Volume 25, Issue 2, 01 August 1956

Corresponding States Treatment of Nonelectrolyte Solutions
View Description Hide DescriptionRecent theories of solutions (Prigogine and co‐workers; Salsburg and Kirkwood) use a theory of corresponding states to deduce the properties of solutions from theoretically derived properties of the pure components (e.g., from the Lennard‐Jones and Devonshire ``free volume'' or ``cell'' model). A characteristic of these theories is that they predict for molecules of the same size and dispersion force interactions a negative volume change on mixing.
Since the ``cell'' model gives very poor agreement with experimental data on energy‐volume and volume‐temperature relations of pure liquids, a corresponding states treatment has been carried through using an experimentalequation of state for the pure liquid. If one assumes two kinds of ``cells'' in the mixture, a type for each of the components, the results agree with experimental data on solutions at least as well as previous theories. As before, contraction on mixing is found for a certain class of dispersion force solutions.
In any corresponding states treatment, the entropy of mixing will not be ideal either at constant pressure or at constant volume.

Proton Relaxation in Solutions of Chromium (III) Complexes
View Description Hide DescriptionSpin‐lattice relaxation times were observed for protons in a number of aqueous solutions of symmetrical chromium (III) complexes. The observed times were in the order to be expected if it is assumed that those ions displaying the greatest tendency to interact with solvent water also exhibit the greatest relaxation effect. Thus, relaxation times for protons in solutions of the ions Cr(H_{2}O)_{6} ^{+3}, CrF_{6} ^{—3}, Cr(NH_{3})_{6} ^{+3}, Cr(C_{2}O_{4})^{—3}, Cr(en)_{3} ^{—3}, and Cr(CN)_{3} ^{—3} were observed to increase in the order given.

Millimeter Wave Spectrum, Molecular Structure, and Dipole Moment of Hydrogen Selenide
View Description Hide DescriptionSeveral rotational transitions of various Se isotopic species of H_{2}Se and D_{2}Se have been measured in the shorter millimeter wave region. These yield the value of 1.460±0.013 A for the bond length and 91.0°±0.6° for the bond angle. From Stark effectmeasurements on two of the transitions the value 0.24±0.02 Debye is obtained for the molecular dipole moment.

Influence of Molecular Electric Quadrupole Moments on Dielectric Constants
View Description Hide DescriptionThe effect of a molecular electric quadrupole moment on the dielectric constant of a gas composed of nonpolar molecules is calculated to the lowest order of density and polarizability in which it appears. The quadrupoles induce electric dipoles in neighboring molecules, and these dipoles interact with an applied uniform electric field. The total effect is a deviation from the Clausius‐Mosotti equation, proportional to the square of the quadrupole moment, and of the same order of magnitude as the deviation due to fluctuations in dipole moment calculated by Kirkwood, and the deviation due to the variation of polarizability with density calculated by Mazur and Jansen. The theory is tested by calculating the quadrupole moment of CO_{2} from dielectric constant data. The result is about five times larger than the value obtained by microwave pressure broadening, and is about forty percent larger than the value obtained by Pople from the second virial coefficient of CO_{2}.

Dipole Moment of the HCN Molecule
View Description Hide Descriptionπ‐electronic and σ‐electronic energy levels of the HCN molecule are calculated by the LCAO method with full inclusion of configuration interaction.
Slater atomic orbitals with effective chargeZ=3.180 for the carbon atom and 3.850 for the nitrogen atom are employed. The C–H distance is assumed to be 1.09 A and the C–N distance 1.15 A. The value 2.664 Debye units is obtained for the dipole moment of the molecule in the ground state, while the experimental value is 2.766 Debye units.

Ultrasonic Absorption Theory of Gierer and Wirtz
View Description Hide DescriptionThe absorption theory of Gierer and Wirtz is applied to a calculation of the temperature coefficient of the ultrasonicabsorption coefficient for a number of liquids, and the results are compared with known experimental values. Where meaningful values are obtained in the theory, the temperature coefficient is always negative, in contrast to the sometimes positive coefficients that have been determined experimentally. It is concluded that the theory is not generally applicable.

Dielectric Absorption in Lithium Fluoride
View Description Hide DescriptionThe dielectric loss in single crystals of lithium fluoride has been examined between temperatures of 0°C and 130°C. At the lower temperatures the dielectric loss, as a function of frequency, passes through a definite maximum and is quite distinct from the background loss due to dc conductivity. From the experimental results, the frequency factor (7×10^{12} sec^{—1}) and energy barrier (0.65 ev) are derived. After darkening with x‐rays the absorption disappears and reappears again after bleaching.

Spectroscopic Studies of Reactive Molecules by the Matrix Isolation Method
View Description Hide DescriptionThe matrix isolation method for the study of reactive molecules is described. The properties that should be possessed by a material suitable for use as a matrix are discussed with particular reference to spectroscopic investigations. Tests of the method have been conducted with infrared spectroscopic techniques using the free radical NO_{2} and the hydrogen bonding molecules HBr, HCN, HN_{3}, NH_{3}, and H_{2}O. Xenon, nitrogen, and argon are effective as matrices in isolating these molecules at 20°K with a mole ratio of matrix to active material in the range 100:1 to 500:1. The vibrational frequencies of these molecules isolated in a matrix are nearly the same as the frequencies in the gas phase.

