Principal equilibrium-determining

For the dissolution of a crystal into a melt, if one wants to predict the interface melt composition (that is, the composition of the melt that is saturated with the crystal), the dissolution rate, and the diffusion profiles of all major components, thermodynamic understanding coupled with the diffusion matrix approach is necessary (Liang, 1999). If the effective binary approach is used, it would be necessary to determine which is the principal equilibrium-determining component (such as MgO during forsterite dissolution in basaltic melt), estimate the concentration of the component at the interface melt, and then calculate the dissolution rate and diffusion profile. To estimate the interface concentration of the principal component from thermod5mamic equilibrium, because the concentration depends somewhat on the concentrations of other components, only... 

Diffusive dissolution of MgO-rich olivine and diffusion profiles MgO is the principal equilibrium-determining component and its diffusion behavior is treated as effective binary. Consider the dissolution of an olivine crystal (Fo90, containing 49.5 wt% MgO) in an andesitic melt (containing 3.96 wt% MgO) at 1285°C and 550 MPa (exp 212 of Zhang et al. 1989). The density of olivine is 3198 kg/m, and that of the initial melt is 2632 kg/m. Hence, the density ratio is 1.215. To estimate the dissolution parameter a, it is necessary to know the interface melt... 

Crystai growth distance and behavior of major component This problem is similar to diffusive crystal dissolution. Hence, only a summary is shown here. Consider the principal equilibrium-determining component, which can be treated as effective binary diffusion. The density of the melt is often assumed to be constant. The density difference between the crystal and melt is accounted for. 

Behavior of trace element that can be treated as effective binary diffusion The above discussion is for the behavior of the principal equilibrium-determining component. For minor and trace elements, there are at least two complexities. One is the multicomponent effect, which often results in uphill diffusion. This is because the cross-terms may dominate the diffusion behavior of such components. The second complexity is that the interface-melt concentration is not fixed by thermodynamic equilibrium. For example, for zircon growth, Zr concentration in the interface-melt is roughly the equilibrium concentration (or zircon saturation concentration). However, for Pb, the concentration would not be fixed. 

Calculate Pe = 2aU/D, where D is the diffusivity of the principal equilibrium-determining component. 

For all of the polymers, the time required for relaxation of the enthalpy to that of the equilibrium glassy state at the various temperatures is extremely long, even at temperatures of the order of 15 C belov the corresponding glass-transition temperatures. The principal rate-determining factor Is the glass-transition temperature, as anticipated frcmi previous studies (1.2). 

Up to the present the principal interest in heteroaromatic tautomeric systems has been the determination of the position of equilibrium, although methods for studying fast proton-transfer reactions (e.g., fluorescence spectroscopy and proton resonance ) are now becoming available, and more interest is being shown in reactions of this type (see, e.g., references 21 and 22 and the references therein). Thus, the reactions of the imidazolium cation and imidazole with hydroxyl and hydrogen ions, respectively, have recently been demonstrated to be diffusion controlled. ... 

We can predict the pH at any point in the titration of a polyprotic acid with a strong base by using the reaction stoichiometry to recognize what stage we have reached in the titration. We then identify the principal solute species at that point and the principal proton transfer equilibrium that determines the pH. 

There are two principal chemical concepts we will cover that are important for studying the natural environment. The first is thermodynamics, which describes whether a system is at equilibrium or if it can spontaneously change by undergoing chemical reaction. We review the main first principles and extend the discussion to electrochemistry. The second main concept is how fast chemical reactions take place if they start. This study of the rate of chemical change is called chemical kinetics. We examine selected natural systems in which the rate of change helps determine the state of the system. Finally, we briefly go over some natural examples where both thermodynamic and kinetic factors are important. This brief chapter cannot provide the depth of treatment found in a textbook fully devoted to these physical chemical subjects. Those who wish a more detailed discussion of these concepts might turn to one of the following texts Atkins (1994), Levine (1995), Alberty and Silbey (1997). 

