Volume 17, Issue 12, 01 December 1949

Rates of Ionic Reactions in Aqueous Solutions
View Description Hide DescriptionThe effect of the addition of ``inert'' salts on ionic reaction rates is discussed. For reactions between ions of the same charge sign, the effect is caused almost exclusively by the concentration and character of salt ions of charge sign opposite to that of the reactants. The rate is not dependent upon the ionic strength of the solutions. In reactions between ions of opposite charge sign, both salt ions may affect the rate, but the effect of one type may be dominant. The effects are quantitatively interpretable in terms of an ion association constant and specific rate constants for the associated and non‐associated reactants. The further introduction of activity coefficients is not necessary. The reactions upon which the Livingston Diagram is based have been explored from this viewpoint and found to be in quantitative accord.

Dipole Moment and Restricted Rotation in Some Chlorinated Hydrocarbons
View Description Hide DescriptionMeasurements of the variation of gas phase dipole moment with temperature of six chlorinated hydrocarbons are described. 1,2‐dichloropropane, and, to a very small extent, 2,3‐dichloropropene and 1,1,2‐trichloroethane display a dependence of dipole moment on temperature. 1,4‐dichlorobutane and the two isomers of 1,3‐dichloropropene have dipole moments constant over the temperature range investigated. The results are analyzed both by adopting simple parametric functions to represent the potential hindering intramolecular rotation, and by computations of intramolecular energies.

Reduced Temperatures for the Liquid State. General Equations for the Orthobaric Densities as Functions of the Reduced Temperature
View Description Hide DescriptionThe reduced temperature θ proposed by Bauer, Magat, and Surdin for the liquid state is presented and their work is reviewed. Attention is directed to the fact that a number of empirical power law equations that represent the variation of a property of a liquid as a function of the van der Waals reduced temperature are directly transformable into analogous functions of θ. General equations are derived for the variation of the orthobaric liquid and vapor densities as function of the reduced temperature.

Effects of Perturbations on Phosphorescence: Luminescence of Metal Organic Complexes
View Description Hide DescriptionFluorescence and phosphorescencespectra,phosphorescence lifetimes, and relative ratios of intensities of fluorescence to phosphorescence of the dibenzoylmethane derivatives of the trivalent ions of Al, Sc, Y, La, Gd, and Lu have been measured. The lifetimes and intensity ratios of the various compounds differ widely, while the spectra are very similar. For instance, although the Lu and Gd compounds have practically indistinguishable phosphorescent spectra, the lifetimes of their phosphorescences differ by a factor of fifty. The results are interpreted in terms of Lewis's triplet theory of the phosphorescent state and spin‐orbit perturbation of the levels. The largest effect is produced by the paramagneticgadolinium ion. The effects produced by the non‐magnetic ions depend on their nuclear charge and on their electronic structure.

The General Kinetics of Co‐Polymerization and an Extension of the Viscosity Method to Determine Velocity Constants
View Description Hide DescriptionCompletely general kinetic expressions have been developed for the co‐polymerization of nmonomers, assuming that the reactivities of the radicals depend only on their terminal groups. Allowance has been made for chain transfer and the fact that thermal and photo‐chemical initiation may proceed via diradicals. The equations are of the same form as those developed previously for a simple polymerization. The latter appear as a special case in which n=1.
It is pointed out that the method previously developed for determining the velocity constants in simple polymerizations can be used without modification in the study of co‐polymerizations. In this way 12 of the 14 velocity constants in a binary co‐polymerization can be determined absolutely, and a relation between the remaining two obtained.

Refractive Indices and Dielectric Constants of Liquids and Gases under Pressure
View Description Hide DescriptionSeveral interpolation formulas are given which reproduce refractive index and dielectric constant data for liquids and gases at high pressures. These formulas involve functions of the refractive indices and dielectric constants which appear in the formulas of Lorentz‐Lorenz, Clausius‐Mosotti, Gladstone and Dale, the empirical Eykman formula, etc. One formula shows the reciprocals of these functions to be linear in the specific volumes at various pressures. Another interpolation formula, involving the reciprocals of the same functions, contains a logarithmic term which is similar to that appearing in the Tait equation for compressibilities of liquids. The parameters involved in the Tait equations for compressibilities and in the analogous interpolation formula for refractive indices and dielectric constants are discussed.
The article also shows that the Tait equation which has been so successfully adapted to compressibility data of liquids can also be applied to gases.

