Activity coefficients water

Grunwald, E. Berkowitz, B. J., The measurement and correlation of acid dissociation constants for carboxylic acids in the system ethanol-water. Activity coefficients and empirical activity functions, j. Am. Chem. Soc. 73, 4939 -944 (1951). 

Bianchi and Longhi (53) Potential -pH diagram (25°C) for copper in sea water activity coefficient corrections included. 

The dependence of solubility on % fill in 0.5M (OH) solution is shown in Fig. 5.(10) The solubility in pure water is an order of magnitude smaller under similar conditions. In pure water, activity coefficient (actually fugacity calculated from appropriate compressibility) estimates enable one to get reasonably accurate values for the equilibrium constant. This treatment suggests that the solubizing reaction in pure water is ... 

For an ideal solution, yw equals 1. A water activity coefficient of 1 is approached for dilute solutions, in which case nw J2jnj- (The expression nw YLjnJ defines a dilute solution.) Using Equation 2.8 and assuming a dilute ideal solution, we obtain the following relations for In aw ... 

Fig. 30. Equilibrium constant in the hydrolytic polymerization of caprolactam. Apparent equilibrium constants (220—265 C) and equilibrium constant corrected for the water activity coefficient (270°C). Data from refs. [2], [14] and [233].

To convert the intra(self-)diffusion coefficients (Dseif) to inter(Fickian)diffusion coefficients (Dchem). Zawodzinski and co-workers [64] have corrected the selfdiffusion coefficients they measured for water activity coefficient variations along the membrane thickness dimension and for the effects of swelling of the polymer [87]. The resulting Dchem for water in the Nafion membrane was 2 x lOr cm /s at 30 °C and did not exhibit a strong dependence on water content (however, recent reevalua-... 

Second, for the water activity coefficient in the binary mixture water (1)—electrolyte (3), one can use the relation ... 

An analysis of the cosolvent concentration dependence of the osmotic second virial coefficient (OSVC) in water—protein—cosolvent mixtures is developed. The Kirkwood—Buff fluctuation theory for ternary mixtures is used as the main theoretical tool. On its basis, the OSVC is expressed in terms of the thermodynamic properties of infinitely dilute (with respect to the protein) water—protein—cosolvent mixtures. These properties can be divided into two groups (1) those of infinitely dilute protein solutions (such as the partial molar volume of a protein at infinite dilution and the derivatives of the protein activity coefficient with respect to the protein and water molar fractions) and (2) those of the protein-free water—cosolvent mixture (such as its concentrations, the isothermal compressibility, the partial molar volumes, and the derivative of the water activity coefficient with respect to the water molar fraction). Expressions are derived for the OSVC of ideal mixtures and for a mixture in which only the binary mixed solvent is ideal. The latter expression contains three contributions (1) one due to the protein—solvent interactions which is connected to the preferential binding parameter, (2) another one due to protein/protein interactions (B p ), and (3) a third one representing an ideal mixture contribution The cosolvent composition dependencies of these three contributions... 

Fig. 8-2. Equilibrium distribution of metastable sulphur species in water activity coefficients of all species arbitrarily set to unity, total dissolved sulphur exclusive of sulphate species = 0.001M, 25 C, total pressure = I atm (reproduced with permission from Economic Geology, v. 64 2, p. 166 fig.7, Granger and Warren, 1969).

Whitfield, M., Activity coefficients in natural waters. Activity coefficients in electrolyte solutions, Pytkowicz, R. M., Ed., 11, pp. 153-299, CRC Press, Boca Raton, Florida, (1979). Cited on pages 9, 10. 

Figure 8. The free-energy relationship between rate of proton dissociation from excited 8-hydroxypyrene-1,3,6-trisulfonate and the activity coefficient of the water. Water activity coefficient was varied by concentrated solution of NaCl ( ), LiBr(A), and Mg CI2 (O, ).

Figure 11. Correlation between water activity coefficient of MgCl2 and NaC104 solutions as estimated from the rate of proton dissociation from two proton emitters, 2-naphthol-6-sulfonate (ordinate) and hydroxypyrene trisulfonate (abcissa). ( ) MgCl2 ( ) NaC104.