Phosphorescence Spectra of the β‐Halonaphthalenes
View Description Hide DescriptionThe ^{3} L_{a} →^{1} Aphosphorescence spectra of the β‐halonaphthalenes have been studied at 20°K in crystals and in dilute solid solutions in naphthalene and in each other. No phosphorescence was observed at 300°K or at 77°K in the pure or mixed crystals. The phosphorescence spectra at 20°K are sharp in the solid solution in naphthalene, whereas the spectra of the pure crystals or of the solid solutions in the β‐halonaphthalenes are broad. The spectra are similar in energy and vibrational structure. The vibrational frequencies which appear in the spectrum can be related to those of naphthalene. From the vibrational analysis, it is concluded that the molecule possesses the same elements of symmetry in both ground and triplet states.
Quenching by impurities in the purest obtainable crystals of naphthalene made it impossible to observe the naphthalene phosphorescence.
The causes for broadening in low‐temperature electronic spectra are discussed.

Rate of Association of n‐Propyl Radicals
View Description Hide DescriptionThe rate of association of n‐propyl radicals has been measured by studying the photolysis of di‐n‐propyl ketone in intermittent light. A value of k _{2}′=1×10^{—8} cc molecule^{—1} sec^{—1} at 100° has been obtained. Possible sources of error have been discussed and it is concluded that the above value may be too high by a factor of the order of 20, thus indicating that reaction probably occurs at every collision. A value of k _{3}/k _{2}=0.125±0.01 has been found, where k _{3} and k _{2} are the rate constants for disproportionation and combination, respectively.

Near Infrared Spectra of Diborane, Pentaborane, and Decaborane
View Description Hide DescriptionSpectra of diborane, pentaborane, and decaborane have been examined in the near ir at high resolution. Assignment of the observed frequencies for diborane have been made. Pentaborane has been subjected to group theoretical reduction considerations to ascertain which overtone frequencies are ir active for this molecule. On the basis of the data obtained, bond energies, bond distances, and force constants have been calculated for the B–H bond in each of these molecules. Spectralstructure comparisons of diborane, ethane, and ethylene have been made.

Space‐Charge Formation in Small PbS Particles
View Description Hide DescriptionA theoretical model is discussed for the effect of oxygen on the electrical properties of PbSthin films. The films are assumed to be composed of very small n‐type microcrystals, on the surface of which oxygen is adsorbed. The adsorbed atoms are singly ionized by electrons from the interior of the microcrystals. The appropriate Poisson‐Boltzmann equation is solved for particles of radius 5×10^{—8} m and 5√10×10^{—8} m, and for donor concentrations of 10^{23} m^{—3} and 10^{24} m^{—3}. The potential distribution is given as a function of the surface acceptor concentration required for the conservation of charge.
Models for the electron and hole conductivities are given, and the results of calculations based on these models are compared with experiment. This theory is contrasted with the earlier bulk diffusion theory of the effect of oxygen. The free energy of adsorption is roughly calculated. Implications of this theory are discussed—on the general character of conduction in PbSfilms, on the temperature coefficient of conduction, and on the nature of photoconduction.

Improved Free‐Volume Theory of Liquids. I
View Description Hide DescriptionTo obtain practical results from the cell theories of liquids, it seems necessary to assume a simple symmetry for the distribution of a molecule about its lattice site. This is accomplished by replacing the interaction of the molecule with its neighbors by some ``suitably averaged'' interaction. In the Lennard‐Jones and Devonshire treatment, the pair interaction is replaced by its spatial average. We find that a Boltzmann‐type average is much more satisfactory. For an assumed symmetry of the distribution, our procedure provides an extension of Kirkwood's theory such that the resulting integral equation for the distribution function can be solved by numerical methods.
The introduction of the Boltzmann‐type averaging provides a pair wise correlation between the motions of molecules in neighboring cells. These correlative effects have been neglected in previous cell theories of the liquid phase. Numerical calculations of the equation of state and thermodynamicalproperties are, at present, being carried out.
In evaluating the integrals which arise in this development, we have found the function L _{0} defined by the double surface integralto be extremely useful. Here, r _{1} and r _{2} are the radii of two spheres, R the separation of their centers, r _{12} the separation of points on the two spheres, and f an arbitrary integrable function of r _{12}/R. L _{0} is found to be a quadratic function of r _{12}, different for various subranges of the interval [r _{12}(max), r _{12}(min)]. For a variety of physical problems such as x‐ray and electron diffraction,L _{0} may have application.

