Volume 19, Issue 7, 01 July 1951

Quantitative Infrared Intensity Measurements. I. Carbon Monoxide Pressurized with Infrared‐Inactive Gases
View Description Hide DescriptionQuantitative infrared intensity measurements on CO pressurized with H_{2}, He, A, O_{2}, and N_{2} for total pressures up to 700 psia have been carried out. The values of integrated absorption for the fundamental and first overtone of CO have been found to be 237 cm^{−2} atmos^{−1} and 1.64 cm^{−2} atmos^{−1}, respectively. The numerical values of integrated absorption were obtained by using an indirect method for the interpretation of experimental data, similar to the extrapolation technique of Wilson and Wells.
The experimental data obtained at very large values of the total pressure should yield correctly the numerical values of the spectralabsorption coefficients. This statement is supported by the fact that the integral over the spectralabsorption coefficients at a total pressure of 700 psia yields values for the integrated absorption of fundamental and first overtone of CO which are in excellent agreement with results obtained by indirect methods.

Quantitative Infrared Intensity Measurements. II. Studies on the First Overtone of Unpressurized CO
View Description Hide DescriptionQuantitative infrared absorption measurements on unpressurized CO have been carried out for the first overtone in cells of different lengths and at different pressures of gas. The experimental data lead to a value for the integrated absorption of the first overtone of CO of 1.69 cm^{−2} atmos^{−1}, which is in excellent agreement with results obtained previously from the study of mixtures of CO pressurized with infrared inert gases.

Transport Phenomena in Dense Media. II. Thermal Diffusion in Compressed Gases
View Description Hide DescriptionFrom the thermodynamics of irreversible processes, values of the thermal diffusion ratio α have been calculated using (1) the virial equation of state, (2) generalized reduced enthalpies, (3) the Lennard‐Jones and Devonshire ``cage'' model for liquids. These results are compared with experiment and with previously published calculations for a van der waals gas. Only the LJD model gave results markedly superior to van der Waals' equation. The LJD model predicts very large positive values of α for compressed liquids.

The Solution of Some Potential Problems in the Theory of Electrolytes
View Description Hide DescriptionThe Poisson‐Boltzmann equation for the potential in an electrolyte is solved for the following cases:
(a) Electrolyte bordered by a uniformly charged plane; (b) two semi‐infinite electrolytes of different composition separated by a plane boundary; (c) electrolyte confined between parallel charged planes; (d) uniformly charged cylinder immersed in an electrolyte; (e) electrolyte in a cylinder with charged walls; (f) electrolyte between two concentric charged cylinders; (g) solid charged sphere in an electrolyte; and (h) sphere of electrolyte immersed in another electrolyte extending to infinity, and of different composition.
All the problems discussed are of interest in the theory of colloids or emulsions. In each case a series solution in powers of a parameter involving the charge or charges on relevant surfaces is given. The first term of each series is the solution of the Poisson‐Boltzmann equation when the so‐called Debye‐Hückel approximation is applied to the equation. The additional terms are built up from the first by an iterative method. No restrictions on the compositions of the electrolytes are required.

The Third Virial Coefficients of Polar Gases
View Description Hide DescriptionThe third virial coefficient is calculated for a gas composed of spherical molecules whose intermolecular potential has a repulsive term proportional to r ^{−12}, an attractive term proportional to r ^{−6}, and which have point‐dipoles at their centers. The calculated values are compared with the experimental results for steam and ammonia, using parameters previously calculated from the second virial coefficient. The agreement is good for ammonia but poor for steam. It is suggested that this is because of the neglect of the higher multipoles in the interaction potential.

The Critical Constants of Polar Gases
View Description Hide DescriptionThe range of usefulness of the virial expansion is discussed. It is shown that this expansion closely resembles the Beattie‐Bridgman equation if terms up to the third virial coefficient are included. This suggests that the ranges of validity of the two equations may be similar—namely, almost up to the critical density. The virial expansion is therefore used to calculate the critical constants of both nonpolar and polar gases. These constants are much less sensitive to the dipole‐energy than are the virial coefficients. The agreement with experiment is satisfactory.

