Chlorides, activity coefficients

The activity coefficient for the counterions was taken to be a constant value of 0.862. This value was derived from the experimental value of 0.745 for NaCJl, which was reported by Moore (20). The sodium ion activity coefficient was obtained as the square root of the sodium chloride activity coefficient. 

Note that the most important assiimptions made here are 1) chloride activity coefficients in isopiestic, NaCl dominated solutions are equal, and 2) the mole fraction statistical hydration model for splitting mean activity coefficients yields reasonable single ion activities. 

Mean sodium chloride activity coefficients have been determined [41] with a sodium ion-selective electrode and silver-silver chloride reference electrode system in mixed sodium chloride-calcium chloride solutions within the range of sodium chloride and calcium chloride levels (0.05-0.5 mol dm ) encountered in extracellular fluids. These show that at constant ionic strength, log /Naci varies linearly with the ionic strength of calcium chloride in the mixture in accordance with Harned s rule [45] ... 

The thickness of the equivalent layer of pure water t on the surface of a 3Af sodium chloride solution is about 1 A. Calculate the surface tension of this solution assuming that the surface tension of salt solutions varies linearly with concentration. Neglect activity coefficient effects. 

Accuracy and Interpretation of Measured pH Values. The acidity function which is the experimental basis for the assignment of pH, is reproducible within about 0.003 pH unit from 10 to 40°C. If the ionic strength is known, the assignment of numerical values to the activity coefficient of chloride ion does not add to the uncertainty. However, errors in the standard potential of the cell, in the composition of the buffer materials, and ia the preparatioa of the solutioas may raise the uacertaiaty to 0.005 pH unit. 

Finally, as an example of a highly soluble salt, we may take sodium chloride at 25° the concentration of the saturated solution is 6.16 molal. The activity coefficient of NaCl, like that of NaBr plotted in Fig. 72, passes through a minimum at a concentration between 1.0 and 1.5 molal and it has been estimated2 that in the saturated solution the activity coefficient has risen to a value very near unity. Writing y = 1.0, we find that the work required to take a pair of ions from the surface of NaCl into pure water at 25° has the rather small value... 

G. Scatchard and R. F. Tefft, "Electromotive Force Measurements on Cells Containing Zinc Chloride. The Activity Coefficients of the Chlorides of the Bivalent Metals", J. Am. Chem. 

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,... 

Van t Hoff introduced the correction factor i for electrolyte solutions the measured quantity (e.g. the osmotic pressure, Jt) must be divided by this factor to obtain agreement with the theory of dilute solutions of nonelectrolytes (jt/i = RTc). For the dilute solutions of some electrolytes (now called strong), this factor approaches small integers. Thus, for a dilute sodium chloride solution with concentration c, an osmotic pressure of 2RTc was always measured, which could readily be explained by the fact that the solution, in fact, actually contains twice the number of species corresponding to concentration c calculated in the usual manner from the weighed amount of substance dissolved in the solution. Small deviations from integral numbers were attributed to experimental errors (they are now attributed to the effect of the activity coefficient). 

Fig. 9. Logarithm of the cation activity coefficient versus the square root of the concentration for the system of manganese ions and cation vacancies in sodium chloride at 500°C. Filled-in circles represent the association theory with Rq = 2a, and open circles the association theory with R = 6/2. Crosses represent the present theory with cycle diagrams plus diagrams of two vertices, and triangles represent the same but with triangle diagram contributions added.

Equations 8 and 9 can be used for values of I up to 1. M. The second term in these equations accounts for the reversal of slope of activity coefficient versus ionic strength from negative to positive as ionic strength increases. Equations 8 and 9 have been widely used in the equilibrium calculations of the lime or limestone processes. With coals of moderate chloride content and for systems without extensive sludge dewatering, the ionic strength is well below 1.0 M, and equations 8 and 9 reasonable. 

For applications where the ionic strength is as high as 6 M, the ion activity coefficients can be calculated using expressions developed by Bromley (4 ). These expressions retain the first term of equation 9 and additional terms are added, to improve the fit. The expressions are much more complex than equation 9 and require the molalities of the dissolved species to calculate the ion activity coefficients. If all of the molalities of dissolved species are used to calculate the ion activity coefficients, then the expressions are quite unwieldy. However, for the applications discussed in this paper many of the dissolved species are of low concentration and only the major dissolved species need be considered in the calculation of ion activity coefficients. For lime or limestone applications with a high chloride coal and a tight water balance, calcium chloride is the dominant dissolved specie. For this situation Kerr (5) has presented these expressions for the calculation of ion activity coefficients. 

