Henry conditions

However, deprotonation of rc-rf-butyldimethylsilyl-protected products 2 (prepared according to the classical Henry conditions )22, and consecutive reprotonation, provides the silylated nitroaldols 2 with high (R, R ) selectivity. Deprotonation of 2 by treatment with lithium diisopropylamide in tetrahydrofuran at — 78 C furnishes nitronates which are stable against / -elimination at that temperature. Protonation of these intermediates is achieved with an acetic acid/tetrahydrofuran (1 1) solution at —100 C. To achieve maximum yields, the mixture should be warmed up slowly before aqueous workup. 

If tire diffusion coefficient is independent of tire concentration, equation (C2.1.22) reduces to tire usual fonn of Pick s second law. Analytical solutions to diffusion equations for several types of boundary conditions have been derived [M]- In tlie particular situation of a steady state, tire flux is constant. Using Henry s law (c = kp) to relate tire concentration on both sides of tire membrane to tire partial pressure, tire constant flux can be written as... 

A two-step synthesis of indoles from o-nitrobenzaldehydes proceeds by condensation with nitromcthanc followed by reductive cyclization. Like the Leim-gruber Batcho method, the principal application of the reaction is to indoles with only carbocyclic substituents. The forniation of the o,p-dinitrostyrenes is usually done under classical Henry condensation conditions but KF/18-crown-6 in propanol was found to be an advantageous reaction medium for acetoxy-substituted compounds[1]. The o,p-dinitrostyrenes can also be obtained by nitration of p-nitrostyrenes[2]. 

Measurement of the retention time (tl) under known flow conditions thus provides a simple means of determining the equihbrium constant (Henry constant) ... 

The solubihty of a gas in water is affected by temperature, total pressure, the presence of other dissolved materials, and the molecular nature of the gas. Oxygen solubihty is inversely proportional to the water temperature and, at a given temperature, directly proportional to the partial pressure of the oxygen in contact with the water. Under equihbrium conditions, Henry s law apphes... 

Under equiUbrium or near-equiUbrium conditions, the distribution of volatile species between gas and water phases can be described in terms of Henry s law. The rate of transfer of a compound across the water-gas phase boundary can be characterized by a mass-transfer coefficient and the activity gradient at the air—water interface. In addition, these substance-specific coefficients depend on the turbulence, interfacial area, and other conditions of the aquatic systems. They may be related to the exchange constant of oxygen as a reference substance for a system-independent parameter reaeration coefficients are often known for individual rivers and lakes. 

Miscellaneous Generalized Correlations. Generalized charts and corresponding states equations have been pubhshed for many other properties in addition to those presented. Most produce accurate results over a wide range of conditions. Some of these properties include (/) transport properties (64,91) (2) second virial coefficients (80,92) (J) third virial coefficients (72) (4) Hquid mixture activity coefficients (93) (5) Henry s constant (94) and 6) diffusivity (95). 

The simplest possible case occurs when (1) both the operating and the equilibrium hues are straight (i.e., there are dilute solutions), (2) Henry s law is valid y /x = yifXj = m), and (3) absorption heat effects are negligible. Under these conditions, the integral term in Eq. (14-20) may be computed by Colburn s equation [Trans. Am. Jn.st. Chem. Eng., 35,211 (1939)] ... 

Method of Moments The first step in the analysis of chromatographic systems is often a characterization of the column response to sm l pulse injections of a solute under trace conditions in the Henry s law limit. For such conditions, the statistical moments of the response peak are used to characterize the chromatographic behavior. Such an approach is generally preferable to other descriptions of peak properties which are specific to Gaussian behavior, since the statisfical moments are directly correlated to eqmlibrium and dispersion parameters. Useful references are Schneider and Smith [AJChP J., 14, 762 (1968)], Suzuki and Smith [Chem. Eng. ScL, 26, 221 (1971)], and Carbonell et al. [Chem. Eng. Sci., 9, 115 (1975) 16, 221 (1978)]. 

The simplest mode of IGC is the infinite dilution mode , effected when the adsorbing species is present at very low concentration in a non-adsorbing carrier gas. Under such conditions, the adsorption may be assumed to be sub-monolayer, and if one assumes in addition that the surface is energetically homogeneous with respect to the adsorption (often an acceptable assumption for dispersion-force-only adsorbates), the isotherm will be linear (Henry s Law), i.e. the amount adsorbed will be linearly dependent on the partial saturation of the gas. The proportionality factor is the adsorption equilibrium constant, which is the ratio of the volume of gas adsorbed per unit area of solid to its relative saturation in the carrier. The quantity measured experimentally is the relative retention volume, Vn, for a gas sample injected into the column. It is the volume of carrier gas required to completely elute the sample, relative to the amount required to elute a non-adsorbing probe, i.e. 

The most important equilibrium pliase relationship is diat between liquid and vapor. Raoult s mid Henry s laws theoretically describe liquid-vapor behavior mid, mider certain conditions, are applicable in practice. Raoult s law, sometimes useful for mi.vtures of components of similar structure, states diat die partial pressure of any component in die vapor is equal to die product of the vapor pressure of the pure component and die mole fracdon of tliat component in die liquid. It may be written in die following maimer... 