The Stability of Gaseous Diatomic Oxides
View Description Hide DescriptionThe instabilities of FeO, NiO, MnO, and SiO_{2} upon vaporization, and upper limits to the heats of dissociation of these oxides and SiO have been determined by effusion experiments. The data available in the literature have been treated to obtain the heats of dissociation, or the upper limits thereof, of the gaseous oxides SnO, ZnO, CdO, CuO, PbO, GeO, and TiO.
The linear Birge‐Sponer extrapolation of vibrational levels appears to give correct dissociation energies for the fourth‐group oxides.

Photoneutron Fission Analysis for U−235 in High Purity U−238
View Description Hide DescriptionThe photoneutron method for the analysis of U−235 in high purity U−238 is described. Special samples have been found to contain as little as 5 parts per million U−235. An upper limit for the thermal neutron fission cross section of U−238 can be set at 5×10^{−28} cm^{2}.

Compressibility of Gases at Pressures up to 50 Atmospheres. V. Carbon Tetrafluoride in the Temperature Range 0°—400°C. VI. Sulfur Hexafluoride in the Temperature Range 0°—250°C
View Description Hide DescriptionThe gaseous compressibilities of carbon tetrafluoride in the temperature range 0–400°C, and sulfur hexafluoride in the temperature range 0–250°C have been measured at pressures up to 50 atmospheres by a method employing gas expansion. The data have been fitted to a series equation of the type,and the virial coefficients are tabulated.

Intermolecular Potentials. I. Carbon Tetrafluoride and Sulfur Hexafluoride. II. Carbon Dioxide
View Description Hide DescriptionExperimental second virial coefficient data for carbon tetrafluoride, sulfur hexafluoride, and carbon dioxide have been used to investigate the intermolecular potentials of these molecules on the basis of a Lennard‐Jones model. Force constants for the fluoride molecules can be fitted rather satisfactorily, but the constants so derived do not agree with those derived from other gaseous properties, e.g., the critical data. This result may be due to the assumption of central forces for the symmetrical fluoride molecules.
For carbon dioxide it was found that the derived force constants varied with temperature, the high temperature data yielding lower values of the collision diameter r _{0}. The results can be interpreted on the basis of a partial association. A likely configuration for the resulting dimer is suggested.

Substituted Ethanes. III. Raman and Infrared Spectra, Assignments, Force Constants, and Calculated Thermodynamic Properties for 1,1,1‐Trichloroethane
View Description Hide DescriptionRaman displacements, semiquantitative relative intensities, and quantitative depolarization factors for liquid 1,1,1‐trichloroethane, and infrared wave numbers and percentage absorption for both the liquid and gaseous states in the region 400–5000 cm^{−1} were obtained and compared with previous data. A normal coordinate treatment, using the Wilson FGmatrix method, was carried out, and a reasonable set of force constants was determined. Assignments were made for all observed bands of the infrared and Raman spectra. The heat content, free energy,entropy, and heat capacity at constant pressure were calculated for 9 temperatures in the range 298.16° to 1000°K. A comparison of calculated and observed entropy values indicated that the potential barrier hindering the internal rotation is about 2840 cal/mole, which leads to a value of 205±20 cm^{−1} for the torsional frequency and to 0.786×10^{−12} erg/radian for the torsional force constant.

Unimerism
View Description Hide DescriptionIt is pointed out that, in the development of structural organic chemistry, those compounds which have no structural isomers play a crucial role. Since no general name has ever been given to compounds which meet this condition, they are here called ``unimers.'' It is further shown that the molecular formula of a unimer must necessarily fulfill certain mathematical conditions. These conditions are set forth in nine theorems. Some of these theorems are almost self‐evident; for others, the proofs, although simple in plan, are exceedingly intricate in application. Consequently, the reader is referred for all proofs to a purely mathematical paper which will be published in the American Journal of Mathematics. Finally, a complete list of unimeric types is given.