Nuclear Magnetic Interactions in the HF Molecule
View Description Hide DescriptionMagnetic relaxation times of hydrogen and fluorine in anhydrous hydrofluoric acid cannot be accounted for on the assumption of a pure dipole‐dipole interaction between the hydrogen and the fluorine nuclei in the same molecule. However, the introduction, in the Hamiltonian, of a scalar term A I·S resulting from the indirect electron‐coupled interaction between the two nuclei removes all the discrepancies between the calculated and observed decay times. Although the splitting due to this scalar term is smeared out by the rapid chemical exchange of the protons with the traces of water present in the acid, the nuclear Overhauser effect provides the extra parameter required to separate the dipole‐dipole interaction from the scalar interaction and to calculate separately the scalar splitting and the exchange rate of the protons. The value obtained for the splitting is A/h=615 cps.
The same method has been applied to investigate the structure of the HF molecule in solutions. The experimental results can be explained qualitatively by the following picture: (a) The fluorine nuclei form long chains that move more slowly than the Larmor frequency of fluorine. (b) The chemical exchange with the relatively large quantity of water present makes the motion of the hydrogen nuclei fast with respect to the hydrogen Larmor frequency. The results are: Long relaxation times for hydrogen with T _{1} and T _{2} equal, relatively short relaxation times for fluorine resonance, with T _{2} shorter than T _{1}.
Solutions of salts of hydrofluoric acid (KF) show the same character as solutions of the acid.

Interpretation of the Kinetics of Mercury Alkyl Pyrolysis
View Description Hide DescriptionThe high frequency factors observed for the thermal decomposition of some mercury dialkyls are shown to be consistent with the hypothesis that the primary step is a fission into three fragments rather than two; this mechanism is possible because of an almost unique thermochemicalproperty of the mercury alkyl system and, within the limitations of the simple approximation used, is not incompatible with the concept of localization of activation energy within the critical bonds.

Treatment of the Equations of Classical Diffusion in Homogeneous Isotropic Media
View Description Hide DescriptionA method is described which utilizes a generalized convolution to produce simplification of the equations of a wide range of classical diffusion processes. The resulting transformation expresses the solutions to these equations in terms of solutions for much simpler problems, many of the latter being already available in textbooks. Demonstrations are given of the use of this method in the facile development of the required concentration mappings for certain systems.

Infrared Spectrum of Hydrogen Fluoride
View Description Hide DescriptionThe infrared vibration‐rotation spectrum of HF has been re‐examined out through J=11 for the fundamental, and through J=8 for the first overtone. Five lines of the pure rotational spectrum of HF (J=10, 11, 12, 14, 15) have been observed in absorption and emission between 15 and 24 μ. Extension of the measurement to larger J values makes it possible to observe the effect of the term H_{v}J ^{3}(J+1)^{3} in the energy, and to obtain H_{v} . With the new data the molecular constants have been re‐evaluated by IBM machine. These constants when used with the energy expression permit accurate prediction of the observed energy levels.

Periodic Precipitation
View Description Hide DescriptionThe phenomenon of periodic precipitation has been subjected to calculations based on the diffusion‐plus‐supersaturation model first proposed by Ostwald. The mathematical difficulty caused by an infinite density of Liesegang rings at the original junction between the two solutions is avoided by the introduction of a thin ``clear'' zone which is supposed to be initially free of reactants. A further simplification results from assuming that one of the reactants is present in considerable excess, so that its diffusion remains essentially unaffected by the precipitation. Calculations show that the ratio between the distances from the initial boundary of two successive rings rapidly approaches a constant value, in agreement with experiment. Results have been obtained for the case where both reactants have the same diffusion coefficient.

Normal Coordinate Treatment for the Out‐of‐Plane Vibrations of Ethylene‐Type Molecules
View Description Hide DescriptionThe s vectors for torsional and out‐of‐plane bending modes of vibration for ethylene‐type molecules are given. Then F‐ and G‐matrix elements are given for all ethylene‐type molecules with the exception of C_{2}XYZW isomers. Finally, numerical calculations are carried out for C_{2}H_{4}, asymmetric C_{2}H_{2}F_{2}, asymmetric C_{2}H_{2}Br_{2}, the cis‐ and trans‐isomers of C_{2}H_{2}Cl_{2} and all of their deuterated analogs. The 57 out‐of‐plane fundamentals were calculated for the above 19 molecules. Of these 57 fundamentals 50 have been reported in the literature and are reproduced in this paper with an average deviation of 2.2 K or to 0.362% error.

Photochemical Oxygen‐Hydrogen Reaction at 1849 A
View Description Hide DescriptionThe photochemical reaction between oxygen and hydrogen was studied at atmospheric pressure in a flowing system using the 1849.6 A mercury resonance line as a light source. The yields of hydrogen peroxide, water and ozone were determined. The results obtained in this work above the convergence limit of the oxygen molecule absorptionspectrum are in agreement with those obtained in other studies below the convergence limit. The predissociation of oxygen molecules to form oxygen atoms as the primary process following light absorption is shown to be the only reaction of optically excited oxygen. The mechanisms used to explain the formation of products, ozone, hydrogen peroxide and water, are compatible with well‐known reactions in various oxygen‐hydrogen systems.