Infinite dilution constant

Hquid-phase activity coefficient (eq. 6) terminal activity coefficient, at infinite dilution constant in Wilson activity coefficient model (eq. 13)... 

Furthermore, it must be clearly stated, if one deals with a conditional constant, being valid for one type of standard state, or with an infinite dilution constant, another type of standard state (i.e. T=25°C and ionic strength 1=0). The latter might be calculated from the former. Standard temperature conditions can be calculated using the van t Hoff equation (Eq. 3), whereas the following equation (Eq. 4) can be applied to determine the effect of pressure ... 

The values for the corrected constants, K, are 22% and 35% greater, respectively, than the infinite dilution constant, K. 

At higher ionic strengths, the activity coefficients could be calculated using the SIT or Pitzer equations and thus a more accurate correction made to the infinite dilution constant, K. 

At infinite dilution, the assumption of a constant relaxation time is reasonable and, using Stokes law as well, we have... 

From equation A2.4.38 we can, finally, deduce Walden s rule, which states that the product of the ionic mobility at infinite dilution and the viscosity of the pure solvent is a constant. In fact... 

L is Avagadro s constant and k is defined above. It can be seen that there are indeed two corrections to the conductivity at infinite dilution tire first corresponds to the relaxation effect, and is correct in (A2.4.72) only under the assumption of a zero ionic radius. For a finite ionic radius, a, the first tenn needs to be modified Falkenliagen [8] originally showed that simply dividing by a temr (1 -t kiTq) gives a first-order correction, and more complex corrections have been reviewed by Pitts etal [14], who show that, to a second order, the relaxation temr in (A2.4.72) should be divided by (1 + KOfiH I + KUn, . The electrophoretic effect should also... 

Experimentally deterrnined equiUbrium constants are usually calculated from concentrations rather than from the activities of the species involved. Thermodynamic constants, based on ion activities, require activity coefficients. Because of the inadequacy of present theory for either calculating or determining activity coefficients for the compHcated ionic stmctures involved, the relatively few known thermodynamic constants have usually been obtained by extrapolation of results to infinite dilution. The constants based on concentration have usually been deterrnined in dilute solution in the presence of excess inert ions to maintain constant ionic strength. Thus concentration constants are accurate only under conditions reasonably close to those used for their deterrnination. Beyond these conditions, concentration constants may be useful in estimating probable effects and relative behaviors, and chelation process designers need to make allowances for these differences in conditions. 

Fiend s Constant. Henry s law for dilute concentrations of contaminants ia water is often appropriate for modeling vapor—Hquid equiHbrium (VLE) behavior (47). At very low concentrations, a chemical s Henry s constant is equal to the product of its activity coefficient and vapor pressure (3,10,48). Activity coefficient models can provide estimated values of infinite dilution activity coefficients for calculating Henry s constants as a function of temperature (35—39,49). 

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. 

Here Q is the solute concentration and R the gas constant. This is in fact obeyed over a rather wide range of concentrations, almost up to solute mole fractions of 0.61, with an error of only 25 percent. This is remarkable, since the van t Hoff equation is rigorous only in the infinitely dilute limit. Even in the case of highly nonideal solutions, for example a solution with a ratios of 1.5 and e ratios of 4, the van t Hoff equation is still obeyed quite well for concentrations up to about 6 mole percent. It appears from these results that the van t Hoff approximation is much more sensitive to the nonideality of the solutions, and not that sensitive... 

The critical hydrogen content for the ductility loss increased with increasing hydrogen solubility in the alloy. The fracture surfaces were not characteristic of those found under conditions of SCC. In terms of hydrogen and deuterium solubility in a similar series of bcc alloys, the equilibrium constants were determined at infinite dilution as a function of temperature The free energy function was expressed in terms of the bound-proton model. 

Numbering the particles in (87) from left to right, the conventional acid dissociation constant is defined at infinite dilution by... 

This means that, with increasing length of chain, the equilibrium constants K1 and K2 (the first and second dissociation constants at infinite dilution of the acid) should not tend to equality rather their ratio K1/K2 should tend toward the value 4, as recognized by Adams.1... 

When the added water has a molarity n, let a fraction g of positive ions be alcoholic ions, while the fraction (1 — g) is in the form of (HjO)+ ions, On extrapolating to infinite dilution, the equilibrium constant of the reaction (43) may be written... 