A Quantum‐Mechanical Theory of Light Absorption of Organic Dyes and Similar Compounds
View Description Hide DescriptionThe most important organic compounds which absorb visible light can be classified into three groups typified: (a) by symmetrical polymethines, (b) by porphyrines, (c) by polyenes.
Recently it was shown that the position of the absorption maxima of symmetrical polymethines and related compounds (symmetrical cyanine and oxanole dyes; Michler's hydrol blue and derivatives; malachite green and other triphenyl methane dyes; etc.) can be calculated by adopting a model of the dye molecule which is analogous to the free‐electron gas model used in particular by Sommerfeld to describe the condition of metals. The π‐electrons of the polymethine chain are considered as a one‐dimensional free‐electron gas which extends itself along the length of the chain.
In the normal state the stablest energy states of the electron gas each contain two electrons in accordance with Pauli's exclusion principle. The remaining states are empty. The existence of the first absorption band is a consequence of the jump of a π‐electron from the highest energy level occupied in the normal state to the lowest empty level.
For the wave‐length of the maximum of the first absorption band of this group of dyes, the relationship obtains thatwhere L is the length of the polymethine zig‐zag chain, N, the number of π‐electrons, m, the mass of the electron, c, the velocity of light, h, Planck's universal constant. Good agreement with experimental results for λ_{1} is obtained by the use of this equation.
The problem of porphyrine and phthalocyaninecompounds can also be dealt with on the basis of a free‐electron gas model. We treat the π‐electrons of the porphyrine ring as electrons which are confined to move in a closed ring‐shaped path in a field of constant potential energy.
In the case of polyenes and related compounds (Carotenes, unsymmetrical cyanines and oxanoles, merocyanines, azo‐ and stilbene dyes, etc.) a description by means of a free‐electron gas model is no longer permissible. The electron gas in this case suffers a disturbance from its condition in the case of the first and second groups of dyes, and, to allow for this, the π‐electrons are considered placed in a one‐dimensional potential having a sine curve periodicity. The wave‐length λ_{1} is expressed bywhere V _{0} is the amplitude of the sine‐shaped potential along the chain.
This relation is confirmed by the experimental data. It also gives an explanation for the markedly different manner (compared with the symmetrical polymethines) in which the position of the absorption bands of polyenes and related compounds depends on the chain length.
The results of the classical color theory of Witt are capable of a simple explanation when considered in the light of the electron gas model.

The Kinetics of Heterogeneous Atom and Radical Reactions. I. The Recombination of Hydrogen Atoms on Surfaces
View Description Hide DescriptionThe data on the kinetics of the recombination of hydrogen atoms on various types of surfaces are analyzed in the light of the theory of absolute reaction rates. Expressions are derived for the recombination coefficient and the first‐order rate constant, enabling these quantities to be calculated on the basis of postulated mechanisms. It is shown that the experimental activation energies are consistent with estimates using either Hirschfelder's rule or an expression utilizing the experimental ``desorption temperature.'' For the reaction on dry oxides and dry glass good agreement is found assuming that reaction occurs between a gas‐phase hydrogen atom and an adsorbed hydrogen atom, the adsorption being of the van der Waals type at low temperatures and chemisorption at higher ones. The mechanism of surface poisoning by water vapor is shown to be not due to the necessity for desorbing the water molecule: in the high temperature region it is due to an increase in activation energy, the mechanism being S–OH+H→S–O+H_{2}; in the low temperature region to a decrease in the number of active centers, the reaction being between a gaseous atom and a van der Waals adsorbed hydrogen atom above the water layer.

