond Energy in Elementary Phosphorus
View Description Hide DescriptionA discussion of the relative stability of the P_{4} molecule and black phosphorus is carried out, with use of hybrid spd bond orbitals. The amount of strain in the P_{4} molecule, in which the bond angles are 60°, is calculated to be 22.8 kcal mole^{−1}. This value is shown to be compatible with thermochemical data; it corresponds to the value 51.3 kcal mole^{−1} for the bond energy of the normal P–P bond. A structure is proposed for red phosphorus and other allotropic forms of the element, and some of their properties are discussed in relation to their structure.

Nuclear Quadrupole Effects and Electronic Structure of Molecules in the Solid State
View Description Hide DescriptionMeasured nuclear quadrupole effects in solids are discussed, compared with nuclear quadrupole coupling in gases, and correlated to some extent with molecular structure in the solid state. The iodine crystal affords a good example of intermolecular interactions in the solid state. In this crystal, nuclear quadrupole effects combined with crystallographic information show two intermolecular covalent bonds per atom, each of about 9 percent importance.

The Interlayer Binding in Graphite
View Description Hide DescriptionThe repulsive energy between layers of the graphite crystal has been calculated as an interaction of LCAO molecular orbitals in the layers. The van der Waals attractive term was found by setting the energy minimum to fall at 3.37A. When values of the effective nuclear charge and effective quantum number proposed by Kohlrausch were used, the interlayer binding energy was found to be 3.99 kcal/mole. The compressibility, calculated under plausible assumptions, is in satisfactory agreement with the experimental value.

Application of the Cell Method to the Statistical Thermodynamics of Solutions
View Description Hide DescriptionThe cell method for pure liquids in the form used by Lennard‐Jones and Devonshire is extended to solutions. It is assumed that (a) the constituents are spherical in shape, with an isotropic field of force, (b) the distance of the maximum interaction for AA, BB, and AB pairs is about the same, and (c) there is random mixing.
For the mean field in the ``cage,'' the complete 6–12 law, the harmonic oscillator, and the smoothed potential model have been studied. The smoothed potential model (potential curve with vertical walls and flat bottom, both depth and width depending on concentration) fits the liquid state best. For this model, one obtains important corrections on both the heat of mixing and the excess entropy to the classical, strictly regular solutions. These corrections are related to the volume changes on mixing resulting from the changes of interactions.
According to the value of ε_{ AB } ^{*}, the excess properties such as volume, entropy, heat of mixing, and free energy present a large variety of shapes, including dissymmetry and inversions which correspond rather nicely to experimental evidence.
This model permits discussion of the severe limitations of Longuet‐Higgins's recent theory of conformal solutions.

A Study of Selection Rules for Vibrational Spectra of Complex Crystals
View Description Hide DescriptionRelations are obtained for the expression of the dipole moment and polarizability matrices for a particular transition in a crystal, in terms of corresponding expressions for molecular or ionic groups within the crystal. The results show that, to the degree of approximation used (quadratic terms in the dipole moment or polarizability expansion and cubic terms in the potential energy), the only cause for the appearance of bands which would be forbidden for a given uncoupled complex ionic or molecular group is the alteration of the normal coordinates of these groups by vibrations of neighboring groups. It is also shown that the bands of fully allowed first overtones and binary combinations of frequencies that are not degenerate or near‐degenerate in a unit cell have a shape that is approximately given from the distributions of frequencies that arise from lattice coupling.
As an incidental result, the dipole moment matrix elements for the first overtones and binary combinations arising from the cubic terms in the potential energy are given explicitly.

The Structure of the Tetrachloroethylene Molecule
View Description Hide DescriptionThe equilibrium distances and average amplitudes of vibration have been determined for the molecule C_{2}Cl_{4} by the analysis of quantitative electron diffraction data. The results are listed in Table II.

An Electron Diffraction Investigation of Cyclooctatetraene and Benzene
View Description Hide DescriptionThe interatomic distances and their vibrational amplitudes have been determined for C_{8}H_{8} and C_{6}H_{6} by quantitative analysis of electron diffraction sector photographs. The D_{2d } tub configuration, with the oblique C–C bonds longer than the horizontal ones, has been confirmed for C_{8}H_{8}. The interatomic distances involving hydrogen atoms have been evaluated.

Collisional Perturbation of Spin‐Orbital Coupling and the Mechanism of Fluorescence Quenching. A Visual Demonstration of the Perturbation
View Description Hide DescriptionA yellow color is produced when two colorless pure liquids, α‐chloronaphthalene and ethyl iodide, are mixed, although no chemical reaction occurs. Spectroscopic examination reveals that the lowest singlet→triplet absorption band of the naphthalene molecule is greatly enhanced in intensity in the presence of the iodide, and that the development of this absorption band is responsible for the color effect. The process is interpreted in terms of a collisional perturbation of spin‐orbital coupling in the π‐electron orbitals of the naphthalene. The significance of this phenomenon in several topics in spectroscopy and chemistry is discussed. In particular, the molecular mechanism of heavy atom quenching of fluorescence by foreign species is resolved. A novel Beer's law anomaly is predicted for intercombinations.

