Solution infinite dilute

The sum of the heats of hydration of the cation and the anion which form an ionic salt MX may be derived from the lattice energy (enthalpy) U and the total heat of solution (infinite dilution) q of the salt by means of the thermochemical equation... 

The lattice enthalpy U at 298.20 K is obtainable by use of the Born—Haber cycle or from theoretical calculations, and q is generally known from experiment. Data used for the derivation of the heat of hydration of pairs of alkali and halide ions using the Born—Haber procedure to obtain lattice enthalpies are shown in Table 3. The various thermochemical values at 298.2° K [standard heat of formation of the crystalline alkali halides AHf°, heat of atomization of halogens D, heat of atomization of alkali metals L, enthalpies of solution (infinite dilution) of the crystalline alkali halides q] were taken from the compilations of Rossini et al. (28) and of Pitzer and Brewer (29), with the exception of values of AHf° for LiF and NaF and q for LiF (31, 32, 33). The ionization potentials of the alkali metal atoms I were taken from Moore (34) and the electron affinities of the halogen atoms E are the results of Berry and Reimann (35)4. 

Ashworth, A. J. Chien, C.-F. Furio, D. L. Hooker, D. Kopecnik, M. M. Laub, R. J. Price, G. J., "Comparison of Static with Gas-Chromatographic Solute Infinite- Dilution Activity Coefficients with Poly(dimethylsiloxane) Solvent," Macromolecules, 17,1090 (1984). 

Abbreviations c, crystalline state 1, liquid state g, gaseous state dil, in dilute aqueous solution , infinite dilution ppt, precipitated solid atnoiph, amorphous state. 

Binary interaction parameters (Ay) and infinite dilution activity coefficients are available for a wide variety of binary pairs. Therefore the ratio of the solute infinite dilution coefficient in solvent-rich phase to that of the second phase ( ) will provide an estimate of the equilibrium distribution coefficient. The method can provide a reasonable estimate of the distribution coefficient for dilute cases. 

There have been a number of modeling efforts that employ the concept of clustering in supercritical fluid solutions. Debenedetti (22) has used a fluctuation analysis to estimate what might be described as a cluster size or aggregation number from the solute infinite dilution partial molar volumes. These calculations indicate the possible formation of very large clusters in the region of highest solvent compressibility, which is near the critical point. Recently, Lee and coworkers have calculated pair correlation functions of solutes in supercritical fluid solutions ( ). Their results are also consistent with the cluster theory. 

Using the information in Problems 7.13 and 8.20, estimate the heat of vaporization for the first bit of ethanol from ethanol-water solutions containing 25, 50, and 75 mol % ethanol and from a solution infinitely dilute in ethanol. How do these heats of vaporization compare with that for pure ethanol computed in Problem 7.13 Why is there a difference between the various heats of vaporization ... 

Polymier-polymer interaction results to formation of stmctures on a supermolecular level. In particular, as getting more concentrated the PVC-solvent system consistently passes a number of stages from isolated PVC maeromolecules in a solution (infinitely diluted solution) to assoeiates and aggregates from macromolecules in a solution. At the further increase of PVC concentration in a solution formation of spatial fluctuational net with structure similar to a structure of polymer in the block occurs. 

An important first step in any model-based calculation procedure is the analysis and type of data used. Here, the accuracy and reliability of the measured data sets to be used in regression of model parameters is a very important issue. It is clear that reliable parameters for any model cannot be obtained from low-quality or inconsistent data. However, for many published experimentally measured solid solubility data, information on measurement uncertainties or quality estimates are unavailable. Also, pure component temperature limits and the excess GE models typically used for nonideality in vapor-liquid equilibrium (VLE) may not be rehable for SEE (or solid solubility). To address this situation, an alternative set of consistency tests [3] have been developed, including a new approach for modehng dilute solution SEE, which combines solute infinite dilution activity coefficients in the hquid phase with a theoretically based term to account for the nonideality for dilute solutions relative to infinite dilution. This model has been found to give noticeably better descriptions of experimental data than traditional thermodynamic models (nonrandom two liquid (NRTE) [4], UNIQUAC [5], and original UNIversal Eunctional group Activity Coefficient (UNIEAC) [6]) for the studied systems. 

Note that in the case of multicomponent solutions infinite dilution means infinite dilution of all components, not just of component /. Thus the Henryan standard states, which seem so unattainable, are actually convenient because some of their properties are the same as those of the infinitely dilute solution, and these are obtainable by extrapolation from measurements at finite concentration. 

The experimental quantities reported in the study publication are indicated in the 10th column density (d) differential density (solution density minus water density) (dd) solution molar volume (V) solution specific volume (Vs) apparent molar volume (Vf) solute infinite dilution partial molar volume (Vo), excess volume (Ve), volume of mixing (Vm), compressibility factor (Z), virial coefficients (B, C, D, E), and soimd velocity (sv). 

