O. K. Rice

Thermodynamics of Phase Transitions in Compressible Solid Lattices

The calculations on the Ising lattice and the order‐disorder phenomenon indicate that the specific heat may become infinite at the λ temperature or transition point. The general thermodynamics of such a system in a variable magnetic field is considered, and the relation to the generalized theories of critical points of Tisza and of Semenchenko is indicated. The general import of these theories is that infinite values of the heat capacity at constant pressure Cp, or the analogous heat capacity in a system with variables other than p, V, and T, can become infinite in a one‐phase system only at a critical point. The existence of a locus of points where Cp = ∞ is thermodynamically possible in the pVT system, and equations analogous to the Clapeyron and Ehrenfest equations may be derived. However, the thermodynamic requirements show that such a locus is not likely to occur. Interesting possibilities occur where there is an interaction between several sets of variables. If an Ising lattice is compressible, for ...

On the Recombination of Iodine and Bromine Atoms

The data on the rate of recombination of iodine and of bromine atoms in the presence of an inert gas have been used, together with the equilibrium data, to calculate the rate of dissociation of I2 and Br2. The results have been used to obtain effective collision radii for the collision of I2 and Br2 molecules with the inert gas molecules. If the inert gas is a monatomic, or sufficiently simple, molecule, these effective radii turn out to be of the order of magnitude of ordinary kinetic theory radii, provided proper allowance is made for the density of energy levels in excited I2 and Br2. The interpretation of abnormally large radii, obtained in some cases, has been discussed.

The Role of Heat Conduction in Thermal Gaseous Explosions

The theory recently developed by Frank‐Kamenetzky for thermal explosions in which heat is removed by conduction only, has been applied to the azomethane, ethyl azide and methyl nitrate explosions. A fairly detailed discussion has been given of the experimental results and their relation to the theory. In the case of azomethane and ethyl azide the conclusion is reached that at low pressures thermal conduction as contrasted to convection is an important, if not the exclusive, method of removal of heat from the reacting gas, with deviation appearing at high pressures. As was already concluded by Rice and Campbell, the results appear to indicate that the methyl nitrate explosion is not a thermal explosion. Certain criticisms directed by Frank‐Kamenetzky against the determination of the heat of reaction from the induction period, as carried out by Rice and Campbell, have been considered and refuted.

Coexistence Curve of the Triethylamine‐Water System

The coexistence curve of the system triethylamine‐water has been determined near its lower critical point. The observed critical temperature Tc is 18.33°C. There is evidence of a small horizontal portion of the coexistence curve, which extends from 0.559 to 0.657 volume fraction water, or from 0.907 to 0.936 mole fraction water, though the evidence is not absolutely certain. On the other hand, our results exclude the possibility of an anomalous phase transition in the concentration interval from 0.35 to 0.90 mole fraction water where, according to a report by J. E. Mayer, such an anomalous transition may occur. Outside the small horizontal portion the coexistence curve shows the same cubic behavior [(T–Tc)⅓, or better (T–Tc+0.007)⅓, proportional to the difference of the volume fractions of the phases in equilibrium] as do coexistence curves of systems with upper critical points, but is much flatter, the proportionality factor having a smaller absolute value.

Critical Isotherm and the Equation of State of Liquid‐Vapor Systems

Pressure‐volume‐temperature data on xenon, carbon dioxide, and hydrogen are analyzed. Special attention is paid to the regions fairly close to, but not in the immediate neighborhood of, the critical point. It is shown that in each case the critical isotherm is of the fourth degree, one degree higher than that of the coexistence curve, as is required by the theorem of Rice. However, the relation between the critical isotherm and the coexistence curve is determined by the almost constant value of ∂2P/∂T∂ρ in the PVT region considered, and this is different from its value at the critical point. The critical isobar is also considered and it is shown that it is of the fourth degree near the critical point, but of lower degree further away. A general equation of state is deduced for the PVT region under discussion, and the implications of this equation of state with respect to the coexistence curve and the critical isotherm are considered.

The Effect of Pressure on Surface Tension

The thermodynamic formula for the change of surface tension with pressure is interpreted for a one‐component system and for a two‐component system consisting of an inert gas over a liquid. In the latter case the effect of pressure on surface tension can be attributed in part to absorption of gas at the surface of the liquid and in part to an intrinsic decrease in density of the liquid in the neighborhood of the surface. The equations are interpreted in terms of the Gibbs adsorption isotherm. The adsorption of gas at the liquid surface has been estimated in several cases from data in the literature.

Entropy and the Absolute Rate of Chemical Reactions I. The Steric Factor of Bimolecular Associations

The equilibrium constant for a bimolecular association may be expressed in terms of the energy change, ΔE, and standard entropy change, ΔS°, on association. On account of the well‐known relation between the equilibrium constant, and the rate constants of the bimolecular association and its reverse, the corresponding unimolecular decomposition, the values of these rate constants could be determined separately, if one could divide each of the terms, ΔE and ΔS°, into two parts, in the proper way. The proper method of dividing ΔE is known; this paper is concerned with the division of ΔS°. Considered from a statistical point of view, the entropy of a system depends upon the volume in phase space available to the system under fixed thermodynamic conditions. The separate rate constants will depend upon the fraction of the phase space in which it is possible for the reaction under consideration to take place. Application of this principle leads to an interpretation of the collision number and the steric factor of...

On the Behavior of Pure Substances Near the Critical Point

It has been suggested several times that the phenomena of condensation could be understood by considering the vapor as a system in which molecules are associating into clusters, these obeying the ordinary laws of equilibrium. One can also consider the liquid as a system in which bubbles of vapor are forming. The present paper attempts to apply these ideas to phenomena occurring in the neighborhood of the critical point. Only thermodynamic methods are used, in conjunction with some general assumptions concerning the properties of the molecules involved. Some aspects of the surface tension of the liquid near the critical point have been considered in some detail. The highest temperature Tm at which a meniscus can exist is assumed to be the temperature at which the surface tension vanishes at the same time that the condition for equilibrium between liquid and vapor phases is fulfilled. It is concluded that the pressure‐volume isotherm at Tm has a finite horizontal region, corresponding to the squeezing out o...

The effect of an impurity on the critical point of a binary liquid system as a surface phenomenon

An impurity which is considerably more soluble in one of the components of a binary liquid system than the other raises the temperature of an upper critical (consolute) point. Since the interfacial tension vanishes at the critical temperature, this effect can be described as a surface effect: The impurity raises the interfacial tension and is thus negatively adsorbed at the interface. The amount of impurity in the interface is assumed to be calculable by summing the dissolved amounts at all points of the interface, and can be seen to depend on the second derivative of the solubility as a function of concentration. These phenomena were treated thermodynamically with the help of the Gibbs adsorption equation in earlier papers, before the nature of the singularities at a critical point were well understood. These ideas are now brought up to date by incorporating the more recent developments about critical points, and scaling laws are found for the solubility and the adsorption at the interface. Renormalizati...

On the Thermodynamic Properties of Nitric Oxide An Example of an Associated Liquid

Liquid nitrix oxide consists largely of double molecules, as evidenced by the abnormally high entropy of vaporization and the high and variable specific heat. By making use of these data it is possible to calculate the extent to which single molecules exist in the liquid, the heat of dissociation of the double molecules, and the value the specific heat would have were the association in the liquid complete. A statistical calculation is made of the entropy of vaporization, and the result compared with the experimental value. An estimate is made of the heat of dissociation in the gas phase.