Volume 21, Issue 6, 01 June 1953
Index of content:
21(1953); http://dx.doi.org/10.1063/1.1699143View Description Hide Description
An expression for the free energy of a binary cubic alloy undergoing the order‐disorder transition is derived by direct evaluation of the configurational partition function.
Thermodynamic Functions from Mayer's Theory of Ionic Solutions. I. Equations for Thermodynamic Functions21(1953); http://dx.doi.org/10.1063/1.1699144View Description Hide Description
For an ionic solute, Mayer has previously derived from statistical mechanics an analytical expression for a mean activity coefficient which, however, is not usually measured. From the partial molal free energy expression defining Mayer's activity coefficient, there are derived in this paper expressions for five usually measured thermodynamic functions. These are the change in partial molal volume with concentration; the change in apparent molal volume with concentration; the relative partial molal heat content; the relative apparent molal heat content; and the stoichiometric mean ionic molar activity coefficient. Formulas for these five functions involve the coefficients of thermal expansion and isothermal compressibility of the solution and solvent; the solventdielectric constant and its pressure and temperature derivatives; and readily computable analytic expressions arising from the theory.
Thermodynamic Functions from Mayer's Theory of Ionic Solutions. II. The Stoichiometric Mean Ionic Molar Activity Coefficient21(1953); http://dx.doi.org/10.1063/1.1699145View Description Hide Description
The formula for the stoichiometric mean ionic molar activity coefficient of strong electrolytes in aqueous solution at 25°C arising from Mayer's theory is compared with published experimental data. The agreement is good for sodium chloride to a concentration of about 0.4 molar; calcium chloride to a concentration of about 0.07 molar; zinc sulfate to a concentration of about 0.01 molar; and lanthanum chloride to a concentration of about 0.017 molar. Tables facilitating the computations and practical methods for the determination of the parameter of closest interionic approach and of the activity coefficient are given.
21(1953); http://dx.doi.org/10.1063/1.1699146View Description Hide Description
The trimethylaluminum dimer has a bridge structure with a skeletal symmetry of D 2h within the accuracy of a structure determination by x‐ray diffraction of single crystals. Bridge bonds, Al–C, equal 2.24A, vs Al–C bonds of 1.99A for the exterior, ``normal'' methyls. The bridge angle Al–C–Al=70°, the exterior angle C–Al–C=124°.
It is shown that a simple model provides the right order of magnitude for the heat of dimerization and indicates the relative importance of Al–C and Al–Al bonds. It is suggested that the sharp bridge angle required for good bridge bonding leads to metal‐metal repulsions which should increase as the size of the metal increases. This probably plays a role in the instability and nature of polymers of the heavier trialkyl‐metal compounds.
21(1953); http://dx.doi.org/10.1063/1.1699147View Description Hide Description
The photolysis of acetone has been studied in the temperature range 130–420°C. Measurements have been made of the rates of most of the possible reactions of CH3 and CD3 radicals with hydrogen, deuterium, and deuterium hydride. The following activation energies for the abstraction of a hydrogen or deuterium atom have been found: CH3+acetone, 9.7; CD3+d acetone, 11.6; CH3+D2, 11.8; CD3+H2, 11.1; CH3+HD→CH4, 10.0; CH3+HD→CH3D, 11.3; CD3+HD→CD3H, 10.7; CD3+HD→CD4, 10.7 kcal. The steric factors are all of the order of 10−3. The results are discussed in terms of isotope effects with particular reference to the deuterium hydride reactions.
21(1953); http://dx.doi.org/10.1063/1.1699099View Description Hide Description
Under intense ultraviolet illumination with an A‐H6 mercury arc, benzene solutions in rigid glass at liquid air temperatures are decomposed. If the solvent molecules contain hydrogen, hexatriene is formed (almost certainly identified by absorptionspectrum and chemical behavior). In a solvent (perfluoro−2‐methyl pentane) containing no hydrogen, the benzene decomposes to an entirely different product, not as yet certainly identified.
