Volume 18, Issue 8, 01 August 1950

The Recombination of Iodine Atoms in Solution
View Description Hide DescriptionA simple theory involving jumps between lattice sites has been used to treat the recombination of atoms produced in solution by photo‐chemical dissociation. The results have been applied to experimental data obtained previously on the photo‐dissociation of iodine in hexane at 25°C.
The treatment indicates that if a pair of atoms is separated by one molecular diameter in the dissociation process, then the probability is 0.40 to 0.50 that these atoms will recombine by diffusion in a period of 10^{−6} second or less. The experimental data for light of 436 mμ indicate that if some of the atoms undergo ``primary recombination'' without escaping from the cage of solvent molecules in which they are formed, then a larger number of atoms must become separated by two or more molecular diameters as a result of the photo‐dissociation.
For light of 578 mμ the data and calculations indicate that about 35 percent of the atoms become completely separated and ultimately combine with atoms from other molecules, about 30 percent become separated by a molecular diameter but recombine rapidly by diffusion, and about 35 percent either fail to undergo predissociation or recombine without escaping from the cage of solvent molecules in which they are formed.

The Concentration and Mobility of Vacancies in Sodium Chloride
View Description Hide DescriptionThe electrical conductivity of sodium chloride, containing cadmium chloride as an impurity, has been determined as a function of temperature. From these data it is calculated that the mobility of the positive ion vacancies is given by the equation μ=(19600/T)exp(−9860/T) cm.^{2}/volt‐sec. between 250°C and 400°C. The concentration of positive ion vacancies in a ``pure'' sodium chloride crystal was 1.0×10^{17} cm^{−3} and independent of temperature below 550°C.

The Experimental Determination of the Thickness of a Shock Front in a Gas
View Description Hide DescriptionEquations are developed from which the density profile of a shock front may be calculated from a knowledge of its reflectivity as a function of wave‐length and angle of incidence. The reflectivities of shock fronts of shock pressure ratio p _{2}/p _{1}=1.71 have been measured in nitrogen at initial pressure, p _{1}, equal to 85, 68, and 42 lb./in.^{2}. From the change of reflectivity with wave‐length, the thickness of the fronts was found to be 1.8×10^{−5} cm, 2.0×10^{−5} cm, and 3.2×10^{−5} cm with an accuracy of twenty‐five percent. An independent but less accurate check was provided by the change of reflectivity with initial pressure, yielding a thickness of 1.5×10^{−5} cm for p _{1}=85 lb./in.^{2}. The weighted mean value, 1.7×10^{−5} cm, for p _{1}=85 lb./in.^{2} is significantly greater than that calculated from the theory of Thomas, 1.0×10^{−5} cm.

The Vibrational Spectra and Structure of Inorganic Molecules. II. Sulfur S_{8}, Sulfur Chloride S_{2}Cl_{2}, Phosphorous P_{4}
View Description Hide DescriptionThe infra‐red spectra from 2–25μ have been obtained for S_{8} as solid and in CS_{2}solution; for S_{2}Cl_{2} as liquid and in CS_{2}solution; and for P_{4} in CS_{2}solution. A satisfactory assignment of the Raman and infra‐red spectrum of S_{8} has been made on the basis of D _{4d } symmetry. The spectrum and valence force calculations are consistent with the C_{2}structure for S_{2}Cl_{2}, and together with the electron diffraction data exclude the C_{2v } form. The vibrational spectrum of P_{4} is interpreted unequivocally on the basis of the tetrahedral structure (T_{d} ).

On the Structure of a Catalyst Surface. II
View Description Hide DescriptionOur previous results have been criticized by T. L. Hill on the ground that we considered energies of adsorption ranging from − ∞ to ∞. We have accordingly revised our former theory.
It appears that, if we assume localized adsorption without interaction, the possible mathematical forms for the adsorption isotherm are very limited. We have studied in detail, for the simplest of these, the distribution function for the adsorption energy. It turns out that this simplest isotherm is a generalization of both the Freundlich and the Langmuir isotherms.

Thermal Diffusion in the Critical Region. II
View Description Hide DescriptionThe previous measurements on thermal diffusion in the critical region for the system ethane‐xenon are extended and completed, with the use of a modified radioactive tracer technique. A rough calculation of cluster size in the critical region is made. A mechanism of molecular motion in the dense gas above the critical point, consistent with the data is present. It is shown that the transformation between dense gas and liquid occurs without discontinuity as far as thermal diffusion is concerned.
The thermal diffusion columns operated in the region of turbulent heat transfer gave a separation as predicted by the modified theory of the column.

