Showing papers in "Journal of Chemical Physics in 1940"
TL;DR: In this article, a relation between the actual transformed volume V and a related extended volume V1 ex is derived upon statistical considerations, and a rough approximation to this relation is shown to lead, under the proper conditions, to the empirical formula of Austin and Rickett.
Abstract: Following upon the general theory in Part I, a considerable simplification is here introduced in the treatment of the case where the grain centers of the new phase are randomly distributed. Also, the kinetics of the main types of crystalline growth, such as result in polyhedral, plate‐like and lineal grains, are studied. A relation between the actual transformed volume V and a related extended volume V1 ex is derived upon statistical considerations. A rough approximation to this relation is shown to lead, under the proper conditions, to the empirical formula of Austin and Rickett. The exact relation is used to reduce the entire problem to the determination of V1 ex, in terms of which all other quantities are expressed. The approximate treatment of the beginning of transformation in the isokinetic range is shown to lead to the empirical formula of Krainer and to account quantitatively for certain relations observed in recrystallization phenomena. It is shown that the predicted shapes for isothermal transfo...
7,448 citations
TL;DR: In this article, an empirical equation for the isothermal variation with density of the work content of pure hydrocarbons in the gaseous or liquid state is given, and a procedure is suggested for determining numerical values of the parameters in the equation.
Abstract: An empirical equation is given for the isothermal variation with density of the work content of pure hydrocarbons in the gaseous or liquid state. From this fundamental equation are derived (a) an equation of state, (b) an equation for the fugacity, and (c) an equation for the isothermal variation of the enthalpy. These equations summarize P‐V‐T properties of the gaseous or liquid phase, critical properties, vapor pressures, and latent heats of evaporation. A procedure is suggested for determining numerical values of the parameters in the equation. Such values are given for methane, ethane, propane, and n‐butane. A comparison is made between observed properties of these hydrocarbons and those predicted by the equations.
519 citations
TL;DR: In this paper, the statistical fluctuations of a simple autocatalytic reaction mechanism are set up and solved completely, and the fluctuations are found to approach a constant limiting value when the amount of reaction product is large compared to the amount which initiates the reaction.
Abstract: The differential equations describing the statistical fluctuations of a simple autocatalytic reaction mechanism are set up and solved completely. The fluctuations are found to approach a constant limiting value when the amount of reaction product is large compared to the amount which initiates the reaction. The relative fluctuations which arise from the reaction mechanism are then equal to the reciprocal of the square root of the initial number of particles. Conversely the fluctuation in the time required to attain a threshold amount of reaction product also approaches a limiting value for high thresholds. This limiting value is greater than one time unit if the reaction is initiated by one particle, and becomes equal to one divided by the square root of the number of initiating particles if this number is large.
256 citations
TL;DR: In this article, the dipole strengths for certain perpendicular-type transitions N→Q in the mixed halogens, the hydrogen and monovalent metal halides, and the alkyl halides are calculated theoretically by the LCAO and by the AO approximations.
Abstract: The dipole strengths for certain perpendicular‐type transitions N→Q in the mixed halogens, the hydrogen and monovalent metal halides, and the alkyl halides, are calculated theoretically by the LCAO and by the AO approximations. The scanty experimental absorption coefficient data on these halides (particularly the hydrogen and alkyl bromides and iodides) are critically examined, and acceptable experimental dipole strengths are obtained for the bromides. These show, very gratifyingly, the same kind of agreement with the calculated values as was found in IX of this series for the N→Q transitions in F2, Cl2, and Br2. The iodides, however, just like I2, show anomalously low strengths for the true N→Q part of the intensity (N→3II1 and N→1II), together with high strength for N→3II0+. These anomalies are ascribed here, as in I2, to partial case c coupling (partial preservation of atomic J's). The comparison between theory and experiment confirms the interpretation of the ultraviolet continua of the hydrogen and a...
249 citations
TL;DR: In this article, a method was developed for calculating thermodynamic functions for long chain molecules with particular attention to normal paraffins, and the calculated entropies were brought into agreement with experimental values on the basis of very reasonable internal rotation restricting barriers.
