Various techniques of molecular thermodynamics and solution theory have been applied, through the transition state theory, to problems in chemical kinetics. These include experimental techniques for ascertaining the structure and properties of the transition states for various classes of reactions, plus analytical methods for using this information to predict the effect of solvents or reactant structure on chemical reaction rates. Such methods provide the chemical engineer with an additional parameter to use in the optimal design of reaction systems–that is, the chemistry of the reaction itself.

251The binary collision theory derives the approximate result thatEquations 14 and 12 provide a simple theory for the density and temperature dependence of 75 which can be checked by nmr experiments performed on highdensity fluids. Preliminary comparison with experiment indicates that the theory is fairly a c c~r a t e .~~?~~ The physical picture associated with eq 14 is reasonable. From the definition of 7~, we expect that 75 should be proportional to the inverse of the average collision frequency since each collision should help a molecule "forget" about its initial angular momentum. It can be shown that the collision frequency is proportional to 7 E -I . Thus, we expect TJ 01 7 E , which iS what eq 14 says. The orientational correlation functions measured by ir experiments28 (eq 15) and by Raman scatter- (15) ing28 (eq 16) can also be described with the binary CAt) = (PJU u(t)I> (16) collision theory. In these equations, u ( t ) denotes the unit vector parallel to an axis of molecule 1 a t time t, and A(x) is the Ith Legendre polynomial of x. The results of the theory are expressed most simply in terms of the Laplace transforms of C i ( t ) ; they are(34) J. DeZwaan, R. J. Finney, and J. Jonas, J Chem Phys., 60, 3223 (1974).where Cliid)(s) denotes the Laplace transform of C l ( t ) for a system of ideal gas (free) molecules. Equations 17 and 14 constitute Gordon's J diffusion model approximation for Cl(t) .35 Experimental tests indicate that the approximation is qualitatively accurate.26J4,36 We note that the microscopic theory used to derive eq 17 does not require one to adopt the unphysical assumptions that are often attributed to Gordon's results. The interested reader should see ref 26.In summary, we have emphasized the following concept: at the high densities which characterize most of the liquid phase, the dynamic and static structures of liquids are dominated by steric (excluded volume) effects. This idea, together with the approximation that the dynamics of hard spheres can be described in terms of uncorrelated binary collisions, gives rise to specific predictions about the density and temperature dependence of several relaxation times and correlation functions. These predictions should be qualitatively accurate for high density liquids composed of fairly spherical molecules. Further, the predictions can be tested by nmr, ir, and Raman experiments. We hope that in the near future constant density and temperature experiments will be performed on dense fluids to investigate fully the strengths and limitations of the theory we have described.Much can be and has been learned by conventional research on rates, activation energies, and solvent and substituent effects, all at atmospheric pressure.High-pressure kinetic studies, however, offer yet another probe, yielding information unobtainable by other means, yet invaluable in elucidating the structure and properties of the reaction transition state. High-pressure kinetics in solution permits observation of the volume of activation of a chemical reaction (...

The radiofrequency (1-20 MHz) ozonizer discharge or "chemical corona" has been compared in its operation in oxygen to the same device operated at 60 Hz. Comparable chemical, energetic, and electrical data were taken. In the high-frequency regime where the behavior of the discharge is dominated by a steady-state accumulation of excess positive ions in the gap, the best energy efficiency is several orders of magnitude worse than at low frequencies. A simple model, assuming minimization of the rate of production of entropy, relating the electrical parameters and the observed contraction of the discharge is seen to account for this difference in chemical efficiency. Regions of E/p sufficiently high to support the underlying ionization avalanche mechanism and to create ozone molecules are seen to be confined to layers comparable in thickness to the Debye length adjacent to the electrode (barrier) and thin compared to the aerodynamic boundary layer which probably accounts for the remarkable insensitivity of this discharge to flow rate.

The partial molal volumes in solution of the transition state of the Menschutkin reaction between pyridine and methyl iodide have been determined. Accurate partial molal volumes of both reactants have been measured and used in conjunction with existing high-pressure kinetic data to find the volumes of the complex. Such results are useful in the interpretation of the structure of the transition state and its intermolecular interactions in solution.

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