The Magnetic Susceptibility of Certain Organic Compounds. Part IV. The Constitution of Ortho, Meta, and Para Nitroanilines21(1953); http://dx.doi.org/10.1063/1.1699100View Description Hide Description
Magnetic susceptibilities of o‐, m‐, and p‐nitroanilines have been measured by the Gouy method. The experimental results showed that for a strong repelling group such as the amino group, the values for the op‐derivatives are lower than the corresponding m‐derivative. This was attributed to the fact that there is a tendency for the amino group to conjugate with the benzene nucleus in the case of o‐ and p‐nitroanilines, accompanied by a lowering in their diamagnetic susceptibility values.
21(1953); http://dx.doi.org/10.1063/1.1699101View Description Hide Description
The repulsive energy of three helium atoms is calculated using the valence bond method. A great reduction of the required number of exchange integrals is found to be possible using group theoretical arguments. It is found that the effect of nonadditivity is negligible for the internuclear distances involved in most physical problems.
21(1953); http://dx.doi.org/10.1063/1.1699102View Description Hide Description
The unification of the atomic orbital and molecular orbital theories of the excited states of diatomic molecules is achieved by means of semi‐localized orbitals. In particular the classification of the states of the fluorine molecule arising from the interaction of two fluorine atoms in their ground state is discussed.
Quantitative calculations are made for the 1Σ g + and 3Σ u + states and a comparison of the singlet‐triplet separation energies and binding energies from the three methods is made. Both two electron and eighteen electron calculations are made. The better molecular orbital calculations give a lower triplet than a singlet state. In the eighteen electron calculation the atomic and semi‐localized orbital methods coincide, and the 1Σ g + state is found to be the ground state.
21(1953); http://dx.doi.org/10.1063/1.1699103View Description Hide Description
The photolysis of azomethane has been investigated over the temperature range 24–190°C. The variation in the rates of production of nitrogen, methane, and ethane with absorbed intensity, azomethane concentration, and temperature may be accounted for quantitatively by the reactions
The quantum yield of nitrogen formation was found to be unity and independent of temperature. For the activation energy difference E 2—½E 3 a value of 7.6 kcal/mole was obtained. Evidence is cited for an association reaction between methyl radicals and azomethane. On the basis of an assumed mechanism, the activation energy of this process is 6.4 kcal/mole.
21(1953); http://dx.doi.org/10.1063/1.1699104View Description Hide Description
Absorption coefficients of oxygen were measured at several hundred wavelengths in the region 1050–1900A with a one‐meter vacuum monochromator and a phosphor‐coated photomultiplier as detector. The absorption intensity of the Schumann‐Runge continuum was found to be somewhat less than previous results, and the intensity distribution was less symmetrical. The 19–0 and 20–0 bands of the Schumann‐Runge progression were observed and the dissociation limit of the B 3Σ u − state was 57140±60 cm−1. Several other bands and continua were found at shorter wavelengths.
21(1953); http://dx.doi.org/10.1063/1.1699105View Description Hide Description
A statistical mechanical theory of the static dielectric constant of polar substances is presented which differs from the previous theories of Kirkwood and Fröhlich in that a precise evaluation of the distortion polarization term is made. The theory is applied to the dielectric constant of ordinary and heavy water and yields 2 percent agreement with experiment over the entire temperature range. Furthermore, the difference between the dielectric constant of water measured at visible and microwave frequencies can be ascribed to vibrations, such as the bending of the O–H–O bond. The calculated dielectric constant of ice agrees with experimental values within a mean deviation of 3 percent over a considerable temperature range using an approximate evaluation of the Pauling model for that substance. Various other liquids are also compared with experiment.
21(1953); http://dx.doi.org/10.1063/1.1699106View Description Hide Description
The basic concepts and procedures underlying the theory of rubberelasticity are analyzed. The arguments advanced by Wall and Flory against the network theory of the authors are shown to be without foundation. The alternative theory which they advocate, and which is rather widely used, is criticized on two grounds: (a) it assumes a distribution of chain extensions that does not vary with network extension in the way the actual distribution functions can be shown to vary, and (b) the methods used to compute the numbers of network configurations from the distributions of chain extensions are invalid, except in the most trivial cases. The concept of ``interval dilation entropy'' is discussed and is shown to lack any physical basis. It is concluded that all the methods of calculation that lead to logarithmic terms in the network configuration entropy are incorrect, and that these terms, which affect the theory of swelling, should be discarded.