Abstract: A method is developed for calculating thermodynamic functions for long chain molecules with particular attention to normal paraffins. In this connection the infinite chain approximation method for calculating vibration frequencies is considered. Starting with the results of Kirkwood, a modification is made which improves the agreement with the exact values for the simpler cases. In addition this method of attack is extended to out of plane motions. This vibrational analysis shows that all skeletal frequencies for molecules of the normal paraffin type can be put into two groups, one fairly narrow band near 1000 cm—1, and a broader band extending from 0 to 460 cm—1. The partition function is then set up on the assumption that motions in the low frequency group can be treated classically, and that the high frequency band can be replaced by a suitable number of 1000 cm—1 frequencies. Contributions from hydrogen atom vibrations are added on later. A formula is finally obtained which is quite simple, considering the complexity of the molecules. The calculated entropies can be brought into agreement with experimental values on the basis of very reasonable internal rotation restricting barriers.
246 citations
TL;DR: In this paper, the authors investigated the kinetics of bleaching by measuring photometrically the concentration of the dye in the photostationary state and derived the initial concentrations and light intensity.
Abstract: Solutions containing thionine and ferrous salts are bleached by illumination and recover their color in the dark. The kinetics of this reaction are investigated, by measuring photometrically the concentration of the dye in the photostationary state. Equations are derived for this state in terms of the initial concentrations and light intensity. At low thionine concentrations the extent of bleaching is proportional to the first power of light intensity and inversely proportional to the concentration of ferric ions. The bleaching reaches a maximum at a certain thionine concentrations and then decreases inversely proportional to the concentration of the dye. The bleaching increases strongly with increasing acidity. Kinetic mechanisms accounting for these relationships are discussed, and quantum yields and velocity constants are estimated. It is pointed out that the accumulation of free radicals (``semiquinones'') and the occurrence of ``circular'' mechanisms maintaining the steady state are typical of photostationary states as distinguished from true equilibria.
229 citations
TL;DR: A theory of depolymerization of long chain molecules is developed on a statistical basis and relationships are established between the average molecular weight of the degraded product and the average number of bonds split per molecule.
Abstract: A theory of depolymerization of long chain molecules is developed on a statistical basis. It is assumed that all bonds connecting monomeric elements in the system have the same probability of being broken regardless of their position in a given polymer and regardless of the size of the polymer in which they are found. Expressions are derived for the distribution of molecular sizes in the depolymerized system as a function of the initial chain length and the average number of bonds split per molecule. Also, relationships are established between the average molecular weight of the degraded product and the average number of bonds split per molecule. Experiments on the acetolytic degradation of cellulose acetate are briefly discussed.
215 citations
TL;DR: In this article, the crossing points between the polar and homopolar states for the reactions M2+X→MX+M are drawn in so close that the interaction is large enough to insure transition.
Abstract: In many of the reactions of the alkali metals with the halogens the reacting system changes from a homopolar to a polar state, or vice versa The possibility of a restriction on this change is considered, and it is concluded that there will be a serious restriction only for some of the atomic reactions M+X→MX, which are of little importance The crossing points between the polar and homopolar states for the reactions M2+X→MX+M M+X2→MX+X are drawn in so close that the interaction is large enough to insure transition Due to the threefold degeneracy of the initial state of b (which arises because X is in a P state) this reaction has the possibility of leading directly to the excitation of the M atom which is formed The nature of the potential surfaces for this process are considered The process first suggested by Polanyi, the excitation of M atoms by vibrationally excited MX molecules, is discussed This process is possible because of a crossing of the two lowest polar states for the M2X system These two surfaces cross for a certain isosceles triangular configuration Reacting systems thus easily go from the lowest to the second state in this region
213 citations
TL;DR: In this article, the photogalvanic potential e* was determined in relation to composition and light intensity, and the results were in a qualitative and partially quantitative agreement with the kinetic theory of the photoglvanic effect.