On the Free Energy of a Mixture of Ions: An Extension of Kramers' Theory
View Description Hide DescriptionA theory of electrolytes founded on the principles of statistical mechanics is presented. The primary physical assumptions are: (1) point ions, and (2) small fluctuations. The theory is a modification of Kramers' theory of electrolytes. The modification consists of a more physically accurate development of assumption (2). The main result of the present theory is that a partition function for the electrolyte is obtained for all concentrations, whereas Kramers' theory breaks down beyond a limiting concentration. The deviation from the Debye‐Hueckel limiting law is in the direction of the experimental observations.

Macro‐Ions. I. Light Scattering Theory and Experiments with Bovine Serum Albumin
View Description Hide DescriptionThe theory of light scattering is extended to include solutions of macro‐ion salts such as charged proteins and polymericelectrolytes.Equations for the angular intensity distribution are obtained for three types of interaction potential: (1) that of rigid, non‐interacting spheres, (2) an electrostatic potential consistent with the Verwey‐Overbeek theory, and (3) a simple Gaussian‐type repulsion. Because the repulsive forces between the macro‐ions are generally strong and long range, the concentration and angular distribution of the scattering may be very pronounced. Two unique and important extremes exist. If the concentration of the macro‐ion salt is altered without introducing additional electrolytes, the effective diameter of the macro‐ion is inversely proportional to the cube root of the concentration. In this situation the essential features of the scattering are quite novel. First, the reciprocal reduced intensity rises steeply from the intercept at zero concentration, bends over and becomes nearly horizontal at moderate concentrations, and second, the dissymmetry falls sharply from the limiting value at zero concentration, passes through a minimum and rises slowly at higher concentrations. With small particles the dissymmetry is always less than unity. In experiments with bovine serum albumin carrying charges up to 50 protons, all of these features have been found and can be accounted for at least semiquantitatively. The second unique case is that occurring when the concentration is altered by isoionic dilution which keeps the effective diameter of the macro‐ion constant. Since it is shown that in the scattering problems the difference between the hard sphere and electrostatic potential is relatively minor, the virial coefficients of Boltzmann can be used to describe the concentration dependence of the absolute intensity of scattering. This procedure permits, in contrast to the previous case, a precise evaluation of the effective ionic diameter. The values so obtained are compared with estimates from the Debye‐Huckel theory. As a consequence of these investigations, it appears that both the thermodynamic behavior and diffraction behavior of macro‐ion solutions are consistent with a relatively simple electrostatic picture.

Rotation‐Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths VII. The Spectrum of Dideuteroacetylene (C_{2}D_{2}) in the Photographic Infrared
View Description Hide DescriptionTwelve absorption bands of C_{2}D_{2} have been observed in the photographic infrared. Eleven of these bands show simple P and R branches with intensity alternation, i.e., they are Σ_{ u } ^{+}—Σ_{ g } ^{+} bands while one band, without intensity alternation, is a difference band of type Π—Π. From the positions of the bands some of the vibrational constants ω_{ i } ^{0} and x_{ik} are determined. In addition, from the rotational fine structure, the rotational constantsB _{[v]} and D _{[v]} are determined. For B _{[0]} the value 0.8478_{7} cm^{−1} is obtained. The α_{ i } values are α_{1}=+0.0057_{8}, α_{2}=+0.0030_{2}, α_{3}=+0.0045_{5}, α_{4}=−0.0012_{0}, α_{5}=−0.0026 cm^{−1}. From the α_{ i } and B _{[0]} one obtains B_{e} =0.8507_{5} cm^{−1}. Combining B_{e} (C_{2}D_{2}) with B_{e} (C_{2}H_{2}) yields, for the internuclear distances in the acetylene molecule, r_{e} (C≡C)=1.201_{0}×10^{−8} and r_{e} (C–H)=1.063_{7}×10^{−8} cm in very satisfactory agreement with the values previously obtained from B_{e} (C_{2}HD) and B_{e} (C_{2}H_{2}). Evidence for l‐type doubling in C_{2}D_{2} is given and approximate values for the l‐type doubling constants q _{4} and q _{5} are obtained.

l‐Type Doubling in Energy Levels of Carbon Dioxide Coupled by Fermi Resonance
View Description Hide DescriptionIn this paper we discuss the l‐type doubling in levels of linear molecules which are coupled by Fermi resonance; in particular we consider here a triad of such levels in carbon dioxide. In principle, it becomes necessary to consider simultaneously the perturbations related to both anharmonic resonance interaction and l‐type doubling. A further analysis reveals, however, that we are justified in carrying out an approximate solution, in which we first consider the resonance interaction as if l‐type doubling did not occur and subsequently find the energy levels associated with +l and —l as a result of small perturbations on the two‐fold degenerate levels involved. It appears that the applicability of the well‐known formula Δν=qJ(J+1), in which q is the l‐type doubling constant, is inherent to this approximation. The agreement between q values computed by our method and those obtained experimentally is very satisfactory indeed.

The Kinetics of Coordinate Bond Formation
View Description Hide DescriptionA novel method has been developed for determining the rates of very fast gas‐phase bimolecular reactions, which is based on interpretation of the temperature gradients in a flow system similar to that used for the study of the reactions of sodium vapor and alkyl halides. The kinetics of the reactions between boron tri‐fluoride and tri‐, di‐, and monomethylamine to form the corresponding coordinately bonded compounds have been studied. These reactions appear to have negligibly small activation energies, and their rates show a pressure dependence consistent with a mechanism:in which the long‐lived intermediate yz ^{*} must be stabilized by loss of energy in a collision. The random scatter of individual rate constants is about 20 percent.