21(1953); http://dx.doi.org/10.1063/1.1699107View Description Hide Description
Under similar conditions of concentration and light absorption the rate of the gas phase reaction is almost the same as the rate in carbon tetrachloride solution, studied previously, although the mechanism is somewhat different. The gas‐phase reaction is not inhibited by products and the bimolecular chain termination step consists in the formation of chlorine, rather than monochloromethyl chloroformate. First‐order removal of chlorine atoms becomes important at low light intensities.
The ratio of the rate constant for hydrogen chloride formation to that for first‐order chain termination is the same in the gas phase as in carbon tetrachloride solution within the accuracy of the measurements.
21(1953); http://dx.doi.org/10.1063/1.1699109View Description Hide Description
Equations are derived for the variation of potential with distance and for the components of charge and capacity in the diffuse double layer at a plane interface for electrolytes of the 1:2 and 2:1 valence types. Some additional relations are also deduced for other valence types.
Infrared and Raman Spectra of Fluorinated Ethanes. VI. The Series CF3CH3, CF3CH2Cl, CF3CHCl2, and CF3CCl321(1953); http://dx.doi.org/10.1063/1.1699110View Description Hide Description
The infrared spectra of gaseous CF3CH2Cl and CF3CHCl2 have been obtained in the range from 2 to 38μ, and the spectra of the liquids in the range from 2 to 22μ, with the aid of LiF, NaCl, KBr, and KRS−5 prisms. The Raman spectra of these compounds in the liquid state have been photographed with a three‐prism glass spectrograph of linear dispersion 15A/mm at 4358A. Depolarization ratios were determined for most of the Raman bands.
All fundamental vibrational frequencies have been assigned; the spectra have been interpreted in detail, and thermodynamic functions have been calculated.
21(1953); http://dx.doi.org/10.1063/1.1699111View Description Hide Description
The infrared spectra of liquid CCl3CF2Cl and of CCl3CFCl2 as glass and in CS2 solution, have been obtained in the region from 2 to 38μ with the aid of LiF, NaCl, KBr, and KRS−5 prisms. The Raman spectra of these compounds in the liquid state, at about 50° and 120°C, respectively, were photographed with a three‐prism glass spectrograph of linear dispersion 15A/mm at 4358A. Relative intensities and depolarization ratios were measured for all but the weakest Raman bands. Complete assignments of fundamental vibration frequencies have been made, the spectra have been interpreted in detail, and thermodynamic functions have been calculated.
21(1953); http://dx.doi.org/10.1063/1.1699112View Description Hide Description
The absorptionspectrum of fluoroform has been investigated with a Perkin‐Elmer double‐pass spectrometer from 2.2 to 20μ. The resolution is sufficient to make possible an unequivocal assignment of all six fundamentals on the basis of the observed band envelopes. An anomaly is found in the symmetrical C–F stretching vibration; on the evidence now available this vibration should be assigned to the parallel band at 1209.3 cm−1 in the infrared (vapor) and to the polarized Raman line (liquid) at 1117 cm−1. Overtone and combination bands measured include the A 1 and E components of the second harmonic of each of the three degenerate fundamentals. The separation of the maxima of the P and R branches of the parallel bands is discussed in relation to the theory of Gerhard and Dennison.
21(1953); http://dx.doi.org/10.1063/1.1699113View Description Hide Description
A model is presented which describes the geometrical effects in the radiolysis of water as a result of the diffusion of free radicals. The motion of secondary electrons immediately following the passage of the ionizing particle is discussed in an appendix, and it is concluded that radicals are most likely formed in pairs at the approximate sites of the original ionizations. Models for the diffusion of these radicals are shown to result in a definite fraction of radicals which undergo initial recombination for gamma‐ and fast beta‐rays, for which the spurs are considered as diffusing independently. For alpha‐rays a connected‐track model is used. For the intermediate case of tritium beta‐rays, a two‐stage model is constructed. In each case the comparative yields of the ``forward'' and ``radical'' reactions (GF and GR ) are calculated. Subsequent chemical effects in pure water and solutions are also considered briefly.
21(1953); http://dx.doi.org/10.1063/1.1699114View Description Hide Description
A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two‐dimensional rigid‐sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four‐term virial coefficient expansion.