Abstract: The oxidation‐reduction system thionine‐iron, described in paper I, provides an extremely sensitive photogalvanic cell. The illuminated half‐cell is negative in respect to the nonilluminated one. The photogalvanic potential e* is determined in relation to composition and light intensity. The results are in a qualitative (and partially quantitative) agreement with the kinetic theory of the photogalvanic effect. In strongly bleached solutions, the electrode potential is maintained by semithionine ions transferring electrons to the electrode, and ferric ions acquiring electrons from the electrode, whereas ferrous ions and leukothionine ions remain practically inactive. In weakly bleached solutions, the mechanism is more complicated.
137 citations
116 citations
TL;DR: In this article, the thermodynamic relations of insoluble monolayers on a mobile subphase are given, and equations for their increase of entropy, heat absorbed, increase of heat content, and increase of internal energy, during expansion.
Abstract: The thermodynamic relations of insoluble monolayers on a mobile subphase are given, and equations are presented for their (a) increase of entropy, (b) heat absorbed, (c) increase of heat content, and (d) increase of internal energy, during expansion. Two different methods of expansion are considered: in spreading the decrease of area of the subphase is equal to the increase of area of the monolayer; in extension the monolayer expands but the area of the clean surface of the subphase remains constant. The two‐dimensional phases are classified as: I. gas; II. liquid (L1) expanded; III. intermediate or transition; IV. liquid (L2) condensed; and V. solid. The extreme limits of molecular area for the intermediate liquid phase are for pentadecylic acid about 22 and 44A2, while those for the liquid phases IV, III, and II, are from about 20.5 to 52A2 which indicates that, beginning with a two‐dimensional liquid in its most condensed condition, the mean molecular distances may be increased by as much as 60 percent...
TL;DR: The absorption coefficient of nitrogen dioxide in the visible spectrum has been measured at pressures up to 70 mm Hg with a 40A or 15A spectrophotometer slit as discussed by the authors.
Abstract: The absorption coefficient of nitrogen dioxide in the visible spectrum has been measured at pressures up to 70 mm Hg with a 40A spectrophotometer slit. Beer's law is obeyed in this region. The transmission as measured when using a tungsten source, is the same as that oftained with either a high or low pressure mercury arc, except at the 4339–4358A group of mercury lines, where the absorption coefficient was found to be 15 percent greater with the mercury source. The absorption coefficient curve obtained with either a 40A or 15A slit is essentially sinusoidal in appearance, the absorption maxima and minima generally differing by about 10 percent in intensity. The maxima are separated by 700±100 cm—1. They appear to be due, not to the ground state of the molecule, but to groups of excited levels which are uniformly separated.
TL;DR: In this article, an anomalous intensity distribution similar to that of S2 is found for NO assuming that the e absorption bands are a continuation of the γ bands. But this is a case of genuine predissociation and not pressure broadening.
Abstract: From the observed anomalous intensity distribution in the S2 bands it is concluded that the dissociation limit for the first predissociation of S2 lies appreciably below the predissociation limit (4.4 ev). It is found that the anomalous intensity as well as the diffuseness persists even at very low pressures (0.01 mm) and that therefore this is a case of genuine predissociation and not pressure broadening as assumed by Lochte‐Holtgreven. The second predissociation of S2 starting with the 18 ‐ 0 band leads to an upper limit of 3.6 ev for the heat of dissociation of S2. An anomalous intensity distribution similar to that of S2 is found for NO assuming that the e absorption bands are a continuation of the γ bands. This indicates a predissociation of NO in the upper 2Σ state of the γ bands into normal atoms with a limit 1.3 ev above the dissociation limit. The remarkable intensity distribution found by Schuler and co‐workers in the CuH emission band λ4280 at low pressure is explained as due to a predissociati...
TL;DR: In this article, the relative partial molal entropy of water, S 1 −S 10, in aqueous electrolyte solutions is calculated from existing data, and an attempt is made to correlate these values with changes in the structure of water in the solutions.
