Activity coefficients of ions in water

Table 8.1 Individual Activity Coefficients of Ions In Water at 25°C 8.3...

Values for the activity coefficients of ions in water at 25°C are given in Table 8.1 in terms of their effective ionic radii. 

Ionic radii in the figure are measured by X-ray diffraction of ions in crystals. Hydrated radii are estimated from diffusion coefficients of ions in solution and from the mobilities of aqueous ions in an electric field.3-4 Smaller, more highly charged ions bind more water molecules and behave as larger species in solution. The activity of aqueous ions, which we study in this chapter, is related to the size of the hydrated species. 

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 presence of an ion of this composition in solution was first deduced from the specific heats of aqueous acids, though the argument was based upon a rather artificial picture of water as a mixture of polymers. Supporting evidence comes from the thermodynamic properties of concentrated acid solutions. The rapid rise in the activity coefficients of electrolytes in concentrated solutions can be attributed largely to the removal of water by ionic hydration, with a consequent increase in the true mole fraction of the solute. A quantitative treatment in terms of a reasonable model " yields the mean hydration numbers of the ions, and a value close to 4 is found for the hydrogen ion. A similar deduction can be made from the indicator equilibria used in determining the acidity of concentrated... 

In 1976, Pitzer and Silvester (18) published the result of their study of modeling the phosphoric acid-water system using the Pitzer equations for activity and osmotic coefficients. As discussed in Chapter IV, Pitzer found the following equation for the activity coefficient of ion i by taking the appropriate derivative of his definition of the excess Gibbs free energy ... 

The activity is related to the concentration (moles/ liter) of the compound (X) by Eq. 5.13, where y is the activity coefficient. Gamma is always less than one, and is an empirically determined factor that mediates the concentration of the compound to reflect the amount of compound free in the solution. The activity coefficient of ions can be estimated from Debye-Huckel theory. Consult any quantitative analysis textbook to get a thorough discussion of activities and activity coefficients. It is particularly important to use activities in place of concentrations for concentrated solutions in water, and for nonaqueous solvents, which are the next two topics. 

Water is a neutral molecule and its activity equals its concentration at all low to moderate ionic strengths. That is, its activity coefficient is unity. In solutions of low to moderate ionic strength, activity coefficients of ions decrease with increasing ionic strength because the ionic... 

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 Orientation of Water Molecules Adjacent to an Ion. Order and Disorder in the Vicinity of Solute Particles. Coulomb Attraction and Repulsion between Ions. Activity Coefficients. The Distance of Closest Approach. Activity Coefficients of Various Solutes. Forces Superimposed on the Coulomb Forces. 

In applying this equation to multi-solute systems, the ionic concentrations are of sufficient magnitude that molecule-ion and ion-ion interactions must be considered. Edwards et al. (6) used a method proposed by Bromley (J7) for the estimation of the B parameters. The model was found to be useful for the calculation of multi-solute equilibria in the NH3+H5S+H2O and NH3+CO2+H2O systems. However, because of the assumptions regarding the activity of the water and the use of only two-body interaction parameters, the model is suitable only up to molecular concentrations of about 2 molal. As well the temperature was restricted to the range 0° to 100 oc because of the equations used for the Henry1s constants and the dissociation constants. In a later study, Edwards et al. (8) extended the correlation to higher concentrations (up to 10 - 20 molal) and higher temperatures (0° to 170 °C). In this work the activity coefficients of the electrolytes were calculated from an expression due to Pitzer (9) ... 

From the formation reaction of protonic defects in oxides (eq 23), it is evident that protonic defects coexist with oxide ion vacancies, where the ratio of their concentrations is dependent on temperature and water partial pressure. The formation of protonic defects actually requires the uptake of water from the environment and the transport of water within the oxide lattice. Of course, water does not diffuse as such, but rather, as a result of the ambipolar diffusion of protonic defects (OH and oxide ion vacancies (V ). Assuming ideal behavior of the involved defects (an activity coefficient of unity) the chemical (Tick s) diffusion coefficient of water is... 

Usnally, only very dilute solutions can be considered ideal. In most aqueous solutions, ions are stabilized because they are solvated by water molecules. As the ionic strength is increased, ions interact with each other. Thus, when calculating the chemical potential of species i, a term that takes into account the deviation from ideal conditions is added. This term is called an excess term and can be either positive or negative. The term usually is written as 7 riny., where y. is the activity coefficient of component i. The complete expression for the chemical potential of species i then becomes... 

Figure 4. Activity coefficients of cations relative to the tetraethylammonium cation in sulphuric acid-water mixtures. A—anilinium ions 1, unsubstituted 2, J5-C1 3, P-NO2 4, m-N02. B—benzamide cation. C—a typical carbonium ion, (p-MeOCgHajsC. A and C, after Boyd, 1963 B, after Sweeting and Yates, 1966.

The activity of ions in a solution is governed by the dielectric constant of the medium they are dissolved in and by the total concentration of ions in solution. For solutions of electrolytes in water with concentrations < 0.5 M the activity of the ions present in solution is usually approximated to their individual concentrations. The mean activity coefficient for an ion in solution is defined as ... 

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