Table B-12 Diffusion Coefficients (Aqueous Solutions, Infinite Dilution) ...

Ben-Naim and Marcus [1] discussed a process termed solvation that applies to a particle of a (non-ionic ) substance transferring from its isolated state in the gas phase into a liquid irrespective of the concentration. The particle would then be surrounded by solvent molecules only in an ideally dilute solution (infinite dilution), or by solvent molecules as well as by molecules of its own kind at any arbitrary mole fraction with regard to the solvent, and by molecules identical with itself only on condensation into its own liquid. The interactions involved and their thermodynamics are aU covered by the same concept of solvation. The solvation process of a solute S is defined [1] as the transfer of a particle of S Ifom a fixed position in the (ideal) gas phase (superscript G) to a fixed position in a liquid (superscript L) at a given temperature T and pressure P. Statistical mechanics specifies the chemical potential of S in the ideal gas phase as ... 

Condensed solution (hquid Diluted ideal solution (solute) Infinitely diluted at T and P M T,P) Xi... 

For a solution infinitely diluted in macromolecular component (Ap= 1), can be defined as follows. 

Figure 4-11. Activity coefficients for noncondensable solutes at infinite dilution.

The Debye-Htickel limiting law predicts a square-root dependence on the ionic strength/= MTLcz of the logarithm of the mean activity coefficient (log y ), tire heat of dilution (E /VI) and the excess volume it is considered to be an exact expression for the behaviour of an electrolyte at infinite dilution. Some experimental results for the activity coefficients and heats of dilution are shown in figure A2.3.11 for aqueous solutions of NaCl and ZnSO at 25°C the results are typical of the observations for 1-1 (e.g.NaCl) and 2-2 (e.g. ZnSO ) aqueous electrolyte solutions at this temperature. 

The solute-solvent interaction in equation A2.4.19 is a measure of the solvation energy of the solute species at infinite dilution. The basic model for ionic hydration is shown in figure A2.4.3 [5] there is an iimer hydration sheath of water molecules whose orientation is essentially detemiined entirely by the field due to the central ion. The number of water molecules in this iimer sheath depends on the size and chemistry of the central ion ... 

Orr W J C 1947 Statistical treatment of polymer solutions at infinite dilution Trans. Faraday Soc. 43 12-27... 

Absorption coefficient, linear decaidic a. K Aqueous solution at infinite dilution aq, CO... 

The solution of 1 mole of HCl gas in a large amount of water (infinitely dilute real solution) is represented by ... 

As written, equation 6.5 is a limiting law that applies only to infinitely dilute solutions, in which the chemical behavior of any species in the system is unaffected by all other species. Corrections to equation 6.5 are possible and are discussed in more detail at the end of the chapter. 

If the mutual solubilities of the solvents A and B are small, and the systems are dilute in C, the ratio ni can be estimated from the activity coefficients at infinite dilution. The infinite dilution activity coefficients of many organic systems have been correlated in terms of stmctural contributions (24), a method recommended by others (5). In the more general case of nondilute systems where there is significant mutual solubiUty between the two solvents, regular solution theory must be appHed. Several methods of correlation and prediction have been reviewed (23). The universal quasichemical (UNIQUAC) equation has been recommended (25), which uses binary parameters to predict multicomponent equihbria (see Eengineering, chemical DATA correlation). 

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. 

II The increment in the free energy, AF, in the reaction of forming the given substance in its standard state from its elements in their standard states. The standard states are for a gas, fugacity (approximately equal to the pressure) of 1 atm for a pure liquid or solid, the substance at a pressure of 1 atm for a substance in aqueous solution, the hyj)othetical solution of unit molahty, which has all the properties of the infinitely dilute solution except the property of concentration. 

The numhers represent moles of water used to dissolve 1 g formula weight of suhstance means infinite dilution and aq means aqueous solution of unspecified dilution. ... 

TABLE 2-225 Heats of Solution of Organic Compounds in Water (at Infinite Dilution and Approximately Room Temperature)... 

FIG. 2-29 Enthalpy-concentration diagram for aqueous sodium hydroxide at 1 atm. Reference states enthalpy of liquid water at 32 F and vapor pressure is zero partial molal enthalpy of infinitely dilute NaOH solution at 64 F and 1 atm is zero. [McCahe, Trans. Am. Inst. Chem. Eng., 31, 129(1935).]... 

The diffusivity of solute 1 in the mixture is related to the binary infinite dilution diffiisivities for each of the other components calculated from Eq. (2-155) or the Umesi method. The viscosities are calculated by the methods in the previous section. Errors are not quantifiable, as little experimental data exist, although these errors would be related to those assumed for the binaiy pairs. 

The solute 1 is dissolved in a solvent pair of 2 and 3. D are infinite dilution binary diffusivities estimated by the proper method discussed previously. The mixture viscosity can be predic ted by methods of the previous section. The average absolute error when tested on 40 systems is 25 percent. The method gives higher errors if the solute is gaseous. 

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