Abstract: The relative partial molal entropy of water, S1–S10, in aqueous electrolyte solutions is calculated from existing data. An attempt is made to correlate these values with changes in the structure of water in the solutions. It is found that cations of small radii and ions capable of forming hydrogen bonds with the water, such as H3O+, OH— and NH+4, help to stabilize the water structure, while large ions and ions of nonspherical and nontetrahedral shapes have an effect in the opposite direction. In dilute solutions the entropy of dilution depends largely on the ionic strength. In all cases deviations from the Debye‐Huckel limiting law are positive.
TL;DR: In this paper, the energy levels for the configuration d3 of the chrome ion in chrome alum are calculated by starting with the empirical spectroscopic data on the free Cr+++ ion, and then making the assumption that the interatomic forces in the solid state can be represented by a crystalline potential of cubic symmetry, whose magnitude is taken from the theory of the magnetic susceptibility.
Abstract: The energy levels for the configuration d3 of the chrome ion in chrome alum are calculated by starting with the empirical spectroscopic data on the free Cr+++ ion, and then making the assumption that the interatomic forces in the solid state can be represented by a crystalline potential of cubic symmetry, whose magnitude is taken from Schlapp and Penney's theory of the magnetic susceptibility. The particular point to be tested is whether in the solid there is a doublet level only 15,000 cm—1 above the basic quartet state, as predicted in the preceding paper from the study of Spedding and Nutting's data on the Zeeman effect. The computed deepest doublet is about 18,200 cm—1 higher than the ground level, but the discrepancy is not excessive in view of uncertainties in the parameters of the crystalline field and the fact that any ``one‐atom'' model is only an approximation in the solid state. As already suggested by Spedding and Nutting, it is very essential in computing the positions of excited levels, to i...
TL;DR: In this paper, the Hertz-Knudsen equation was used to derive the rate of adsorption and desorption of a gas molecule in the presence of an adsorbing center on the solid surface.
Abstract: By regarding the process of adsorption as involving a reaction between a molecule of gas and an adsorbing center on the solid surface, it has been possible, with the aid of the theory of absolute reaction rates, to derive for the rates of adsorption and desorption of gases simple equations which can be tested experimentally. Different results are obtained according as the adsorbed gas forms an immobile or a mobile layer on the surface: in the latter circumstance, which does not appear to be common, the rate of adsorption would be given by the Hertz‐Knudsen equation, provided there were no activation energy for adsorption. Combination of the expressions for the rates of adsorption and desorption gives an adsorption isotherm of the same form as that originally derived by Langmuir. Various cases of adsorption accompanied by dissociation of the adsorbed molecule are considered and the appropriate rate equations are deduced. If the molecule undergoes dissociation in the course of adsorption and the atoms remai...
TL;DR: In this paper, the complete energy matrix is set up for external and (hindered) internal rotations of ''pseudo-rigid'' molecules; i.e., molecules consisting of a rigid framework to which symmetric hindered rotators are attached.
Abstract: The complete energy matrix is set up for external and (hindered) internal rotations of ``pseudo‐rigid'' molecules; i.e., molecules consisting of a rigid framework to which symmetric hindered rotators are attached. The reduced secular equation for the energy levels of such a molecule with one internal rotation is given explicitly. By using the perturbation method of Wilson, the partition function for this model is found, correct to the second order. Effects due to angular momentum couplings are included. A simple method for the calculation of thermodynamic contributions of hindered internal rotations is given. As an example, the application of the method to propylene is described; in this case, the coupling terms here included may amount to as much as 19 percent of the effect of the hindering potential on the thermodynamic contributions.
TL;DR: In this paper, the Ramaman spectra were analyzed for CH3·ND2, NH3+ and NH2 groups, and the corresponding deformation frequencies of the NH2 and NH3 groups were found to be near 1620.
Abstract: Raman Spectra are reported for CH3·ND2, CH3·ND3+, +D3N·ND3+ and +D3N·ND2. Comparison with the spectra of the corresponding compounds containing no deuterium reveals three classes of frequencies: (1) Those arising from the methyl group are unchanged within the experimental error by deuterium substitution in the amino group. (2) The amino and ammonium group frequencies are higher in the H than in the D compounds by a factor of 1.33 to 1.36. Among these a characteristic —ND3+ valence vibration is found near 2180 cm—1, corresponding to an —NH3+ vibration near 2970. These frequencies are broad and rather faint, and are lower by several hundred wave numbers than the corresponding sharp intense lines arising from the uncharged —NH2 and —ND2 groups. The principal deformation frequency of the NH3+ and NH2 groups appear to be near 1620; the corresponding frequency of the —ND3+ and —ND2 groups is near 1200. (3) Other frequencies are changed by a factor of less than 1.3 when deuterium is substituted for hydrogen in t...