Thermal Diffusion in the System Methane‐Xenon
View Description Hide DescriptionThermal diffusion measurements have been carried out for the system methane‐xenon at a temperature 100°C above the critical using two thermal diffusion columns. The results confirm the column theory presented in an earlier paper, and are consistent with the results obtained on the system ethane‐xenon.

The Electrostatic Contribution to the Lattice Energy of Some Ordered Spinels
View Description Hide DescriptionThe electrostatic contribution to the lattice energy of some ordered spinels is calculated. It is made plausible that also in the case of certain spinels that do not show any long‐range ordering, a considerable amount of short‐range order is to be expected. As a consequence the lattice energy of ``inversed'' spinels containing different ions at octahedral positions, is increased with respect to the corresponding ``normal'' spinels containing one type of ions at octahedral interstices.

X‐Ray Diffraction by Solid Soaps
View Description Hide DescriptionArguments are presented to show that x‐ray diagrams obtained by using the powder technique for common soap samples can be interpreted in terms of two kinds of disordering. The first kind of disorder, a stacking disorder of micellar layers, makes the layers optically independent for certain diffraction maxima so that continuous diffraction bands arise rather than discrete maxima. A second kind of disorder within a layer in which long chain ions are randomly oriented with respect to rotation about their long axes causes all but one set of bands to be weak. A consideration of these two disorders permits extensive unification of the results of x‐ray diffraction experiments for poorly crystallized soaps. The use of such diffraction patterns for phase studies is subject to severe uncertainties.

Radial Distribution Functions and the Equation of State of a Fluid Composed of Rigid Spherical Molecules
View Description Hide DescriptionThe integral equation for the radial distribution function of a fluid of rigid spherical molecules has been integrated numerically in the Kirkwood approximation and in the Born‐Green approximation over a wide range of densities. The distribution functions so obtained have been used to calculate the equation of state and excess entropy of the fluid. The results are compared with those obtained by means of the free volume theory of the liquid state.

Isotope Effect on Bond Rupture by Electron Impact on Hydrogen, Deuterium, and Tritium
View Description Hide DescriptionThe relative yields by electron impact of atomic and molecular ions, x ^{+}/x _{2} ^{+} ratios, from hydrogen, deuterium, and tritium have been measured with a 60° sector type mass spectrometer. It is shown that the major part of the previous disagreement between calculated and observed values can be understood on the basis of voltage discrimination by the ion source. By using magnetic scanning and a high ion accelerating voltage the experimental ratios are: H^{+}/H_{2} ^{+}=0.013, D^{+}/D_{2} ^{+}=0.0070, T^{+}/T_{2} ^{+}=0.0036 for 30 volt electrons. These are to be compared with the calculated ratios: H^{+}/H_{2} ^{+}=0.016, D^{+}/D_{2} ^{+}=0.0072, T^{+}/T_{2} ^{+}=0.0038.

Thermodynamic Properties of the Internal Rotation in Methyl Alcohol Vapor from 200 to 500°K
View Description Hide DescriptionAt ordinary and lower temperatures the thermodynamic properties of the methyl alcohol internal rotation are beyond the limits of available tabulations. For any internal rotator, of a given symmetry, with a fixed moment of inertia and potential barrier, two limiting values of each property can be calculated for any chosen temperature. Available tables are restricted to those cases for which the differences between the limiting values can be neglected. When, as with methyl alcohol, the differences are large, the representative values can be found by taking proper account of the symmetry and the dependence of the internal rotator energy levels upon the external rotations.
For methyl alcohol, the correct intermediate thermodynamic properties are obtained by using for the partition function and its derivatives the numerical mean of the limiting values of these sums obtained for the general rotator. This simple rule, however, is not necessarily applicable to other compounds.
Heat capacities and entropies, calculated from the spectroscopic potential barrier of 932 cal./mole and other molecular constants, are considered in relation to experimental data.

On the Vibrational Spectra of Crystals
View Description Hide DescriptionIn order to check the accuracy of distributions of characteristic vibration frequencies in crystals as calculated by approximate methods proposed by various workers, the frequency distribution is calculated rigorously for a lattice for which this is possible, viz., a two‐dimensional square lattice with vibrations perpendicular to the lattice plane. The calculation is then repeated by the use of the various approximate methods, and comparisons are drawn. The effect of using any of the approximate distributions in place of the exact one in the calculation of thermodynamic functions is illustrated by a calculation of the specific heat of this same crystal. Finally, an extension to three dimensions is discussed.