For those dilute mixtures where the solute and the solvent are chemically very different, the activity coefficient of the solute soon becomes a function of solute mole fraction even when that mole fraction is small. That is, if solute and solvent are strongly dissimilar, the relations valid for an infinitely dilute solution rapidly become poor approximations as the concentration of solute rises. In such cases, it is necessary to relax the assumption (made by Krichevsky and Kasarnovsky) that at constant temperature the activity coefficient of the solute is a function of pressure but not of solute mole fraction. For those moderately dilute mixtures where the solute-solute interactions are very much different from the solute-solvent interactions, we can write the constant-pressure activity coefficients as Margules expansions in the mole fractions for the solvent (component 1), we write at constant temperature and at reference pressure Pr ... 

For gas-liquid solutions which are only moderately dilute, the equation of Krichevsky and Ilinskaya provides a significant improvement over the equation of Krichevsky and Kasarnovsky. It has been used for the reduction of high-pressure equilibrium data by various investigators, notably by Orentlicher (03), and in slightly modified form by Conolly (C6). For any binary system, its three parameters depend only on temperature. The parameter H (Henry s constant) is by far the most important, and in data reduction, care must be taken to obtain H as accurately as possible, even at the expense of lower accuracy for the remaining parameters. While H must be positive, A and vf may be positive or negative A is called the self-interaction parameter because it takes into account the deviations from infinite-dilution behavior that are caused by the interaction between solute molecules in the solvent matrix. 

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

The change in the sedimentation constant with concentration enters solely from the change in 1//, and it is customary therefore to extrapolate a plot of 1/s against c to infinite dilution. The results of sedimentation studies by Newman and Eirich on several polystyrene... 

Experimental results are consistent with this relation, but inaccuracies in sedimentation constants preclude precise evaluation of the empirical exponent. Similarly, the diffusion constant at infinite dilution, given by... 

All in aqueous solution at 25°C standard states are 1 M ideal solution with an infinitely dilute reference state, and the pure liquid for water equilibrium constants from reference 100, except as noted. 

The net retention volume and the specific retention volume, defined in Table 1.1, are important parameters for determining physicochemical constants from gas chromatographic data [9,10,32]. The free energy, enthalpy, and. entropy of nixing or solution, and the infinite dilution solute activity coefficients can be determined from retention measurements. Measurements are usually made at infinite dilution (Henry s law region) in which the value of the activity coefficient (also the gas-liquid partition coefficient) can be assumed to have a constant value. At infinite dilution the solute molecules are not sufficiently close to exert any mutual attractions, and the environment of each may be considered to consist entirely of solvent molecules. The activity... 

It can be immediately seen that for components exhibiting Raoultian behaviour, the activity coefficient is equal to unity. The Henry s law constant k is nothing but the activity coefficient Yj. Noting that Henrian behaviour is exhibited when the component i is present in very low concentrations, the constant is also expressed in this case as y and is known as the activity coefficient at infinite dilution. Henry s law may now be stated as... 

In the relationship shown above, A and B are constants depending on temperature, viscosity of the solvent, and dielectric constant of the solvent, C is the concentration expressed in gram equivalents per liter, and Ac represents the equivalent conductance of the solution. A0 is the equivalent conductance at infinite dilution - that is, at C = 0, when the ions are infinitely apart from one another and there exists no interionic attraction, a represents the degree of dissociation of the electrolyte. For example, with the compound MN... 

The electrical conduction in a solution, which is expressed in terms of the electric charge passing across a certain section of the solution per second, depends on (i) the number of ions in the solution (ii) the charge on each ion (which is a multiple of the electronic charge) and (iii) the velocity of the ions under the applied field. When equivalent conductances are considered at infinite dilution, the effects of the first and second factors become equal for all solutions. However, the velocities of the ions, which depend on their size and the viscosity of the solution, may be different. For each ion, the ionic conductance has a constant value at a fixed temperature and is the same no matter of which electrolytes it constitutes a part. It is expressed in ohnT1 cm-2 and is directly proportional to the mobilities or speeds of the ions. If for a uni-univalent electrolyte the ionic mobilities of the cations and anions are denoted, respectively, by U+ and U, the following relationships hold ... 

Arrhenius postulated in 1887 that an appreciable fraction of electrolyte in water dissociates to free ions, which are responsible for the electrical conductance of its aqueous solution. Later Kohlrausch plotted the equivalent conductivities of an electrolyte at a constant temperature against the square root of its concentration he found a slow linear increase of A with increasing dilution for so-called strong electrolytes (salts), but a tangential increase for weak electrolytes (weak acids and bases). Hence the equivalent conductivity of an electrolyte reaches a limiting value at infinite dilution, defined as... 

The constants in any of the activity coefficient equations can be readily calculated from experimental values of the activity coefficients at infinite dilution. For the Wilson equation ... 

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