TL;DR: In this article, the Raman spectra of P(CH3)3 and As(CH 3)3 have been photographed and studied in relation to the methyl compounds of nitrogen, antimony and bismuth.
Abstract: The Raman spectra of P(CH3)3 and As(CH3)3 have been photographed and studied in relation to the spectra of the methyl compounds of nitrogen, antimony and bismuth. The low lying frequencies of all of these molecules can be interpreted in terms of a pyramidal structure with the methyl groups acting as units. The existence of only two low lying lines in the spectra of Sb(CH3)3 and Bi(CH3)3 is attributed to an accidental degeneracy resulting from the relatively large mass of the central atom and a particular value of the apex angle. The frequencies computed from a two‐constant valence force potential function are in good agreement with those observed. The force constants obtained are tabulated.
TL;DR: The wave numbers and relative intensities of 500 of the absorption bands of benzene vapor in the 2600A region have been determined as discussed by the authors, and a detailed study has been made of the variation of intensity with temperature of the main band of the A, B, and D progressions.
Abstract: The wave numbers and relative intensities of 500 of the absorption bands of benzene vapor in the 2600A region have been determined. A detailed study has been made of the variation of intensity with temperature of the main band of the A, B, and D progressions. These three bands have been assigned to the ground state, the 606‐cm—1 and 2×606‐cm—1 vibrational states, respectively, by Sponer and collaborators. The experimental data are in good agreement with a statistical calculation of the population factors for these states.
TL;DR: In this paper, a theory of phase changes due to hindered molecular rotation in crystals is developed on the basis of classical statistical mechanics, and it is demonstrated that local hindrance of relative rotation of neighboring molecules in the lattice can produce a non-uniform distribution in orientation below a certain critical temperature.
Abstract: A theory of phase changes due to hindered molecular rotation in crystals is developed on the basis of classical statistical mechanics. It is demonstrated that local hindrance of relative rotation of neighboring molecules in the lattice can produce a non‐uniform distribution in orientation below a certain critical temperature. The theory provides a semi‐quantitative description of the behavior of the hydrogen halides in certain of their lambda‐transitions, with a relative torque potential of the form (e/2) cos γ for a pair of neighboring molecules, the axes of which are inclined at an angle γ to each other. The barrier height e is estimated to be between 200 and 300 cal./mole for hydrogen iodide and hydrogen bromide.
TL;DR: In this paper, the absorption spectrum of furan vapor between 2200 and 1550A shows three band systems which overlap slightly, one with a 0-0 band at 52,230 cm-1 has sharp bands which could be analyzed to reveal three prominent symmetrical vibration frequencies of the excited molecule of 1395 cm.
Abstract: The absorption spectrum of furan vapor between 2200 and 1550A shows three band systems which overlap slightly. The second of these with a 0–0 band at 52,230 cm—1 has sharp bands which could be analyzed to reveal three prominent totally symmetrical vibration frequencies of the excited molecule of 1395 cm—1, 848 cm—1 and 1068 cm—1. Other characteristic frequency differences in the more diffuse bands are noted. Since the furan was found to be comparatively stable to photochemical decomposition, measurements of the intensity of absorption were made.
TL;DR: In this article, the vibration spectra of hydrazoic acid, methyl azide, and methyl isocyanate have been investigated in the spectral region between 2 and 20μ.
Abstract: The vibration spectra of hydrazoic acid, methyl azide, and methyl isocyanate have been investigated in the spectral region between 2 and 20μ. Correlation of the spectra of these structurally similar molecules has made possible the determination of all the fundamental frequencies of hydrazoic acid and all but the methyl torsion frequency in the methyl compounds. From these fundamental frequencies and the known rotational constants, the usual thermodynamic functions of hydrazoic acid have been calculated to the harmonic oscillator‐rigid rotator approximation. Equilibrium constants for some characteristic reactions have also been obtained.
