Water osmotic coefficients

The activity coefficient of water is related to the osmotic coefficient by the formula ... 

Rard (1992) reported the results of isopiestic vapor-pressure measurements for the aqueous solution of high-purity NiCl2 solution form 1.4382 to 5.7199 mol/kg at 298.1510.005 K. Based on these measurements he calculated the osmotic coefficient of aqueous NiCb solutions. He also evaluated other data from the literature and finally presented a set of smoothed osmotic coefficient and activity of water data (see Table IV in original reference). 

The activity coefficient of the solvent remains close to unity up to quite high electrolyte concentrations e.g. the activity coefficient for water in an aqueous solution of 2 m KC1 at 25°C equals y0x = 1.004, while the value for potassium chloride in this solution is y tX = 0.614, indicating a quite large deviation from the ideal behaviour. Thus, the activity coefficient of the solvent is not a suitable characteristic of the real behaviour of solutions of electrolytes. If the deviation from ideal behaviour is to be expressed in terms of quantities connected with the solvent, then the osmotic coefficient is employed. The osmotic pressure of the system is denoted as jz and the hypothetical osmotic pressure of a solution with the same composition that would behave ideally as jt. The equations for the osmotic pressures jt and jt are obtained from the equilibrium condition of the pure solvent and of the solution. Under equilibrium conditions the chemical potential of the pure solvent, which is equal to the standard chemical potential at the pressure p, is equal to the chemical potential of the solvent in the solution under the osmotic pressure jt,... 

For water at 0°C (the osmotic coefficient is mostly determined from cryoscopic measurements),... 

The ideality of the solvent in aqueous electrolyte solutions is commonly tabulated in terms of the osmotic coefficient 0 (e.g., Pitzer and Brewer, 1961, p. 321 Denbigh, 1971, p. 288), which assumes a value of unity in an ideal dilute solution under standard conditions. By analogy to a solution of a single salt, the water activity can be determined from the osmotic coefficient and the stoichiometric ionic strength Is according to,... 

Figure 3. Gurney parameters for + — pairs determined by fitting data for osmotic coefficient and conductivity A (38J. The line in the figure represents ideal correlation. The data are for alkali halides, except fluorides, in water. The parameter d+. is defined for a simpler MM-level model than Equation 9 in Ref. 38 it is reported that d+./k T = 0.75 + 3.6 A+, /k T. These correlations have been found by Justice and Justice...

This hydrodynamic contribution to n is determined by the dielectric constant (e) and the viscosity of water (u), the surface charge density of the pore (Z), the pore radius (rp), and the proton conductivity of the pore (cTpore)- The hydrodynamic electro-osmotic coefficient for a typical pore with Tp = 1 nm is found in the range of [i.e., n ydr -1-10]. 

The total electro-osmotic coefficient = Whydr + mo includes a contribution of hydrodynamic coupling (Whydr) and a molecular contribution related to the diffusion of mobile protonated complexes—namely, H3O. The relative importance, n ydr and depends on the prevailing mode of proton transport in pores. If structural diffusion of protons prevails (see Section 6.7.1), is expected to be small and Whydr- If/ ori the other hand, proton mobility is mainly due to the diffusion of protonated water clusters via the so-called "vehicle mechanism," a significant molecular contribution to n can be expected. The value of is thus closely tied to the relative contributions to proton mobility of structural diffusion and vehicle mechanism. ... 

The osmotic coefficient of water in NaCl solutions of varying concentration can be calculated from data in Ref. 15. From the resulting values of the osmotic coefficients, the effect of NaCl concentration on the equilibrium temperature for Equation (13.16) can be determined. The results of some calculations for a constant pressure of 1 atm are shown in Figure 20.5 (16). 

Two other important electrolyte properties for the PEFC system are the water diffusion coefficient and electro-osmotic drag coefficient. These two param-... 

In the above, D rn is the water diffusion coefficient through the membrane phase only. Note also that the water fluxes through the membrane phase, via electro-osmotic drag and molecular diffusion, represent a source/sink term for the gas mixture mass in the anode and cathode, respectively. 

