Equilibrium distribution constant

Further clarification is obtained from Figure 2 where the relations are depicted by a composition diagram where the vapor phase composition is the ordinate and the condensed phase composition is the abscissa. A straight line with a slope equal to the equilibrium distribution constant KiD is the locus of all equilibrium compositions. The curved line represents a set of nonequilibrium conditions for condensation out of the vapor phase. The departure from equilibrium can be projected on either axis, and the lengths of the projections correspond to the two expressions for potential difference shown above. Refs. 2 and 10 treat the boundary layer in detail. 

The capacity factor takes into account the fact that the observed retention will be determined by the equilibrium distribution constant corrected for the relative volumes of the two phases. 

Mass transfer capacity coefficient Equilibrium distribution constant Volume... 

The capacity factor, K (equation (2)), can be related to the equilibrium distribution constant by the ratio VsfVm, known as the phase ratio (3) (equation (5)) ... 

The general theory of micellar electrokinetic chromatography represents a confluence of chromatographic and electrophoretic principles. The expressions for electrophoretic mobility under different separation conditions are summarized in Table 8.4 [161,162]. These relationships allow the determination of the critical micelle concentration and equilibrium distribution constants for solute-micelle association complexes under typical conditions for micellar electrokinetic chromatography [60-64,161-164]. These properties change significantly with the composition of the electrolyte solution, and are generally different to common reference values for pure water. 

V Here Z equals [(change on solute ion)/(charge on mobile>phase ion)] Z luistlresame significance in ion exchange as Z has for RPLC. The parameter ft die equilibrium distribution constant for ion-exchange retention. 

Cd and C are the total concentrations in the donor and acceptor phases, respectively D is the equilibrium distribution constant between the acceptor and the donor phases... 

It is desired to find the required number of ideal stages in the extraction cascade illustrated in Fig. 5.1. Take the feed-to-solvent ratio (L/K) and equilibrium distribution constant (K) to be unity, then = L/(KV) = 1. Pure solvent is specified, so = 0 kg solute/kg solvent, and the feed is ATq = 1 kg solute/kg carrier. It is desired to produce a rich extract product such that Yi = 0.9 kg solute/kg solvent. 

The pseudophase equilibrium model considers solutes to be dissolved in continuous and discrete (micelles or droplets) phases in a way similar to the partition in conventional two-phase systems of oil and water [3, 4j. The equilibrium distribution constants are... 

Distribution constant in which concentration in the stationary phase is expressed as weight of substance per volume of the phase Equilibrium distribution constant Distribution constant... 

There is still some debate regarding the form of a dynamical equation for the time evolution of the density distribution in the 9 / 1 regime. Fortunately, to evaluate the rate constant in the transition state theory approximation, we need only know the form of the equilibrium distribution. It is only when we wish to obtain a more accurate estimate of the rate constant, including an estimate of the transmission coefficient, that we need to define the system s dynamics. 

A prediction of AE /AEq to within 0.1 kcal/mol may produce a AG /AGq accurate to maybe 0.2 kcal/mol. This corresponds to a factor of 1.4 error (at T = 300 K) in the rate/equilibrium constant, which is poor compared to what is routinely obtained by experimental techniques. Calculating AG /AGq to within 1 kcal/mol is still only possible for fairly small systems. This corresponds to predicting the absolute rate constant, or the equilibrium distribution, to within a factor of... 

The equilibrium between monomer and living polymer is dynamic and therefore the molecular weight distribution of the polymer will change with time until the equilibrium distribution is reached. This is a peculiar process in which the amount of polymer present in the system, as well as its number average molecular weight is constant. This means also that, the number of polymeric... 

The quantities n, V, and (3 /m) T are thus the first five (velocity) moments of the distribution function. In the above equation, k is the Boltzmann constant the definition of temperature relates the kinetic energy associated with the random motion of the particles to kT for each degree of freedom. If an equation of state is derived using this equilibrium distribution function, by determining the pressure in the gas (see Section 1.11), then this kinetic theory definition of the temperature is seen to be the absolute temperature that appears in the ideal gas law. 

If the two representations are equivalent then Eqs. (3.79) and (3.80) describe how A s and B s must be transformed in terms of a s and /Ts. (These identities are performed explicitly by Sanchez and Di Marzio, [49]. Frank and Tosi [105] further show that if a s and /Ts are chosen to satisfy detailed balance conditions, that is equilibrium behaviour, then the occupation numbers of the two representations are only equivalent if the nv s are in an equilibrium distribution within each stage. This is likely to be true if there is a high fold free energy barrier at the end of each stem deposition, and thus will probably be a good representation for most polymers. In particular, the rate constant for the deposition of the first stem, A0 must contain the high fold free energy term, i.e. ... 

Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefficients or distribution constants of the ions, 5 (M+) and B X ), are related to the extraction constant the... 

The standard distribution constant describing the equilibrium in the system... 

Figure 4.17 General phenonenaloglcal retention model for a solute that participates in a secondary chemical equilibrium in liquid chromatography. A - solute, X - equilibrant, AX analyte-equilibrant coeplex, Kjq - secondary chemical equilibrium constant, and and are the primary distribution constants for A and AX, respectively, between the mobile and stationary phases.

The first factor on the right-hand side of the above equation, p(z0), is the distribution of initial conditions zo, which, in many cases, will just be the equilibrium distribution of the system. For a system at constant volume in contact with a heat bath at temperature T, for instance, the equilibrium distribution is the canonical one... 

Thus, in according to the concept of equilibrium distribution, the relation of an organic pollutant concentration in the soil solid and liquid phase is constant at any moment (Vasilyeva and Shatalov, 2004). The example of such an approach application for assessing exposure pathways of POPs to living biota is shown in Box 1. 

---