TL;DR: In this article, the third and fourth harmonics of the N-H stretching frequency in hydrazoic acid, at 9547.31 and 12,412.19 cm-1, respectively, have been studied photographically under high dispersion.
Abstract: The third and fourth harmonics of the N–H stretching frequency in hydrazoic acid, at 9547.31 and 12,412.19 cm—1, respectively, have been studied photographically under high dispersion. The rotational structure has been well resolved and completely analyzed, to yield the rotational constants in the ground and excited states. The effective moments of inertia in the ground state have been combined with other information to determine the structure of the molecule; the best values of the molecular parameters are: N1–H=1.012AN2–N3=1.128AN1–N2=1.241AΔHN1N2=110∘52′.
TL;DR: In this article, it was shown that the normal modes of vibration of chain molecules fall into two classes; end vibrations in which the amplitude falls off exponentially from the ends towards the middle, and chain vibrations that it varies harmonically as in a standing wave.
Abstract: Theory indicates that the normal modes of vibration of chain molecules fall into two classes; end vibrations in which the amplitude falls off exponentially from the ends towards the middle, and chain vibrations in which it varies harmonically as in a standing wave. The transition from one class to the other takes place via chain vibrations with a small number of nodes of amplitude along the chain. For a long chain we expect only those chain vibrations to show up in the infra‐red spectrum for which the phase of the electric moment is constant along the chain.These considerations have been applied to predict the vibration spectra of the straight chain paraffins, assumed to consist of a zigzag chain of carbon atoms each carrying two hydrogen atoms in a plane perpendicular to the chain and alternately above and below it.The infra‐red spectrum of undecane has been measured from 1 to 15μ on a prism spectrometer, the positions of 31 bands being determined. Accepted values of the interatomic distances and angles ...
TL;DR: In this paper, a continuation of measurements on the gaseous heat capacities by the adiabatic expansion method is presented, where the compounds with which the present paper deals are dimethyl ether, ethylene oxide, dimethyl acetylene, cis-butane-2 and trans-butene-2.
Abstract: The present paper presents a continuation of measurements on the gaseous heat capacities by the adiabatic expansion method. The apparatus and the experimental procedure are exactly the same as described in the previous papers denoted herein as Part I and Part II. The compounds with which the present paper deals are dimethyl ether, ethylene oxide, dimethyl acetylene, cis-butane-2 and trans-butene-2. For the correction of the experimental data to the ideal gas state several procedures had to be used, as discussed in Part II.
TL;DR: In this paper, the vibration of the O-H group in alcohol and HDO has been studied in the 3μ region for solutions and ternary mixtures at different concentrations and temperatures.
Abstract: The vibration of the O–H group in alcohol and HDO has been studied in the 3μ region for solutions and ternary mixtures at different concentrations and temperatures. The experimental results are discussed in terms of association and addition‐compound formation.
TL;DR: In this paper, it was shown that such a relation does exist between those quantities for series of diatomic molecules belonging to the same row in the periodic table, provided one uses an effective internuclear distance re−dij.
Abstract: With a view to obtaining the internuclear distances and dissociation energies of individual bonds in polyatomic molecules purely from a knowledge of force constants the consequences of assuming that the potential energy of any di‐atom may be expressed in the form V=—α/rm+β/rn have been further investigated. In addition to giving a relation between internuclear distance and force constant of the form suggested empirically by Badger, this assumption leads to a relation between force constant (ke), internuclear distance (re) and dissociation energy (De) of the form De=(kere2)/mn. It is found that such a relation does exist between those quantities for series of diatomic molecules belonging to the same row in the periodic table, provided one uses an ``effective'' internuclear distance re—dij. This was also used by Badger in his relation of force constant to internuclear distance and the values of dij obtained by the two different methods are in reasonably good agreement. The values obtained for the product mn...