To use the ECES system, activity coefficient data for FeCl2 had to be developed. A recent paper by Susarev et al (15) presented experimental results of the vapor pressure of water over ferrous chloride solutions for temperatures from 25 to 100°C and concentrations of 1 to 4.84 molal. This data was entered into the ECES system in the Data Preparation Block with a routine VAPOR designed to regress such data and develop the interaction coefficients B, C, D of our model. These results replaced an earlier entry which was based on more limited data. All other data for studying the equilibria in the FeCl2-HCl-H20 system was already contained within the ECES system. 

Excluding activity coefficients, three relationships are required in addition to the nine thermodynamic equilibria in order to calculate concentrations of the 12 unknown species. These relationships are the mass balances for magnesium and chloride, and the electroneutrality equation. 

Even this diagram does not give a clear impression of the relative proportions of the various copper compounds present in solution. However, provided no polynuclear species are present, it is a relatively simple matter to use the values of x to evaluate these proportions and to plot them as a function of a single variable. Figure 6 shows a diagram of this kind using the same data as figure 5 calculated for pE = 10 and variable chloride activity under the assumption that all compounds have the same activity coefficient. It would not be difficult to allow for different values of activity coefficients if these were known. 

With an aqueous fluid phase of high ionic strength, the problem of obtaining activity coefficients may be circumvented simply by using apparent equilibrium constants expressed in terms of concentrations. This procedure is recommended for hydro-metallurgical systems in which complexation reactions are important, e.g., in ammonia, chloride, or sulfate solutions. 

Generally, mn+ estimated from Equation (20.8) by inserting an approximate value of K and neglecting the activity coefficients. Thus, it is possible to obtain tentative values of — (RT/S ) In fC and hence K at various concentrations of acetic acid, sodium acetate, and sodium chloride, respectively. The ionic strength / ... 

The individual activity coefficients calculated from (4.12), suitable for calibration of ISEs for chloride ions, the alkali metal and alkaline earth ions, are given in tables 4.1 and 4.2. Ion activity scales have also been proposed for KF [141], choline chloride [98], for mixtures of electrolytes simulating the composition of the serum and other biological fluids (at 37 °C) [106,107], for alkali metal chlorides in solutions of bovine serum albumine [132] and for mixtures of electrolytes analogous to seawater [140]. 

Table 4.1. Single ion activity coefficients (molal scale) for uni-univalent chlorides at 25° C derived from hydration theory [11].

It can be shown that the virial type of activity coefficient equations and the ionic pairing model are equivalent, provided that the ionic pairing is weak. In these cases, it is in general difficult to distinguish between complex formation and activity coefficient variations unless independent experimental evidence for complex formation is available, e.g., from spectroscopic data, as is the case for the weak uranium(VI) chloride complexes. It should be noted that the ion interaction coefficients evaluated and tabulated by Cia-vatta [10] were obtained from experimental mean activity coefficient data without taking into account complex formation. However, it is known that many of the metal ions listed by Ciavatta form weak complexes with chloride and nitrate ions. This fact is reflected by ion interaction coefficients that are smaller than those for the noncomplexing perchlorate ion (see Table 6.3). This review takes chloride and nitrate complex formation into account when these ions are part of the ionic medium and uses the value of the ion interaction coefficient (m +,cio4) for (M +,ci ) (m +,noj)- Io... 

Because the values for the various salts in solution may be experimentally obtained with a satisfactory precision, equation 8.35 is used to derive the corresponding values of individual ionic activity coefficients from them. For instance, from a generic univalent chloride MCI, the y of which is known, we may derive the 7+ of M+ by applying... 

Figure 8.9 Mean activity coefficients for chlorides and sulfides, plotted following ionic strength of solution. Reprinted from Garrels and Christ (1965), with kind permission from Jones and Bartlett Publishers Inc., copyright 1990.

We are interested in the behavior of surfactant molecules in the mixed adsorbed film. The nonideal behavior of a mixed adsorbed film is correlated to activity coefficients of surface-active components with reference to the pure adsorbed film of each component. In the same manner as the previous paper ( ), we can express the chemical potentials of 1-octadecanol and dodecylammonium chloride in the mixed adsorbed film as follows ... 

---