An existing lO-in. I.D. packed tower using 1-inch Berl saddles is to absorb a vent gas in water at 85°F. Laboratory data show the Henry s Law expression for solubility to be y = 1.5x, where y is the equilibrium mol fraction of the gas over water at compositions of x mol fraction of gas dissolved in the liquid phase. Past experience indicates that the Hog for air-water system will be acceptable. The conditions are (refer to Figure 9-68). 

M. Amon and C. D. Denson [33-34] attempted a theoretical and experimental examination of molding a thin plate from foamed thermoplastic. In the first part of the series [33] the authors examined bubble growth, and in the second [34] — used the obtained data to describe how the thin plate could be molded with reference to the complex situation characterized in our third note. Here, we are primarily interested in the model of bubble growth per se, and, of course, the appropriate simplification proposals [33]. Besides the conditions usual for such situations ideal gets, adherence to Henry s law, negligible mass of gas as compared to mass of liquid, absence of inertia, small Reynolds numbers, incompressibility of liquid, the authors postulated [33] several things that require discussion ... 

The chemical yield of the classical Henry reaction is not always good and depends on steric factors thus, highest yields are obtained when nitromethane is used. Performing the reaction under high pressure (9 kbar, 30 °C) with tetrabutylammonium fluoride catalysis19 enlarges the scope of the reaction dramatically. Thus, addition of nitropropane to 2-methylcyclohexanone, which is not reactive under the classical conditions, was achieved in 40 % yield. Improved yields... 

In the presence of a catalytic amount of tetrabutylammonium fluoride, either freshly dried over molecular sieves22 or as the trihydrate16, silylnitronates 2 derived from primary nitroalkanes react readily at — 78 C or below, via their in situ generated nitronates. with aromatic and aliphatic aldehydes to give the silyl-protected (/J, S )-nitroaldol adducts 3 in excellent yield4,22-24-26,27. Silylnitronates, derived from secondary nitroalkanes. afford the adducts in 30 40% overall yield24. In contrast to the classical Henry reaction (vide supra), the addition of silylnitronates to aldehydes is irreversible. Ketones are unreaetive under such conditions. 

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. 

NOTE The proportionality constant k is reduced with increase in temperature. Under these hot DA conditions, the solubility of oxygen is very low (as per Henry s Law). 

The kinetics of transport depends on the nature and concentration of the penetrant and on whether the plastic is in the glassy or rubbery state. The simplest situation is found when the penetrant is a gas and the polymer is above its glass transition. Under these conditions Fick s law, with a concentration independent diffusion coefficient, D, and Henry s law are obeyed. Differences in concentration, C, are related to the flux of matter passing through the unit area in unit time, Jx, and to the concentration gradient by,... 

We can predict how the composition of a reaction mixture at equilibrium tends to change when the conditions are changed by following the general principle identified by the French chemist Henri Le Chatelier (Fig. 9.9) ... 

Solution The experimental conditions are consistent with Equation (11.26) so that kiAi was measured. The experimental result was reported as KgAi because the overall mass transfer coefficient was based on the equivalent gas-phase driving force expressed in partial pressure units rather than concentration units. Because a pure gas was sparged, kg oo and Kj = k . Equation (11.3) relates Kg and Ki through Henry s law constant. 

Solution The phase in which reaction occurs will be denoted by the subscript /, and the other phase wiU be denoted by the subscript g. Henry s law constant will be replaced by a liquid-liquid partition coefficient, but will still be denoted by Kh- Then the system is governed by Equations (11.29) and (11.30) with = —kai and ( ) = 0. The initial conditions are... 

A quick qualitative indication of how a system at equilibrium responds to a change in conditions can be obtained using Le Chatelier s principle, which was first formulated in 1884 by Henri-Louis Le Chatelier, a French industrial chemist. 

The resulting pyruvate may be measured by coupling the reaction with lactic dehydrogenase and NADH, or chemically by using dini-trophenylhydrazine. The kinetic method has been revised by Henry and co-workers to optimize the analytical conditions, and still is the method of choice (28). 

The Henry (nitroaldol) reaction was reported under very mild reaction conditions, in aqueous media using a stoichiometric amount of a nitroalkane and an aldehyde, in NaOH 0.025 M and in the presence of cetyltrimethylammonium chloride (CTAC1) as cationic surfactant (Eq. 8.94) 240 Good to excellent yields of (i-nitroalkanol are obtained. Under these conditions several functionalities are preserved, and side-reactions such as retro-aldol reaction or dehydration of 2-nitroalcohols are avoided. 

Enzyme Catalyzed. The enzyme aldolases are the most important catalysts for catalyzing carbon-carbon bond formations in nature.248 A multienzyme system has also been developed for forming C-C bonds.249 Recently, an antibody was developed by Schultz and co-workers that can catalyze the retro-aldol reaction and Henry-type reactions.250 These results demonstrate that antibodies can stabilize the aldol transition state but point to the need for improved strategies for enolate formation under aqueous conditions. 

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