Principle of mobile equilibrium

The principle has been enunciated, more especially in connexion with chemical reactions, by van t Hoff, under the name of the Principle of Mobile Equilibrium, and by Le Chatelier, as the Principle of Reaction. 

Van t Hoff s boiling-point equation, 295 freezing-point equation, 299 theory of solution, 287 principle of mobile equilibrium, 304, 340... 

Using the equilibrium constant and v ant Hoff equations (Frames 46 and 47) it is possible to determine quantitatively the effect of pressure and temperature on the position of equilibrium taken up by a reversible reaction (see Section 49.4, this frame). Similar conclusions can be reached qualitatively using the principle of mobile equilibrium originally developed independently by Le Chatelier and by Braun, but now referred to simply as Le Chatelier s principle. 

Show that the relationships [d(AF)/dT]p — AiSand [.d AF)/dP ]T = AV, which are applicable to any physical or chemical change, constitute the basis of the Le ChateUer principle of mobile equilibrium. Make use of equation (25.40).]... 

Chemical equilibrium in homogeneous systems, from the thermodynamic standpoint—Gaseous systems—Deduction of the law of mass action—The van t Hoff isotherm—Principle of mobile equilibrium (Le Chateher and Braun)— Variation of the equilibrium constant with temperature—A special form of the equilibrium constant and its variation with pressure... 

The Principle of Le Chatelier and Braun, or The Principle of Mobile Equilibrium ... 

Equation (5), first deduced by van t Hoff, has led to some of the most important results of physical chemistry. Since B and T are positive, K and q must always have the same sign. Hence van t Hoff s principle of mobile equilibrium follows directly, viz, If the reaction absorbs heat, it advances with rise of temperature if the reaction evolves heat it retrogrades with rise of temperature and if the reaction neither absorbs nor evolves heat, the state of equilibrium is stationary with rise of temperature. 

Le Chatelier-Braun s Principle or Principle of Mobile Equilibrium This principle was presented already at the end of the nineteenth century and is often mentioned in connection with our current discussion. Chemists use it to predict whether the extent of a reaction in equilibrium will be shifted forward or backward when certain parameters are changed, especially pressure, temperamre, amounts of reactants and products, etc. We have found our answers in what we have already discussed, so we can avoid using this principle. For completeness sake, and because of the problems it causes even today, we will deal with it briefly. We will choose one of the various ways it can be formulated which is close to its original version, but we will avoid misunderstandings by using explanatory additions [in square parentheses] ... 

Van t Hoff then deals with chemical equilibrium on the basis of the law of mass action, and the change of equilibrium constant with temperature, introducing the case of condensed systems in the absence of vapour and a transition point (point de transition). Physical equilibria are special cases of chemical equilibria. Graphical methods with vapour pressure curves (e.g. for the allotropic forms of sulphur) are introduced. The principle of mobile equilibrium is explained for homogeneous and heterogeneous equilibria, and the Thomsen-Berthelot principle criticised (see pp. 614, 620). The last chapter, on affinity ,gives the definition The work of affinity (A) is equal to the heat produced in the transformation (q), divided by the absolute temperature of the transition point (P) and multiplied by the difference between this and the given temperature (P) ... 

At about the same time as van t Hoffs book appeared, the Frenchman Henri Louis Le Chatelier (1850-1936) stated the principle named after him, that when a change is imposed on a system in dynamic equilibrium, the system will respond in such a way as to tend to reduce the imposed change. Van t Hoffs principle of mobile equilibrium was thus shown to be a special case of Le Chatelier s principle. 

Varft Hoff recognised that change of temperature always affects equilibrium position. In his principle of mobile equilibriumy van t Hoff stated that an increase of temperature would favour the endothermic reaction. 

Nevertheless it does not change the principle of the mechanism proposed by Scholten and Konvalinka, i.e. the ability to act catalytically of only the superficial palladium centers released from the vicinity of the interstitial hydrogen. Bearing in mind the dynamic character of the equilibrium in a palladium-hydrogen system as a whole is to regard such centers as being mobile in the surface layer of the hydride. 

We may point out parenthetically that it is usually customary to attribute the expansion to electrostatic repulsions between the net (positive) charges on the polymer molecule which are uncompensated due to loss of counter-ions to the outer solution. It may be shown that the osmotic force owing to the excess of mobile ions within the molecule must be equal to the force of electrostatic repulsion when the molecule is in equilibrium with its surroundings. Hence either point of view is equally satisfactory in principle. The two are, of course, mutually related no net charge would develop in the molecule were it not for the mobile counter-ions, and no excess of mobile ions would be retained to exert an osmotic pressure if it were not for the charges on them. 

The fundamental principles of pK determination by CE rely upon measuring the ionic effective mobility of the solute as a function of pH. Consequently, the pK value is obtained by fitting an equilibrium equation to the effective mobility and pH data with a non-linear regression technique (Figure 1). Depending on the chemical character of the compound... 

Earlier, Gavach et al. studied the superselectivity of Nafion 125 sulfonate membranes in contact with aqueous NaCl solutions using the methods of zero-current membrane potential, electrolyte desorption kinetics into pure water, co-ion and counterion selfdiffusion fluxes, co-ion fluxes under a constant current, and membrane electrical conductance. Superselectivity refers to a condition where anion transport is very small relative to cation transport. The exclusion of the anions in these systems is much greater than that as predicted by simple Donnan equilibrium theory that involves the equality of chemical potentials of cations and anions across the membrane—electrolyte interface as well as the principle of electroneutrality. The results showed the importance of membrane swelling there is a loss of superselectivity, in that there is a decrease in the counterion/co-ion mobility, with greater swelling. 