Figure 11.5 Chloride distribution and the GABAa response. The change in membrane voltage (Fm) that results from an increase in chloride conductance following activation of GABAa receptors is determined by the resting membrane potential and the chloride equilibrium potential (Fci)- (a) Immature neurons accumulate CF via NKCC, while mature neurons possess a Cl -extruding transporter (KCC2). (b) In immature neurons GABAa receptor activation leads to CF exit and membrane depolarisation while in mature neurons the principal response is CF entry and h5q)erpolarisation. This is the classic inhibitory postsynaptic potential (IPSP)...

Conventional bulk measurements of adsorption are performed by determining the amount of gas adsorbed at equilibrium as a function of pressure, at a constant temperature [23-25], These bulk adsorption isotherms are commonly analyzed using a kinetic theory for multilayer adsorption developed in 1938 by Brunauer, Emmett and Teller (the BET Theory) [23]. BET adsorption isotherms are a common material science technique for surface area analysis of porous solids, and also permit calculation of adsorption energy and fractional surface coverage. While more advanced analysis methods, such as Density Functional Theory, have been developed in recent years, BET remains a mainstay of material science, and is the recommended method for the experimental measurement of pore surface area. This is largely due to the clear physical meaning of its principal assumptions, and its ability to handle the primary effects of adsorbate-adsorbate and adsorbate-substrate interactions. 

In case of the asymmetric hydrogenation with Rh complexes this disturbance in the equilibrium establishment is shown in pressure-dependent e.e. values (see [21 b]). Djega-Mariadassou and Boudart [3] describe this phenomenon as kinetic coupling see also G. Djega-Mariadassou, Catal. Lett. 1994, 7. In this context, we point out that under kinetic coupling conditions it is principally not possible experimentally to determine a partial order of 1 with respect to hydrogen. 

Ketene dimerization is the principal synthetic route to 4-methylene-2-oxetanones. This reaction proceeds very satisfactorily for ketene and methylketene, but disubstituted ketenes dimerize only to cyclobutane-1,3-diones. The cycloaddition reaction of r-butylcyanoketene to ketene and to methylketene gives a-cyanoalkylidene-/3-lactones in about 40% yield in addition to the cyclobutane-1,3-dione dimer of f-butylcyanoketene. A mechanism has been proposed for the formation of both types of dimers from a common zwitterionic intermediate (equation 111), with the relative amount of each product determined by the configurational equilibrium of the intermediate (80JOC4483, 75JOC3417). 

Molecular weight determinations indicate that in solution U(OMe)s is probably a tetramer in equilibrium with a dimer, whereas the other alkoxides are principally dimeric in non-aqueous media unless the alkyl group is bulky as in the compounds U OCEt3)5 and U OC(MeEtPri) 5, which are monomers in solution. 

Identification of crystals under the microscope. Of the characteristics which are most useful for identification purposes the most readily determined are shape and refractive indices, The determinative method which has proved most valuable for microscopic crystals (such as those in the average experimental or industrial product) is to measure the principal refractive indices (up to three in number, depending on the symmetry of the crystal) and, if possible, to find the orientation of the principal opticafdirections with respect to the geometrical form of the crystal. This information, which can all be obtained by simple and rapid microscopio methods, is usually sufficient to identify any crystalline substances whose properties have previously been recorded. Mixtures of two or more crystalline substances can be identified by the same method in phase equilibrium studies and in industrial research it is not uncommon to encounter mixtures of three or four constituents, all of which can be identified in this way. 

For practical reasons, the blast furnace hearth is divided into two principal zones the bottom and the sidewalls. Each of these zones exhibits unique problems and wear mechanisms. The largest refractory mass is contained within the hearth bottom. The outside diameters of these bottoms can exceed 16 or 17 m and their depth is dependent on whether underhearth cooling is utilized. When cooling is not employed, this refractory depth usually is determined by mathematical models these predict a stabilization isotherm location which defines the limit of dissolution of the carbon by iron. Often, this depth exceeds 3 m of carbon. However, because the stabilization isotherm location is also a function of furnace diameter, often times thermal equilibrium cannot be achieved without some form of underhearth cooling. 

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