Ionic strength molal

Fig. 8.4. Activity coefficients y0 for neutral, nonpolar species as a function of ionic strength (molal) at 25 °C, 100 °C, and 300 °C, according to the activity model of Helge-son (1969).

Pt,H2(1 atm) I HOAc(CHOAc).NaOAc(cNaOAc).MaCI(CNaci).AgCI (sat d) Ag without Ionic Strength (molality) and Temperature (°C) ... 

I - ionic strength, molality basis - mxrber of charges on the cation z - niBiioer of charges on the anion... 

Find the ionic strength of (i) 0.05 molal sodium sulfate (Na,SO ) solution, and (ii) 0.25 molal nitric acid (HNO,) and 0.4 molal barium nitrate (Ba(NO,) ) together ill one solution. 

It can be seen from Figure 7.8(b) that the curved lines predicted by the extended form of the Debye-Hiickel equation follow the experimental results to higher ionic strengths than do the limiting law expressions for the (1 1) and (2 1) electrolytes. However, for the (2 2) electrolyte, the prediction is still not very good even at the lowest measured molality.0... 

Gangue minerals and salinity give constraints on the pH range. The thermochemical stability field of adularia, sericite and kaolinite depends on temperature, ionic strength, pH and potassium ion concentration of the aqueous phase. The potassium ion concentration is estimated from the empirical relation of Na+/K+ obtained from analyses of geothermal waters (White, 1965 Ellis, 1969 Fournier and Truesdell, 1973), experimental data on rock-water interactions (e.g., Mottl and Holland, 1978) and assuming that salinity of inclusion fluids is equal to ffZNa+ -h m + in which m is molal concentration. From these data potassium ion concentration was assumed to be 0.1 and 0.2 mol/kg H2O for 200°C and 250°C. 

Figure 1.96. Log /oj-pH diagram constructed for temperature = 200°C, ionic strength = 1, ES = 10 m, and EC = 10 m. Solid line represents aqueous sulfur and carbon species boundaries which are loci of equal molalities. Dashed lines represent the stability boundaries for some minerals. Ad adularia. Bn bomite, Cp chalcopyrite, Ht hematite, Ka kaolinite, Mt magnetite, Po pyrrhotite, Py pyrite, Se sericite. Heavy dashed lines (1), (2), and (3) are iso-activity lines for ZnCOs component in carbonate in equilibrium with sphalerite (1) 4 co3=0-1- (2) 4 ,co3=0-01- (3) 4 co3 =0-001 (Shikazono, 1977b).

Lewis and Randall stated that in dilute solutions the activity coefficient of a strong electrolyte is the same in all solutions of the same ionic strength this statement was confirmed in thermodynamic deductions of activity coefficients. The molality version of 7 can be applied in a fully analogous way and allows a more straightforward treatment of solution properties. [Conversion of molality into molarity requires the solution densities e.g., for a solute of molar mass M and a solution of density q we have... 

In fact, the symbol Ic should be used, as the molality ionic strength Im can be defined analogously in dilute aqueous solutions, however, values of c and m, and thus also Ic and Im, become identical.) Equation (1.1.21) was later derived theoretically and is called the Debye-Huckel limiting law. It will be discussed in greater detail in Section 1.3.1. 

If the ionic strength in concentrated aqueous or non-aqueous solutions is expressed in terms of the molalities, then the constants A = A fp and B = BVp are used, where p is the density of the solvent. 

Can the species activity coefficients be calculated accurately An activity coefficient relates each dissolved species concentration to its activity. Most commonly, a modeler uses an extended form of the Debye-Hiickel equation to estimate values for the coefficients. Helgeson (1969) correlated the activity coefficients to this equation for dominantly NaCl solutions having concentrations up to 3 molal. The resulting equations are probably reliable for electrolyte solutions of general composition (i.e., those dominated by salts other than NaCl) where ionic strength is less than about 1 molal (Wolery, 1983 see Chapter 8). Calculated activity coefficients are less reliable in more concentrated solutions. As an alternative to the Debye-Hiickel method, the modeler can use virial equations (the Pitzer equations ) designed to predict activity coefficients for electrolyte brines. These equations have their own limitations, however, as discussed in Chapter 8. 

Variable di in Equation 8.2 is the ion size parameter. In practice, this value is determined by fitting the Debye-Huckel equation to experimental data. Variables A and B are functions of temperature, and I is the solution ionic strength. At 25 °C, given I in molal units and taking a, in A, the value of A is 0.5092, and B is 0.3283. 

As can be seen in Figure 8.1, the Davies equation does not decrease monotoni-cally with ionic strength, as the Debye-Huckel equation does. Beginning at ionic strengths of about 0.1 molal, it deviates above the Debye-Huckel function and at about 0.5 molal starts to increase in value. The Davies equation is reasonably accurate to an ionic strength of about 0.3 or 0.5 molal. 

Helgeson (1969 see also Helgeson and Kirkham, 1974) presented an activity model based on an equation similar in form to the Davies equation. The model, adapted from earlier work (see Pitzer and Brewer, 1961, p. 326, p. 578, and Appendix 4, and references therein), is parameterized from 0°C to 300 °C for solutions of up to 3 molal ionic strength in which NaCl is the dominant solute. The model takes it name from the B-dot equation,... 

Fig. 8.5. Water activity aw versus stoichiometric ionic strength 7s of NaCl solutions at 25 °C and 300 °C, according to the activity model of Helgeson (1969). Dashed line shows 3 molal limit to the model parameterization values to right of this line are extrapolations of the original data.

Fig. 10.1. Relationship (Eqn. 10.6) between surface charge density cr and surface potential T for a sorbing surface in contact with solutions of differing ionic strengths I (molal).

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