Salts activity coefficients

By measuring the solubility, r, of the silver chloride in different concentration of added salt and extrapolating the solubilities to zero salt concentration, or better, to zero ionic strength, one obtains the solubility when v = 1. and from Eq. (29) K can be found. Then y can be calculated using this value of K and any measured solubility. Actually, this method is only applicable to sparingly soluble salts. Activity coefficients of ions and of electrolytes can be calculated from the Debye-HOckel equations. For a uni-univalent electrolyte, in water at 25 C, the equation for the activity coefficient of an electrolyte is... 

The first term on the right is the salt dependence of In Kohs, expressed in molal concentration units. The second term can be calculated from the dependence of the salt activity coefficient on salt concentration... 

Extrathermodynamic methods represent powerful tools for the evaluation of single-ion solvation quantities, but the available data are rather low in accuracy. Accurate knowledge of solubility and salt activity coefficients is highly desirable. Estimation of liquid-liquid junction potentials (particularly at nonaqueous-aqueous electrolyte... 

Activity Coefficient for a Trace Component in a Mixed Electrolyte Solution. If the salt MpXq is present in the electrolyte mixture in only a very minute quantity, it may be seen that its contribution to I, E, and m are negligible. Applying equation 19, and treating the trace salt as any other component, it becomes apparent that any interaction terms with an Mp dependence will be vanishingly small. Also, when k = p, any terms multiplied by E may be neglected since they will approach zero. The result of such a treatment is that the trace salt activity coefficient will be largely determined by the activity coefficient of the pure salt in a solution at the same ionic strength as the mixture (15). 

Fig. 7 (a) Solvent-shared ion pair (SIP) in aqueous sodium chloride solution [75]. The central water oxygen (red) coordinates the sodium itm (yellow) while this molecule is at the same time forming a hydrogen bond with the chloride ion (blue), (b) SIP in aqueous sodium (blue) acetate solution [70], In this system, changes in the exeess number of SIPs (the observed munber of SIPs minus the number expected at the corresponding distance if all ions are statistically distributed) within the Li, Na, K ion series are responsible for changes in the salt activity coefficient... 

In contrast to most activity coefficients of uncharged species, salt activity coefficients can significantly differ from unity. As a result, they must be always carefully considered in order to make proper calculations, whenever the chemical potential of an electrolyte in solution is involved. 

In the case of a binary system, the mean salt activity coefficients can be directly related to the molar osmotic coefficient cp of the solution via the Gibbs-Duhem equation ... 

As it can be observed from Fig. 1, electrolyte solutions are highly nonideal from the thermodynamic point-of-view, i.e., the solvent activity coefficient as well as the salt activity coefficient strongly deviates from unity (ideal solution). Activity coefficients fr depend on temperature and composition of the considered electrolyte... 

The decisive difference between solvent (fsolvent) 3nd salt activity coefficients (1 ) is that fsolvent becomes unity for the pure-component state whereas f, becomes unity for the infinite-diluted state ... 

Fig. 2 Solution densities, vapour pressures, salt activity coefficients, and solubility behaviour of KBr/water solutions. Symbols represent experimental data, lines are ePC-SAFT modelling...

It can be observed from Fig. 2 that ePC-SAFT allows for quantitative descriptions of solution densities (a), vapor pressures (b), salt activity coefficients (c), and solubilities (d). 

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. 

The following data (for 25°C) were obtained at the pzc for the Hg-aqueous NaF interface. Estimate and plot it as a function of the mole fraction of salt in solution. In the table,/ is mean activity coefficient such that a = f m , where m is mean molality. 

There is a third experimental design often used for studies in electrolyte solutions, particularly aqueous solutions. In this design the reaction rate is studied as a function of ionic strength, and a rate variation is called a salt effect. In Chapter 5 we derived this relationship between the observed rate constant k and the activity coefficients of reactants l YA, yB) and transition state (y ) ... 

An effect of ionic strength on as a consequence of effects on the activity coefficient ratio is called a primary salt effect. We will, in Section 8.3, consider this effect quantitatively. 

