Henry theory

V. Henri, Theorie generale de Faction de quelques diastases. Comptes Rend. Acad. Sci. Paris 135, 916 919 (1902). 

Equations (4.8) and (4.9) differ by a factor of 1.5 in the denominator because the Hiickel theory assumes that the charged particle has no influence on the local applied field, while Smoluchowski theory assumes that the applied field is uniform and parallel to the particle surface. Henry theory covers the transition from Ka < 1 (Hiickel theory) to Ka > 100 (Smoluchowski theory) by taking account of both frictional force and electrophoretic retardation,... 

In highly charged macromolecules Eq. (5.8.16) does not apply. It is then necessary to generalize these arguments to include hydration and deviations from spherical shape. However there are even more formidable complications to consider first. In aqueous solution, the macroion is surrounded by an ion atmosphere composed mainly of ions of opposite charge. This means that the local field —the field felt by the macroion— will be considerably different than the applied field. Corrections for this effect can be made if one uses the Debye-Huckel-Henry theory to calculate the properties of the ion atmosphere (see Chapters 9 and 13). An estimate (Tanford, 1961) gives... 

Electrophoretic mobility (p.) of a charged molecular species can be approximated from the Debye-Huckel-Henry theory... 

The constants in Eqs. XVII-88-XVI1-90 may be calculated fiom theory to give the Henry s law constant K from Eq. XVII-87, the experimental n /P dien gives the surface area. Alternatively, the constants may be arrived at from an experimental K (assuming that A is known) and either the isosteric heat of adsorption... 

Substances at high dilution, e.g. a gas at low pressure or a solute in dilute solution, show simple behaviour. The ideal-gas law and Henry s law for dilute solutions antedate the development of the fonualism of classical themiodynamics. Earlier sections in this article have shown how these experimental laws lead to simple dieniiodynamic equations, but these results are added to therniodynaniics they are not part of the fonualism. Simple molecular theories, even if they are not always recognized as statistical mechanics, e.g. the kinetic theory of gases , make the experimental results seem trivially obvious. 

A few studies have found potential surfaces with a stable minimum at the transition point, with two very small barriers then going toward the reactants and products. This phenomenon is referred to as Lake Eyring Henry Eyring, one of the inventors of transition state theory, suggested that such a situation, analogous to a lake in a mountain cleft, could occur. In a study by Schlegel and coworkers, it was determined that this energy minimum can occur as an artifact of the MP2 wave function. This was found to be a mathematical quirk of the MP2 wave function, and to a lesser extent MP3, that does not correspond to reality. The same effect was not observed for MP4 or any other levels of theory. 

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

The solvophobic model of Hquid-phase nonideaHty takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. Eirst, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbabiHty, Henry s constant, and aqueous solubiHty (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

Henry Eyring is one of llie most active and honored chemists of our time. His advancement of the theory of reaction rates benefits practically every field of chemistry and chemical technology. His 300 published papers and five books range through chemistry, physics, metallurgy, and biology. 

In Planck s investigation of equilibrium in dilute solutions, the law of Henry follows as a deduction, whereas in van t Hoff s theory, based on the laws of osmotic pressure ( 128), it must be introduced as a law of experience. The difference lies in the fact that in Planck s method the solution is converted continuously into a gas mixture of known potential, whilst in van t Hoff s method it stands in equilibrium with a gas of known potential, and the boundary condition (Henry s law) must be known as well. Planck (Thermodynamik, loc. cit.) also deduces the laws of osmotic pressure from the theory. 

Muraour, Henri (1881—1954). Fr scientist, a specialist in expls (Ingenieur general des poudres) and ballistics. Published more than 200 papers from WW1 thru 1952 (Ref 2) on expls, proplnts, combstn of proplnts, expl phenomena, antiflash agents, purification of TNT, theory of expl reactions, etc, as well as a widely read book (Ref 1)... 

The most widely accepted treatment of reaction rates is transition state theory (TST), devised by Henry Eyring.17 It has also been known as absolute rate theory and activated complex theory, but these terms are now less widely used. 

HARRIOTT 25 suggested that, as a result of the effects of interfaeial tension, the layers of fluid in the immediate vicinity of the interface would frequently be unaffected by the mixing process postulated in the penetration theory. There would then be a thin laminar layer unaffected by the mixing process and offering a constant resistance to mass transfer. The overall resistance may be calculated in a manner similar to that used in the previous section where the total resistance to transfer was made up of two components—a Him resistance in one phase and a penetration model resistance in the other. It is necessary in equation 10.132 to put the Henry s law constant equal to unity and the diffusivity Df in the film equal to that in the remainder of the fluid D. The driving force is then CAi — CAo in place of C Ao — JPCAo, and the mass transfer rate at time t is given for a film thickness L by ... 

Building on the Lindemarm Theory described above, Henry Eyring, and independently also M.G. Evans and Michael Polanyi, developed around 1935 a theory for the rate of a reaction that is still used, namely the transition state theory. 

Henry, J. Occult qualities and the experimental philosophy active principles in pre- Newtonian matter theory. Hist Sci 24 (1986) 335-381. 

The basic principle of air stripping is to provide contact between air and water to allow the volatile substances to diffuse from the liquid to the gaseous phase. Mass transfer occurs across the air-water interface. The theory of air stripping is related to Henry s law. At a given temperature, the partition of VOCs in the contacting air and water follows Henry s law ... 

GIL in Equation 18.17a is the theoretical air/water ratio required for the removal efficiency/for a specific contaminant following Henry s law. In this context, the GIL is denoted (GIL)theory, indicating the theoretical air/water ratio. This also means that a minimum amount of air must be brought into contact with the water for a certain length of detention time, the sparging size of the water droplets also affects the mass transfer, as does the air pressure. 

In Chapters 4 and 5 we made use of the theory of radiationless transitions developed by Robinson and Frosch.(7) In this theory the transition is considered to be due to a time-dependent intramolecular perturbation on non-stationary Bom-Oppenheimer states. Henry and Kasha(8) and Jortner and co-workers(9-12) have pointed out that the Bom-Oppenheimer (BO) approximation is only valid if the energy difference between the BO states is large relative to the vibronic matrix element connecting these states. When there are near-degenerate or degenerate zeroth-order vibronic states belonging to different configurations the BO approximation fails. 

Microscopists were not entirely idle, however, and after Giovanni Battista Amici (1786-1863) introduced achromatic lenses in France in 1827, the cell theory was not far behind. Henri Dutrochet (1776-1847) had already proposed that animal and plant tissues were constituted of cells, a view reiterated by many, notably Jan Evangelista Purkyne (1787-1869), Johannes Muller (1801 -1858), andjacob Henle (1809-1885). Felix Dujardin... 

The interaction between experiment and theory is very important in the field of chemical transformations. In 1981 Kenichi Fukui and Roald Hoffmann received a Nobel Prize for their theoretical work on the electronic basis of reaction mechanisms for a number of important reaction types. Theory has also been influential in guiding experimental work toward demonstrating the mechanisms of one of the simplest classes of reactions, electron transfer (movement of an electron from one place to another). Henry Taube received a Nobel prize in 1983 for his studies of electron transfer in inorganic chemistry, and Rudolf Marcus received a Nobel Prize in 1992 for his theoretical work in this area. The state of development of chemical reaction theory is now sufficiently advanced that it can begin to guide the invention of new transformations by synthetic chemists. 

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