Spectral Resemblances between Azulenes and Their Corresponding Six‐Carbon Ring Isomers
View Description Hide DescriptionThe spectra of odd‐ring compounds, azulene, 1,2‐benzazulene, 2‐phenyl azulene, and indeno‐azulene are compared with those of their corresponding regular isomers, naphthalene, phenanthrene, phenylnaphthalene, and benzfluorene in part from 1730 to 7500A. The five band systems found in the azulenes seem to correspond with respect to intensity, vibrational structure, and sequence to the five found in their corresponding isomers except that the former are shifted to lower frequencies. The lowest frequency band is shifted some 17,000 cm^{−1} to the red in the azulenes, which accounts for the color observed in these compounds, whereas the four transitions at higher frequencies are shifted about 8000 to 9000 cm^{−1} as compared with the corresponding regular isomers. Decreases in total oscillator strengths with non‐linearity of these planar molecules as compared with the linear compounds (a type of C _{2v } symmetry about the long axis) are noted as has previously been shown in the comparison of anthracene and phenanthrene, and tetracene and 1,2‐benzanthracene and chrysene.

On the Notion of Pressure in a Canonical Ensemble
View Description Hide DescriptionRecently a controversy has arisen between J. De Boer and H. S. Green concerning the notion of pressure in a canonical ensemble. According to Green, only classically is the pressure as derived from the partition function equal to that obtained from the virial theorem, while at low temperatures, at which quantum effects become important, there will be considerable deviations between the two. De Boer attempts to prove that the two pressures are actually identical. We have come to the same conclusion, and shall show this in several ways; first, by considering a simple example (Section 2), and then in general using the energy representation (Section 3). We believe that the discrepancy between the two pressures which Green has found is in fact due to improper handling of the effect of the wall of the vessel in which the particles are contained. Finally, we are of the opinion that Green's criticism of De Boer's calculation is not justified, and in the last section arguments are given to show that the traces of all commutators of interest in quantum statistical mechanics are zero.

Molecular Orbitals for H_{3} ^{+}
View Description Hide DescriptionA somewhat more general concept of molecular orbitals than used heretofore is applied to H_{3} ^{+}. It is shown to be superior to the Heitler‐London approximation, but inferior to the HLSP‐plus‐ionic‐terms treatment of Hirschfelder. Relations between the HLSP and molecular orbital approaches to wave functions are discussed.

Substituted Methanes. II. Vibrational Spectra and Calculated Thermodynamic Properties of Deuterotribromomethane
View Description Hide DescriptionRaman displacements, semiquantitative relative intensities, quantitative depolarization factors, and wave numbers and percent transmission for the infra‐red bands in the region 400–5000 cm^{−1} have been obtained for CBr_{3}D. Details about the measurement of the depolarization factors are given. Thermodynamic properties—heat content, free energy,heat capacity, and entropy—have been calculated from the spectroscopic and molecular structure data for eight temperatures from 298.16° to 1000°K.

Substituted Methanes. III. Raman Spectra, Assignments, and Force Constants for Some Trichloromethanes
View Description Hide DescriptionRaman displacements, semiquantitative relative intensities, and precise depolarization factors for trichloromethane, fluorotrichloromethane, and bromotrichloromethane were obtained in the liquid state. Several overtones and combination bands hitherto unreported are given and frequency assignments are made. The Raman data in the literature for CCl_{3}H, CCl_{3}D, CCl_{3}F, CCl_{4}, and CCl_{3}Br in the liquid state have been collected and the probable values ascertained. Force constants in modified valence force potential functions containing all possible interaction constants were calculated for the five molecules.

Substituted Methanes. IV. Vibrational Spectra and Calculated Thermodynamic Properties of Deuterotrichloromethane
View Description Hide DescriptionRaman displacements, semiquantitative relative intensities, quantitative depolarization factors, and wave numbers and percent transmission for the infra‐red bands in the region 400–5000 cm^{−1} have been obtained for CCl_{3}D. Thermodynamic properties—heat content, free energy,entropy, and heat capacity—have been calculated from the spectroscopic and molecular structure data, to a rigid rotator, harmonic oscillator approximation, for nine temperatures from 298.16° to 1000°K.

The Conductance of Potassium Chloride, Potassium Bromide and Potassium Iodide in Aqueous Solutions from 5 to 55°
View Description Hide DescriptionThe equivalent conductivities of dilute solutions of potassium chloride, potassium bromide, and potassium iodide have been measured at various temperatures, and extrapolated to infinite dilution. These results, when combined with those of A. R. Gordon and others, yield limiting equivalent conductivities of each of the three potassium salts at 10° intervals between 5 and 55°C.