Electrolytes, activity coefficients ionic atmosphere

ACTIVITY COEFFICIENT CORRECTIONS. To eliminate uncertainties arising from activity constant variations, it is common practice to keep activity coefficients constant by use of a "background electrolyte or "constant ionic atmosphere" (e.g., 0.10 M NaC104). Since the glass electrode measu es (for practical purposes) hydrogen ion activity, i.e., pHmeas - -log H+] = -log[H+]y+, it is necessary to convert activity to concentration in the calculations that follow. The relationship of equation 22-4 may be used, where the activity correction C = log Y+-... 

Ionic activity essentially represents the concentration of a particular type of ion in aqueous solution and is important in the accurate formulation of thermodynamic equations relating to aqueous solutions of electrolytes (Barrow, 1979). It replaces concentration because a given ion tends not to behave as a discrete entity but to gather a diffuse group of oppositely charged ions around it, a so-called ionic atmosphere. This means that the effective concentration of the original ion is less than its actual concentration, a fact which is reflected in the magnitude of the ionic activity coefficient. 

A particular case of electrolyte mixtures occurs if one electrolyte is present in a large excess over the others, thus determining the value of the ionic strength. In this case the ionic atmospheres of all the ions are formed almost exclusively from these excess ions. Under these conditions, the activities of all the ions present in the solution are proportional to their concentrations, the activity coefficient being a function of the concentration of the excess electrolyte alone. 

A new theory of electrolyte solutions is described. This theory is based on a Debye-Hiickel model and modified to allow for the mutual polarization of ions. From a general solution of the linearized Poisson-Boltzmann equation, an expression is derived for the activity coefficient of a central polarized ion in an ionic atmosphere of non-spherical symmetry that reduces to the Debye-Hiickel limiting laws at infinite dilution. A method for the simultaneous charging of an ion and its ionic cloud is developed to allow for ionic polarization. Comparison of the calculated activity coefficients with experimental values shows that the characteristic shapes of the log y vs. concentration curves are well represented by the theory up to moderately high concentrations. Some consequences in relation to the structure of electrolyte solutions are discussed. 

These two experiments coupled with ordinary conductance and activity coefficient studies demonstrate conclusively the correctness of the basic posmlate of the Debye-Hiickel theory, that is, the existence of the ionic atmosphere which is itself a manifestation of the inter-ionic interactions occurring in electrolyte solutions. They also suggest that the main properties of the ionic atmosphere which must be taken into consideration in developing a theory of conductance are ... 

Electrostatic interactions give a large deviation from ideality in equilibrium properties of solutions containing low molecular weight electrolytes. This deviation was most successfully disposed of by the Debye-Huckel theory [2]. According to this theory, the ionic species are not distributed in solution in a random manner, but form an ionic atmosphere structure, and the thermodynamic properties such as the activity coefficient of solvent (or the osmotic coefficient), the mean activity coefficient of solute, and the heat of dilution, decrease linearly with the square root of the concentration, in conformity with experimental observations. 

In very dilute solutions, the effects of the ionic atmosphere may be approximated by using the Debye-Hiickel theory, which predicts that the mean ionic activity coefficient, 7+ is, for an electrolyte with positive ions with charge z+, negative ions with charge 2., is given by ... 

Debye and Hiickel rationalized the way in which the conductances of strong electrolyte solutions were observed to vary with their concentration by proposing models of the ion distribution and applying to them well-established relationships of thermodynamics and electrostatics. The concept of ion atmospheres, formed by the preferential distribution of ions about a given central ion carrying charge of opposite sign, when developed in this way, provided experimentally verifiable expressions for the mean ion activity coefficients of electrolytes. These expressions make possible the determination of thermodynamic equihbrium constants in electrolyte systems and the interpretation of ionic reaction rates in solution. 

At finite concentrations this formula needs modifying in two ways. In the first place, diffusion is governed by the osmotic pressure, or chemical potential, gradient (not, strictly, by the concentration gradient), so that the mean activity coefficient of the electrolyte must be taken into account. In the second place, ionic atmosphere effects must be allowed for. In diffusion, unlike conductance, the two ions are moving in the same direction, and the motion causes no disturbance of the symmetries of the ionic atmospheres there is therefore no relaxation effect. There is a small electrophoretic effect, however, the magnitude of which for dilute solutions has been worked out by Onsager, and the most accurate measurements support the extended formula based on these corrections. 

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