Magnetic Susceptibilities of Praseodymium Oxides
View Description Hide DescriptionThe magnetic susceptibilities of the three oxides of praseodymium, Pr_{2}O_{3}, PrO_{2}, and Pr_{6}O_{11}, have been measured with the faraday magnetic balance over a range of temperatures from 80° to 300°K. The sesquioxide and the dioxide have been found to have moments of 3.55 and 2.48 Bohr magnetons, respectively, and to obey the Weiss modification of the Curie law, χ(T+Δ)=C, over the range of temperatures studied with corresponding values of Δ equal to 55.0° and 104°. A curvature was noted in the plot of 1/χ vs T for the oxide Pr_{6}O_{11}. Thus the Weiss‐Curie law does not adequately express the relationship between the susceptibility and the temperature for this oxide. A moment of 2.8 Bohr magnetons was calculated for Pr_{6}O_{11} from the slope of the above plot between 200° and 300°K.

Thermodynamics and Chemical Kinetics of One‐Dimensional Nonviscous Flow through a Laval Nozzle
View Description Hide DescriptionExplicit relations have been obtained for the enthalpy changes in one‐dimensional nonviscous flow through a Laval nozzle, where arbitrary deviations from thermodynamic equilibrium of chemical composition and of internal electronic, vibrational, or rotational energy states may occur. These relations are of interest in connection with calculations on the effect of deviations from equilibrium on performance of jet engines.
Starting with the equation of continuity for a multicomponent mixture of reacting gases, criteria for near‐equilibrium and for near‐frozen flow with respect to chemical reactions are derived. The near‐equilibrium criteria agree with results obtained previously. The near‐frozen flow criteria are new and have not yet been applied to the study of chemical reactions during nozzle flow.

The Experimental Determination of the Intensities of Infrared Absorption Bands. IV. Measurements of the Stretching Vibrations of OCS and CS_{2}
View Description Hide DescriptionThe absolute intensity of the infrared stretching vibrations of the molecules CS_{2} and OCS have been measured. For CS_{2}, the intensity of ν_{3} was found to be 7560×10^{10} cycles sec^{−1} (cm of vapor at NTP)^{−1}. For OCS, the results were 110 and 7900×10^{10} for ν_{1} and ν_{3}. A normal coordinate analysis of the stretching vibrations of OCS was carried out to obtain ∂μ/∂r for the bonds and to compare them with those for CS_{2} and the previously obtained results for CO_{2}. The results for a reasonable value of the interaction constant were 6.7 and 4.3×10^{−10} esu for the CO and CS bonds, while in CO_{2} and CS_{2} they were 6.0 and 5.6×10^{−10} esu. The bearing of these results on the amount of resonance in OCS is discussed. Arguments are presented which suggest that, in spite of the electronegativity difference between oxygen and sulfur, resonance in OCS is not markedly different from that in CO_{2} and CS_{2}.

Determination of Isotope Ratios, e.g., in Tracer Work, by an Infrared Absorption Method
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Kinetics of OH Radicals from Flame Emission Spectra. III. Total Transition Probabilities and the Energetic Distribution of OH(^{2}Σ^{+}) and O_{2}(^{3}Σ_{ u } ^{−}) in the Oxy‐Hydrogen Flame
View Description Hide DescriptionThe energetic distribution of OH(^{2}Σ^{+}) and O_{2}(^{3}Σ_{ u } ^{−}) in hydrogen‐oxygen flames has been investigated. The measurements were made in the inner cones of these flames burning with various fuel ratios (lean, stoichiometric, and rich) at atmospheric pressure. The relative concentrations of the excited species were determined by comparing the calculated equilibrium intensity ratios of OH(^{2}Σ^{+}) and O_{2}(^{3}Σ_{ u } ^{−}) with the experimental intensity ratios. The electronic, vibrational, and rotational transition moments relevant to this calculation have been computed. The good agreement between the experimental intensity ratios and the calculated equilibrium intensity ratios indicates that the electronically excited O_{2}(^{3}Σ_{ u } ^{−}) is in thermal equilibrium with OH(^{2}Σ^{+}). It is possible, therefore, that O_{2} is excited thermally in the hydrogen‐oxygen flame.