On the Theory of the π‐Electron System in Porphines
View Description Hide DescriptionThe failure of certain LCAO molecular orbital calculations of the spectrum of porphine is attributed to the incorrect assumption of complete ``aromaticity.'' A division of the π‐electron system into non‐interacting parts is supported by the fact that the dynamical properties of the divided system, as calculated by the free‐electron model, are in approximate agreement with experiment. A proof of the equivalency of the LCAO method (with overlap neglected) and an approximation to the free‐electron method is indicated for certain dynamical systems.

A Kinetic Study of the Thermoluminescence of Lithium Fluoride
View Description Hide DescriptionThe isothermal decay of the thermoluminescence of single crystals of lithium fluoride activated by x‐rays has been determined at various temperatures. The results are interpreted in terms of a simple reaction rate mechanism based on a picture of the thermoluminescent process similar to that of Johnson. The analysis of the isothermal decay studies is in agreement with the results of ``glow curve'' experiments on similar lithium fluoride samples where the intensity of luminescence is measured as the temperature of the crystal is heated at a constant rate.
Two principal types of electron traps in lithium fluoride are found to have trapping energies of 19,800 cal./mole and 45,300 cal./mole respectively.

Electrochemical Thermodynamics and Kinetics of Hydrogen Overvoltage
View Description Hide DescriptionThe problem of hydrogen overvoltage is attacked by a method making systematic use of chemical and electrochemical potentials. More precise formulas are thereby obtained than in previous theories and a more definite interpretation of the transfer coefficient of Erdey‐Grúz and Volmer is arrived at. The Tafel empirical equation is discussed and the existence, in some cases, of several Tafel regions is considered. Activation free energies,energies, and entropies for the discharge process are calculated and the mechanism involving formation of atomic hydrogen is shown to be entirely plausible.

The Infra‐Red Spectrum and Molecular Configuration of Hydrogen Persulfide
View Description Hide DescriptionThe infra‐red spectrum of hydrogen persulfide has been investigated in the region 1.5 to 15μ, and vibrational assignments have been made. The perpendicular band at 2μ has been studied under high resolution and a value for one of the rotational constants has been obtained. The data strongly support a chain structure for hydrogen persulfide and probably exclude cis‐ or trans‐planar structures, but give no very definite information regarding the azimuthal angle.

The Vibrational Spectra of Molecules and Complex Ions in Crystals. II. Benzene
View Description Hide DescriptionThe infra‐red spectrum of crystalline benzene has been studied at −12°C, −65°C and −170°C as well as the liquid at 28°C. The lines are extremely sharp, the mean line width for fundamentals being 7 cm^{−1} in the crystal. In three cases, it is less than the spectral slit width. All out‐of‐plane degenerate modes are split by about 10 cm^{−1}. Selection rules are obeyed and agree with the reported x‐ray structure. All ungerade fundamentals are observed directly, some for the first time. Fifty‐two combination bands are observed. The frequency assignments of Ingold et al. are confirmed except for the B _{2u } species. Evidence is cited for re‐assigning ν_{14} from 1648 cm^{−1} to 1310 cm^{−1} and ν_{15} from 1110 cm^{−1} to 1150 cm^{−1}. Ingold's isotopic data does not conflict with this change. Combination frequencies involving torsional lattice modes are apparently observed at −170°C.

Formulas and Numerical Tables for Overlap Integrals
View Description Hide DescriptionExplicit formulas and numerical tables for the overlap integral S between AO's (atomic orbitals) of two overlapping atoms a and b are given. These cover all the most important combinations of AO pairs involving ns, npσ, and npπ AO's. They are based on approximate AO's of the Slater type, each containing two parameters μ [equal to Z/(n—δ)], and n—δ, where n—δ is an effective principal quantum number. The S formulas are given as functions of two parameters p and t, where p=½(μ_{ a }+μ_{ b })R/a _{H} , R being the interatomic distance, and t=(μ_{ a }—μ_{ b })/(μ_{ a }+μ_{ b }). Master tables of computed values of S are given over wide ranges of p and t values corresponding to actual molecules, and also including the case p=0 (intra‐atomic overlap integrals). In addition, tables of computed S values are given for several cases involving 2‐quantum s, p hybrid AO's.
Hybrid S values for any desired type of hybrid can be obtained very easily from the tables as simple linear combinations of non‐hybrid S values. It is shown how S values corresponding to orthogonalized Slater AO's and approximate S values for SCF (self‐consistent‐field) AO's can also be obtained as linear combinations of the Slater‐AO S values. S values for carbon‐carbon 2pσ‐ and 2pπ‐bonds using SCF carbon AO's have been computed (see Table in Section Vb); they correspond to stronger overlap than for Slater AO's. Non‐localized MO group‐orbital S values are also discussed, and are illustrated by an application to H_{2}O. The use of the tables to obtain dipole moments for electronic transitions in certain cases is also mentioned. The use of the tables to obtain S values for various specific atom‐pairs and bond‐types, and resulting conclusions, will be discussed in another paper.