There are some similarities between these two sites the lifetime of 0-, the rate of proton escape (k23), and even the apparent rate of proton recombination (A2i-[H+]). The implication of these values will be discussed below. What markedly differentiates the two sites is the rate of proton dissociation (ki2). In both sites, the rate of proton dissociation is significantly slower than in water, implying that in these sites the water molecules are at a state that is not suitable for rapid (sub-picosecond) hydration of the discharged proton. The equivalent water activity coefficients, as estimated from the kinetic method described in Section III. are... 

Figure 8.3 Predicted dependencies of the water activity coefficient jw on the mole fraction of HP in aqueous solution at T = 52 1 K i — integration of Duhem s equation 2 — Il-parameter approximation and 3 — Ill-parameter approximation.

Let us assume that concentrations of these iron ions are balanced. They interact according to semi-reactions Fe + e = Fe +. Standard electrode potential of this reactions is equal to 10, IglCp = -13, z =. n fresh water activity coefficients may be equalled to 1. 

YJ infinite dilution activity coefficient of solute in 1-octanol saturated with water activity coefficient of solute in cosolvent Y activity coefficient of solute in water... 

For this purpose, the values obtained from the vapor pressure equations for both components are multiplied with a factor which is specific for each dataset If the Antoine equation is used, this can be achieved by simply changing the parameter A in Eq. 3.30. The solid line in Figure F.8 shows that the correct slope of the bubble point line can be represented. The water activity coefficient at infinite... 

Solution. Acetone-water. Activity coefficients and activities for acetone are plotted in Fig. 3.2 at 25 C. 

Mow—chemical potential in a standard state R— gas constant T—absolute temperature Uw— water activity coefficient The interaction of two systems in different energy states is manifested by the energy exchange. This exchange proceeds until the equilibrium state is achieved, which is the state in which chemical potentials of two systems are the same. 

For a two-component solution with a volatile solvent such as water and a nonvolatile solute, values of the activity of the solvent can be determined for several values of the solvent mole fraction between unity and the composition of interest. Integration of the Gibbs-Duhem relation can then give the value of the activity coefficient of the solute. The activity of the solvent is usually determined using the isopiestic method. The solution of interest and a solution of a well-studied nonvolatile reference solute in the same solvent are placed in a closed container at a fixed temperature. A solution of KCl is usually used as the reference solute for aqueous solutions, since accurate water activity coefficient data are available for KCl solutions. The solutions are left undisturbed at constant temperature until enough solvent has evaporated from one solution and condensed into the other solution to equilibrate the solvent in the two solutions. 

Assuming complete dissociation, and assuming that the water activity coefficient equals unity, calculate the osmotic pressure at 25.00°C of a solution of 2.500 g of KCl in 1.000 kg of water. The density of the solution is equal to 1.002gcm . ... 

To conclude this section, let us have a look at the variation of the activity coefficient of water in simple electrolyte solntions (see Fig. 4). As can be seen, the water activity coefficient in some solntions is slighdy increasing at medium salt concentrations, up to values higher than one. This means that a small tendency of demixing exists, which is, of conrse, overcompensated by the entropy gain and the favourable solution effect on the salt. 

Fig. 4. Water activity coefficients in some simple salt solutions as a function of salt molality at 25°C. As in Fig. 2, the corresponding water activity coefficients in water-methanol mixtures are added for comparison. (After Hamer and Wu. )...

The water activity coefficient (WAC) directly yields the deviation of the behaviour of water in the mixture from that in the pure-component state ( OW) at the same temperature. It can thus be obtained as the ratio of the two fugacity coefficients ... 

Fig. 3. Water activity coefficients of (a) three bronfide and (b) three hydroxide aqueous salt solutions at 25°C as function of salt molality. Experimental data Li+ — squares, Na+ — circles, K+ — triangles. The lines represent MSA-NRTL calculations. Activity coefficients decrease with decreasing size of the cation K+ > Na+ > Li+ for bromide solutions but in the reversed order for hydroxide solutions.

Figure 5 shows the influence of alkali cations [Fig. 5(a)] and halide anions [Fig. 5(b)] on the water activity coefficients in aqueous solutions of alkali halides. 

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