Parameters for mixed electrolytes with the virial coefficient equations (at 25°C) [Pg.463]

The importance of the virial-coefficient equations is especially great for mixed electrolytes. Of the needed virial coefficients for a complex mixture such as sea water, most are determined by the pure electrolyte measurements and all the others of any significance are determined from data on simple mixtures such as NaCl-KCl, NaCl-MgC, NaCl-Na.SO, etc., which have been measured. The effect of the terms obtained from mixtures is very small in any case and these terms can be ignored for all but the most abundant species. [Pg.458]

Fig. 17. The osmotic coefficient < ) calculated from the virial equation as a function of the electrolyte concentration c for |

Among the virial coefficients in these equations, B and are functions of ionic strength, while C, and ifj are independent of /. Millero (1983) gives general equations for B, B and C for 1-1 (same as 2-1) and 2-2 electrolytes. For salt MX, the expressions are [Pg.141]

The mixed electrolyte terms in 0 and account for differences among interactions between ions of like sign. The defining equations for the second virial coefficients, 0,.. > are given by Equations (13), [Pg.462]

To make the basic Pitzer equation more useful for data correlation of aqueous strong electrolyte systems, Pitzer modified it by defining a new set of more directly observable parameters representing certain combinations of the second and third virial coefficients. The modified Pitzer equation is [Pg.63]

There are also many less severe tests (11) of predictions for mixed electrolytes which illustrate the accuracy to be expected in various cases. Thus it is well-established that the virial coefficient equations for electrolytes yield reliable predictions of [Pg.458]

The osmotic coefficients from the HNC approximation were calculated from the virial and compressibility equations the discrepancy between ([ly and ((ij is a measure of the accuracy of the approximation. The osmotic coefficients calculated via the energy equation in the MS approximation are comparable in accuracy to the HNC approximation for low valence electrolytes. Figure A2.3.15 shows deviations from the Debye-Htickel limiting law for the energy and osmotic coefficient of a 2-2 RPM electrolyte according to several theories. [Pg.497]

In Pitzer s model the Gibbs excess free energy of a mixed electrolyte solution and the derived properties, osmotic and mean activity coefficients, are represented by a virial expansion of terms in concentration. A number of summaries of the model are available (i,4, ). The equations for the osmotic coefficient (( )), and activity coefficients (y) of cation (M), anion (X) and neutral species (N) are given below [Pg.59]

The most general approach (Pitzer and Brewer, 1961, p. 326) would be to start with the D-H limiting law (Equation 15.26) and add a power series of virial coefficients, as for gases. A simpler approach, begun by Scatchard in 1936, and used by Pitzer and Brewer (1961, pp. 326, 578 and Appendix 4), is to define a deviation function B (called B to distinguish it from the first virial coefficient, which in a sense it replaces) as the difference between observed and predicted activity coefficients for an electrolyte such as NaCl. This is [Pg.442]

The convergence of the Mayer expansion and the Stell-Lebowitz expansions for the free energy is slow, and accurate estimates of the thermodynamic properties for a model electrolyte at concentrations near 1 M are difficult to obtain. A way out of this difficulty is to consider approximations for the radial distribution functions which correspond to the summation of a certain class of terms which contribute to all of the virial coefficients. The integral-equation approximations, such as the HNC, PY, and MS approximations, attempt to do just this. They also provide information on the structure of the solutions to varying degrees [Pg.115]

The alternative route to aqueous solute properties based on FST was to use a finite pressure refereuce state where properties could be obtained, and compute the difference in Gibbs energy between the desired state and the reference state (Sedlbauer, O Connell, and Wood 2000). This allows calculations for electrolytes, which would not have second virial coefficients that could be used at low densities as in Equation 9.41. The relation here for is similar to Equation 9.41, [Pg.242]

Debye-Huckel effects are significant in the dilute range and are not considered, and (2) the usual composition scale for the solute standard state is molality rather than mole fraction. Both of these problems have been overcome, and the more complex relationships are being presented elsewhere (17). However, for most purposes, the virial coefficient equations for electrolytes are more convenient and have been widely used. Hence our primary presentation will be in those terms. [Pg.456]

Edwards et al. (6) made the assumption that

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