Measurements of Normal Burning Velocities and Flame Temperatures of Bunsen Flames
View Description Hide DescriptionStroboscopically illuminated particle tracks are used to accurately measure normal burning velocities of laminar flames. The precision of the measurements is increased by the use of a constant‐velocity profile nozzle which gives a straight‐sided Bunsen cone. Normal burning velocity data are presented for 3.7 to 5.3 percent propane‐air mixtures. The value for the stoichiometric flame was determined to be 44.8 cm/sec.
From stroboscopic and streak photographs of particle tracks it is possible to obtain the maximum flame temperature and temperature distribution in the flame front. Measurements from the two types of photographs are combined with the equation of continuity and the equation of state to obtain the flame temperature. The flame temperature for a stoichiometric propane‐air flame was determined to be 2220°K. An extension of this method is used to obtain an approximation of the temperature distribution in the flame front.

Some Properties of van der Waals' Liquids
View Description Hide DescriptionA theoretical consideration of the volume of a van der Waals' liquid suggests some new rules, comparable to that of Trouton, relating coefficients of expansion and compressibility to heats of vaporization. According to the simplest and most reliable of these new relationships, the product of the coefficient of cubical expansion and the heat of vaporization, αΔH_{v}, is the same for many liquids and equal to about 10 cal./deg. It is further shown that at a given temperature, ΔH_{v} ^{2}β/V is also constant where β is the compressibility and V the volume of the liquid. Certain corollary rules are derived by combining the above two with each other and with Trouton's law. These new rules should prove of some value in estimating compressibilities and heats of vaporization from coefficients of expansion.

A Normal Coordinate Analysis of the Planar Vibrations of Substituted Ethylenes. I. CH Bending Modes
View Description Hide DescriptionA normal coordinate analysis of the planar vibrations of some substituted ethylenes is carried out. Thirteen compounds are studied, including mono‐substituted and 1:1‐ and cis‐ and trans−1:2‐disubstituted ethylenes. Various solutions for the CH bending force constants are obtained and correlated. Some attempt is made to study the range of allowed solutions, and to examine the coupling of the different coordinates in the potential function.

Physical Properties of Polonium. I. Melting Point, Electrical Resistance, Density, and Allotropy
View Description Hide DescriptionMeasurements on the electrical resistance, thermal coefficient of electrical resistance, melting point and density of polonium are reported. An abrupt change in the electrical resistance near 100°C indicates that polonium exists in two allotropic forms. Observations which indicate that the temperature for crystal transformation is a function of the size and history of the specimen are reported.

Physical Properties of Polonium. II. X‐Ray Studies and Crystal Structure
View Description Hide DescriptionStructures are proposed which account for the powder diffraction patterns obtained from samples of polonium containing various amounts of lead. Unusual temperature effects are recorded for α‐polonium. It is suggested that the Pb and Po are present in interpenetrating primitive cubic lattices which are indistinguishable because the atomic numbers are nearly the same.

The Physical Properties of Polonium. III. The Half‐Life of Polonium
View Description Hide DescriptionThe half‐life of polonium has been measured by a calorimetric method. The reproducibility and precision of the data is much greater than has been previously reported. The value is found to be 138.3±0.1 percent days.