Dissociation Energies of the Cd^{++} Vacancy Complex and of the Double Vacancy in Sodium Chloride
View Description Hide DescriptionDissociation energies for two types of lattice imperfection (namely, the impurity ion vacancy complex and the double vacancy) have been determined theoretically for NaCl, using the semiclassical model of ionic crystals developed by Born and Mayer. The procedure followed in calculating these energies was based on the method developed by Mott and Littleton for computing the formation energies of single vacancies. The numerical results which were obtained are 0.44 ev and 0.89 ev for the dissociation energies of the complex and double vacancy, respectively.

Overlap and Bonding Power of 2s,2p‐Hybrid Orbitals
View Description Hide DescriptionA classification and nomenclature for 2s−2p hybrid AO's (atomic orbitals) of any degree of hybridization is proposed, and the concepts of cohybrids, antihybrids, and orthohybrids are defined. Overlap integrals S as follows are computed and tabulated as a function of the hybridization coefficient and the interatomic‐distance parameter for the case of two like first‐row atoms: S(h _{β}, h _{β}; ρ), S(h _{β}, h_{o}β; ρ), and S(1s, h _{β}; ρ). (See also Figs. 1 and 2.) Here h _{β} denotes any 2s−2p hybrid, and h_{o}β the corresponding orthohybrid. Slater AO's were used, and also, for selected ρ values for the case of C–C bonds,SCF AO's.
In connection with this work, and extending fragmentary tables given in a previous paper, complete tables from ρ=3 to ρ=14, for the case of two like atoms, are given for the overlap integrals S(1s, 2s), S(2s, 2s), S(1s, 2pσ), S(2s, 2pσ), S(2pσ, 2pσ), and S(2pπ, 2pπ) using orthogonalized Slater 2s AO's, and carbon SCF 2pσ and 2pπ AO's.
Tables of Slater‐AO overlap integrals S(1s, hβ) are given as a function of β for the radicals FH, OH, NH, and CH at their equilibrium distances, also similar tables based on SCF AO's for the case of C–H bonds of lengths 1.12, 1.09, and 1.06A. (See also Fig. 3.)
The various tables and figures show that ``a little hybridization goes a long way''; that is to say, a small amount of s character in a pσ AO, or of pσ character in an s AO, causes a large change in S. Applications of this fact to problems of chemical binding are briefly suggested. These will be developed in a following paper. (Also see Note added in proof at end of this paper.)

Orthonormal Sets of LCAO Molecular Orbitals for Second‐Row Homopolar Diatomic Molecules
View Description Hide DescriptionThe forms of the LCAO MO's (molecular orbitals approximated by linear combinations of atomic orbitals) of any homopolar second‐row diatomic molecule are studied under the restriction that they shall form an orthogonal set. The requirement of orthogonality per se causes 1s−2s−2pσ hybridization (forced hybridization) among the AO's (atomic orbitals) used in constructing the LCAO's. Equations, tables, and figures are given showing how the degrees of hybridization in the members of mutually orthogonal sets of σ_{ g } LCAO MO's, likewise of σ_{ u } LCAO MO's, are related, as a function of two parameters: (a) assumed degree of hybridization in any one member of the set; (b) a parameter proportional to interatomic distance times effective nuclear charge. This is done using primarily Slater AO's, but the effect of using SCF (self‐consistent‐field) AO's is also studied.
Assuming that overlap integrals are good measures of bond strengths, it is shown that the effect of forced hybridization is to diminishbond strengths. It is concluded that this bond‐weakening effect in LCAO MO valence theory is the counterpart of certain exchange repulsions which appear in the Heitler‐London valence bond theory, namely those between bonding electrons on one atom and electrons in different (either bonding or lone‐pair) AO's on the other atom. The procedure used promises to give a good measure of the strengths of inner shell‐outer shell interatomic repulsions; it tends to indicate that these are, in general, not large but not negligible. A paradox resulting from forced hybridization is touched on and more or less resolved; this paradox has to do with the method of counting the numbers of s and pσ electrons per atom in a molecule described by LCAO methods.