The activity of water is related formally to the molality of the electrolyte by means of the osmotic coefficient, (p, of the solution ... 

This expression is analogous to Eiq. (2.3), in that (1 — (p) expresses the contribution of the solvent and In y+ that of the electrolyte to the excess Gibbs energy of the solution. The calculation of the mean ionic activity coefficient of an electrolyte in solution is required for its activity and the effects of the latter in solvent extraction systems to be estimated. The osmotic coefficient or the activity of the water is also an important quantity related to the ability of the solution to dissolve other electrolytes and nonelectrolytes. 

Values of osmotic coefficients for single electrolytes have been compiled by various authors, e.g., Robinson and Stokes [22]. The activity of water can also be calculated from the known activity coefficients of the dissolved species. 

The activity of water is obtained by inserting Eq. (6.12) into Eq. (6.11). It should be mentioned that in mixed electrolytes with several components at high concentrations, it is necessary to use Pitzer s equation to calculate the activity of water. On the other hand, uhjO is near constant (and = 1) in most experimental studies of equilibria in dilute aqueous solutions, where an ionic medium is used in large excess with respect to the reactants. The ionic medium electrolyte thus determines the osmotic coefficient of the solvent. 

In natural waters the situation is similar the ionic strength of most surface waters is so low that the activity of H20(l) can be set equal to unity. A correction may be necessary in the case of seawater, where a sufficiently good approximation for the osmotic coefficient may be obtained by considering NaCl as the dominant electrolyte. 

S. Matsumoto and M. Kohda The Viscosity of W/OAV Emulsions An Attempt to Estimate the Water Permeation Coefficient of the Oil Layer from the Viscosity Changes in Diluted Systems on Aging under Osmotic Pressure Gradients. J. Colloid Interface Sci. 73,13 (1980). 

To calculate the osmotic pressure we used values of osmotic coefficients from ref. (lOj. Total organic carbon analysis (Beckman 914A] of samples from the water filled compartment verified that the membranes are impermeable to sucrose, so that the reflection coefficient a is equal to unity. 

Over the last 20-30 years not too much effort has been made concerning the determination of standard potentials. It is mostly due to the funding policy all over the world, which directs the sources to new and fashionable research and practically neglects support for the quest for accurate fundamental data. A notable recent exception is the work described in Ref. 1, in which the standard potential of the cell Zn(Hg)jc (two phase) I ZnS O4 (aq) PbS O4 (s) Pb(Hg)jc (two phase) has been determined. Besides the measurements of electromotive force, determinations of the solubility, solubiKty products, osmotic coefficients, water activities, and mean activity coefficients have been carried out and compared with the previous data. The detailed analysis reveals that the uncertainties in some fundamental data such as the mean activity coefficient of ZnS04, the solubility product of Hg2S04, or even the dissociation constant of HS04 can cause uncertainties in the f " " values as high as 3-4 mV. The author recommends this comprehensive treatise to anybody who wants to go deeply into the correct determination of f " " values. 

Mixtures of these surfactants with water result in solutions with unique properties that we want to consider. We will use the alkylpyridinium chlorides as examples. Figure 18.11 compares the osmotic coefficient 0, apparent relative molar enthalpy 4>L, apparent molar heat capacity Cp, and apparent molar volumes V as a function of molality for two alkylpyridinium chlorides in water.w19... 

The three terms in these equations reading from left to right are related to 7, a , and to of Eq. 2.13, respectively. The activity coefficient and the osmotic coefficient measure the degree to which solute concentrations and the activity of water (aw) depart from ideal solutions, respectively. For ideal solutions, a = to and 7 = 1.0 (Eq. 2.13) or Gex = 0 (Eq. 2.32). Similarly, aw = 1.0 for an ideal solution. In the real world, solutions are rarely ideal, except in the infinitely dilute case we therefore need a model for calculating and (f>[= f(aw)]. An early model based on statistical mechanics was developed by Debye and Hiickel (1923). Their equations are... 