The authors first mentioned investigated an anion-exchange membrane consisting of polyethylene imine crosslinked with epichlorohydrin in equilibrium with KC1 solutions. The concentration of Cl- ions and K+ ions in the membrane were determined analytically. The mobility of the Cl- ions in the membrane was determined according to the principle of the moving boundary. Thus in a membrane strip a sharp boundary is formed between the OH- and Cl- ions. This boundary will move under the influence of an electric field. This may be made visible with the aid of an indicator. The speed of the boundary is determined by the slowest ion, by consequence the Cl- ion in this instance. 

Assuming that the major conformation determines the product. In fact, in a mobile equilibrium the product ratio depends on the relative reactivities, not relative amounts, of the conformers (the Curtin-Hammett principle [35]). 

Countercurrent chromatography (CCC) is a support-free liquid-liquid partition system in which solutes are partitioned between the mobile and stationary phases in an open-column space. The instrumentation, therefore, requires a unique approach for achieving both retention of the stationary phase and high partition efficiency in the absence of a solid support. A variety of existing CCC systems may be divided into two classes [1] (i.e., hydrostatic and hydrodynamic equilibrium systems). The principle of each system may be illustrated by a simple coil as shown in Fig. 1. 

Figure 1 indicates the principle of use of any CCC device for the equilibrium of two liquid, nonmisdble phases. In this case, the stationary phase which is chosen is the lighter phase of the solvent system (dark gray in Fig. 1), whereas the mobile phase is indicated in white. For simplification, the coil is considered as an empty cylinder and the phenomena which occur inside the column are highly schematized as a stack of disks of mobile and stationary phases. This allovre us to visualize the progression of the mobile phase inside the column. After the solvent system has reached equilibrium (complete settling of the two phases), the phase chosen as the stationary phase is pumped into the apparatus. The latter is considered as filled as soon as droplets of this stationary phase are expelled out of the column this is Step 1 of Fig. 1. 

The plate models assume that the column is divided into a series of an arbitrary number of identical equilibrium stages, or theoretical plates, and that the mobile and the stationary phases in each of these successive plates are in equihbrimn. The plate models are in essence approximate, empirical models because they depict a continuous column of length I by a discrete number of well-mixed cells. Although any mixing mechanism is dearly absent from the actual physical system, plate models have been used successfully to characterize the column operation physically and mathematically. Therefore, by nature, plate models are empirical ones, which cannot be related to first principles. 

The B° concentration under equilibrium deduced from spectrum (a) of Fig. 7.7 is 7 x 1011cm-3, and it corresponds to a RT resistivity of about 18kQ cm (a value of 195cur V s is taken for the RT hole mobility [162]) and the estimated [B J from spectrum (b) is 1A x 1012 cm 3. As already mentioned for donors, PTIS is much more sensitive than absorption spectroscopy, however, because of the principles of this method, compensation effects are not so clearly dealt with by PTIS, and the lines of the compensating species neutralized by band-gap illumination appear as negative peaks in the PTI spectra. 

The next question regards the means by which values of any of these quantities to be used in reservoir-engineering calculations may be obtained. There is a continuing history of theoretical attempts to calculate the mobility of foam starting from known quantities and familiar principles of two-phase flow in porous rocks. One of these principally considers the effect of capillary pressure and concludes that this quantity is a principal determinant of the stability and therefore of the population of lamellae. Presuming equilibrium conditions in which the radii of curvature of the Plateau boundaries determines the excess of absolute pressures in the gas over that in the liquid, Khatib et al. (16) computed a limiting value of the capillary pressure. Above this value, the lamellae become too thin for the surfactant to stabilize. Increasing the gas fractional flow decreases the water saturation and raises the capillary pressure. 

Chromatography encompasses a number of variations on the basic principle of the separation of components in a mixture achieved by a successive series of equilibrium stages. These equilibria depend on the partition or differential distribution of the individual components between two phases a mobile phase... 

Simulated Moving-Bed Chromatography (SMBC) As the name suggests, this technique is based on the principle of liquid mobile phase and chromatography phase moving in opposite directions. Establishment of equilibrium helps in the improved efficacy of separation of the component of a mixture—often, a mixture of two enantiomers—which are fed into the middle of the column. The advantages are the continuous feeding of the sample... 

Another method which is interesting in principle is to find from the conductivity of pm water. Given that the molecular conductivity is known, and that the mobilities of the two ions are measured separately by the use of acid or alkali, the concentrations of the ions may he calculated and worked out. The difficulty is to know when the water is pure, since normally it contains dissolved substances which contribute far more to the conductivity than its own ions do. The problem was solved by a special device. The temperature coefficient of the dissociation of water is high, since it depends upon the displacement of an equilibrium moreover, the numerical value may be known from the heat of the dissociation (which is nothing other than the heat of neutralization of strong acid by strong alkali) by the application of the thermodynamic equation dluK/dT = The temperature coefficient of the... 

Because the principle of SEC with LALLS was discussed in Chapter 4, only the results of SEC with LALLS are presented here. The water-methanol mixed mobile phase used for SEC was also suitable for the determination of molecular weight by LALLS because no preferential solvation of PVP by water or methanol occurred in the mixed mobile phase. This was demonstrated by monitoring the equilibrium concentrations of water and methanol with crosslinked PVP. Furthermore, the differential refractive index increments of PVP in water and PVP in methanol are very close. Lack of preferential solvation in the mixed mobile phase was also demonstrated by the fact that the of a PVP K-90 sample was found to be similar, as measured by static LALLS, in the mixed mobile phase (1.43 x 10 AMU) and in water with 0.1 M UNO3 (1.57 X 10 AMU). 

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