Examples of Values of L and AF°. As a first example we may evaluate both L and AF° for a moderately soluble salt in aqueous solution. At 25° a saturated solution of potassium perchlorate has a concentration of 0.148 mole of KCIO4 in a 1000 grams of water that is to say, y+ = y = 0.148/55.5. The activity coefficient in the saturated solution has been taken1 to be 0.70 + 0.05. Using this value, we can estimate the work required to take a pair of ions from the crystal surface to mutually distant points, when the crystal is in contact with pure solvent at 25°C ... 

As another example we may discuss silver iodide. As mentioned in Sec. 49 a saturated aqueous solution of this salt at 25°C contains only 9.08 X 10-9 mole in 1000 grams of water. At this low concentration the activity coefficient does not differ appreciably from unity we have then... 

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... 

The Change of Solubility with Temperature. The solubilities of various salts have been measured in aqueous solution at various temperatures. But from these measurements we cannot derive values of L as a function of temperature, until the activity coefficients in the various saturated solutions have been accurately measured. In dilute solutions... 

Values of the distance of closest approach derived from experimental values of the activity coefficients are given in column 2 of Table 40. It will be seen that for the lithium and sodium salts the value is greater than the crystal-lattice spacing (given in column 4) by rather more than 1 angstrom, as is expected. For the salts of cesium, rubidium, and potassium, on the other hand, the distance of closest approach... 

It is important to note that the solubility product relation applies with sufficient accuracy for purposes of quantitative analysis only to saturated solutions of slightly soluble electrolytes and with small additions of other salts. In the presence of moderate concentrations of salts, the ionic concentration, and therefore the ionic strength of the solution, will increase. This will, in general, lower the activity coefficients of both ions, and consequently the ionic concentrations (and therefore the solubility) must increase in order to maintain the solubility product constant. This effect, which is most marked when the added electrolyte does not possess an ion in common with the sparingly soluble salt, is termed the salt effect. 

The pH will depend upon the ionic strength of the solution (which is, of course, related to the activity coefficient — see Section 2.5). Hence, when making a colour comparison for the determination of the pH of a solution, not only must the indicator concentration be the same in the two solutions but the ionic strength must also be equal or approximately equal. The equation incidentally provides an explanation of the so-called salt and solvent effects which are observed with indicators. The colour-change equilibrium at any particular ionic strength (constant activity-coefficient term) can be expressed by a condensed form of equation (4) ... 

Conductivity measurements yield molar conductivities A (Scm2 mol-1) at salt concentration c (mol L-1). A set of data pairs (Af, c,), is evaluated with the help of non linear fits of equations [89,93,94] consisting of the conductivity equation, Eq. (7), the expression for the association constant, Eq. (3), and an equation for the activity coefficient of the free ions in the solution, Eq.(8) the activity coefficient of the ion pair is neglected at low concentrations. 

The nature of the Debye-Hiickel equation is that the activity coefficient of a salt depends only on the charges and the ionic strength. The effects, at least in the limit of low ionic strengths, are independent of the chemical identities of the constituents. Thus, one could use N(CH3)4C1, FeS04, or any strong electrolyte for this purpose. Actually, the best choices are those that will be inert chemically and least likely to engage in ionic associations. Therefore, monovalent ions are preferred. Anions like CFjSO, CIO, /7-CIC6H4SO3 are usually chosen, accompanied by alkali metal or similar cations. 

If one of the partners in a second-order reaction is not an ion, then in ideal solutions there will be little effect of added salts on the rate. The activity coefficient of a nonelectrolyte does not depend strongly on ionic strength the way that the activity coefficients of ions do. In a reaction with only one participating ion, it and the transition... 

For symmetric electrolytes i=l for 1 2 electrolytes (e.g., Na2S04), 1 3 electrolytes (AICI3), and 2 3 electrolytes ([Al2(S04)3], the corresponding valnes of A, are 1.587, 2.280, and 2.551. Mean ionic activity coefficients of many salts, acids, and bases in binary aqneons solutions are reported for wide concentration ranges in special handbooks. 

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