To our knowledge, no one has ever worked out the mathematics for directly estimating the pressure dependence of the osmotic coefficient (or aw) using the Pitzer approach. However, Monnin (1990) developed an alternative model based on the Pitzer approach that allows calculation of the pressure dependence for the activity of water (aw). The density of an aqueous solution (p) can be calculated with the equation... 

Equilibria among water ice, liquid water, and water vapor are critical for model development because these relations are fundamental to any cold aqueous model, and they can be used as a base for model parameterization. For example, given a freezing point depression (fpd) measurement for a specific solution, one can calculate directly the activity of liquid water (or osmotic coefficient) that can then be used as data to parameterize the model (Clegg and Brimblecombe 1995). These phase relations also allow one to estimate in a model the properties of one phase (e.g., gas) based on the calculated properties of another phase (e.g., aqueous), or to control one phase (e.g., aqueous) based on the known properties of another phase (e.g., gas). 

Table A.2 is model output for seawater freezing at 253.15 K. Beneath the title, the output includes temperature, ionic strength, density of the solution (p), osmotic coefficient amount of unfrozen water, amount of ice, and pressure on the system. Beneath this line are the solution and gaseous species in the system. The seven columns include species identification, initial concentration, final (equilibrium) concentration, activity coefficient, activity, moles in the solution phase, and mass balance. The mass balance column only contains those components for which a mass balance is maintained. The number of these components minus 1 is generally the number of independent components in the system (in this case, 8 — 1 = 7). The mass balances (col. 7) should equal the initial concentrations (col. 2). This mass balance comparison is a good check on the computational accuracy.

Up to now, only two sets of data of the osmotic coefficient of rod-like polyelectrolytes in salt-free solution are available 1) Measurements by Auer and Alexandrowicz [68] on aqueous DNA-solutions, and 2) Measurements of polyelectrolyte PPP-1 in aqueous solution [58]. A critical comparison of these data with the PB-cell model and the theories delineated in Sect. 2.2 has been given recently [59]. Here it suffices to discuss the main results of this analysis displayed in Fig. 8. It should be noted that the measurements by the electric birefringence discussed in Sect. 4.1 are the most important prerequisite of this analysis. These data have shown that PPP-1 form a molecularly disperse solution in water and the analysis can therefore assume single rods dispersed in solution [49]. 

There are many measurement techniques for activity coefficients. These include measuring the colligative property (osmotic coefficients) relationship, the junction potentials, the freezing point depression, or deviations from ideal solution theory of only one electrolyte. The osmotic coefficient method presented here can be used to determine activity coefficients of a 1 1 electrolyte in water. A vapor pressure osmometer (i.e., dew point osmometer) measures vapor pressure depression. 

Analysis of ion-ion interactions in aqueous salt solutions using the pair potential summarized in eqn (21) in conjunction with theHNC technique (Friedman, 1971) has proved interesting. The value of this approach is indicated by the good agreement between observed and theoretical MacMillan-Mayer osmotic coefficients for lithium chloride in water at 298 K as shown in Fig. 23 (Friedman and Krishnan 1973a). For alkali metal halides in water, Ai3 parameters are... 

Wood et a/.74 have found that the osmotic coefficients for alkali metal halides and nitrates in NMA are much higher than those for the same salts in water. This is attributed to the higher dielectric constant of NMA. Nevertheless the order of the... 

The osmotic coefficients do not appear to be very sensitive to solvent structural differences and, indeed, this also has been noted when results from salt solutions in water and deuterium oxide were compared178). 

For an ideal solution, Jq = I and is unity. Then Eq. (9) is consistent with Eq. (10 11), since the total molality of all solute species is vm for a completely dissociated solute of molality m. For ionic solutions, the Debye-Hiickel theory predicts a value of yo different from unity and therefore a deviation of g from unity. A treatment of this aspect of the Debye-Hiickel theory is beyond the scope of this book, and we shall merely state the result. The osmotic coefficient g at 0°C for dilute solutions of a single strong electrolyte in water is given by... 

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