Solutions of strong electrolytes

Solutions of electrolytes form a class of thermodynamic systems for which the concept of species is all-important. In this section we discuss the problems of reference and standard states for strong electrolytes as solutes dissolved in some solvent. 

Equation (8.178) is the basic equation that is needed, and is applicable to all solutes that are assumed to be strong electrolytes. 

We recognize that we cannot determine experimentally the thermodynamic properties of a single type of ion in solution, because both positive and negative ions must be present to satisfy the condition of electrical neutrality. However, we can use equations based on those previously derived, and express the chemical potential of a single type of ion in terms of the concentration variables at a given temperature and pressure. We follow convention here and use molalities and activity coefficients. Then we have 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by 

These equations are used whenever we need an expression for the chemical potential of a strong electrolyte in solution. We have based the development only on a binary system. The equations are exactly the same when several strong electrolytes are present as solutes. In such cases the chemical potential of a given solute is a function of the molalities of all solutes through the mean activity coefficients. In general the reference state is defined as the solution in which the molality of all solutes is infinitesimally small. In special cases a mixed solvent consisting of the pure solvent and one or more solutes at a fixed molality may be used. The reference state in such cases is the infinitely dilute solution of all solutes except those whose concentrations are kept constant. Again, when two or more substances, pure or mixed, may be considered as solvents, a choice of solvent must be made and clearly stated. 

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Battery electrolytes are concentrated solutions of strong electrolytes and the Debye-Huckel theory of dilute solutions is only an approximation. Typical values for the resistivity of battery electrolytes range from about 1 ohmcm for sulfuric acid [7664-93-9] H2SO4, in lead—acid batteries and for potassium hydroxide [1310-58-3] KOH, in alkaline cells to about 100 ohmcm for organic electrolytes in lithium [7439-93-2] Li, batteries. 

For strong electrolytes the molar conductivity increases as the dilution is increased, but it appears to approach a limiting value known as the molar conductivity at infinite dilution. The quantity A00 can be determined by graphical extrapolation for dilute solutions of strong electrolytes. For weak electrolytes the extrapolation method cannot be used for the determination of Ax but it may be calculated from the molar conductivities at infinite dilution of the respective ions, use being made of the Law of Independent Migration of Ions . At infinite dilution the ions are independent of each other, and each contributes its part of the total conductivity, thus ... 

It must be noted here that a decrease of the value of a is not the sole reason for a decrease in conductivity with increasing concentration. In 1900, Friedrich Kohlrausch found that in binary solutions of strong electrolytes for which a = 1 (i.e., does not change with the concentration), the conductivity is a linearly function of the value of... 

At the beginning of the twentieth century the idea was put forward that in solutions of strong electrolytes the degree of dissociation is not simply high but dissociation of the solute is complete (i.e., equilibrium between ions and undissociated molecules does not exist). This point is particularly evident for ionophors, which in the solid state do not possess individual molecules and for which it is unlikely that undissociated molecules should appear in a solution. 

We can see from Eig. 7.4, curve la, that this equation describes the experimental data in very dilute solutions of strong electrolytes (i.e., for 1 1 electrolytes approximately up to 10 M) for other electrolytes the concentration limit is even lower. It correctly conveys the functional dependence on the charge of the ions and the ionic strength of the solution (as well as the lack of dependence on individual properties of the ions) it can, moreover, be used to calculate the value of empirical constant h in Eq. (7.27). 

In aqueous electrolyte solutions the molar conductivities of the electrolyte. A, and of individual ions, Xj, always increase with decreasing solute concentration [cf. Eq. (7.11) for solutions of weak electrolytes, and Eq. (7.14) for solutions of strong electrolytes]. In nonaqueous solutions even this rule fails, and in some cases maxima and minima appear in the plots of A vs. c (Eig. 8.1). This tendency becomes stronger in solvents with low permittivity. This anomalons behavior of the nonaqueous solutions can be explained in terms of the various equilibria for ionic association (ion pairs or triplets) and complex formation. It is for the same reason that concentration changes often cause a drastic change in transport numbers of individual ions, which in some cases even assume values less than zero or more than unity. 

The beginning of the twentieth century also marked a continuation of studies of the structure and properties of electrolyte solution and of the electrode-electrolyte interface. In 1907, Gilbert Newton Lewis (1875-1946) introduced the notion of thermodynamic activity, which proved to be extremally valuable for the description of properties of solutions of strong electrolytes. In 1923, Peter Debye (1884-1966 Nobel prize, 1936) and Erich Hiickel (1896-1981) developed their theory of strong electrolyte solutions, which for the first time allowed calculation of a hitherto purely empiric parameter—the mean activity coefficients of ions in solutions. 

Any one of these expressions for fCa represents what is known as Ostwald s dilution law, which has essentially been obtained by applying the law of mass action to solutions of weak electrolytes. It deals with the variation in the degree of dissociation with concentration or dilution of solutions of weak electrolytes. It is not applicable to solutions of strong electrolytes. The failure of strong electrolytes to obey Ostwald s dilution law is known as the anomaly of strong electrolytes. 

This solution of strong electrolyte conducts a current very well. 

For a general review, see T. F. Young, F. F. MaranviUe, and H. M. Smith, Raman spectral investigations of ionic equihhria in solutions of strong electrolytes, in The Structure of Electrolytic Solutions, W. J. Hamer ed., Wiley, New York, 1959, pp. 35-63. 

After this publication, Prigogine suddenly quit this research line (this was, however, continued by a group of his co-workers). One may wonder a posteriori what motivated the choice of this field of research, so singular in Prigogine s work. (Note, however, that his Master s thesis (1939) was already devoted to solutions of strong electrolytes, and, as noted above, half of his treatise on thermodynamics treats the same subject.) The problem of time that would... 

SOL. 1.1. Prigogine, La structure de solutions d electrolytes forts en solution concentree (Structure of solutions of strong electrolytes in concentrated solution). Bull. Soc. Chim. de Belg. 50, 89—98 (1941). 

Scatchard, G. Concentrated solutions of strong electrolytes, Chem. Rev., 1936, 19, 309-327. 

The values of A, 2, and 2 decrease with increasing electrolyte concentration, due to the influence of ion-ion interactions. Kohlrausch found the following experimental relation for dilute solutions of strong electrolytes ... 

Now that we have an idea of the composition of solutions of strong electrolytes, we can move on to consider what happens when we pour one solution into another. A solution of sodium chloride consists of hydrated Na+ cations and hydrated Cl- anions. Similarly, a solution of silver nitrate, AgN03, consists of hydrated Ag+ cations and hydrated NO, anions. When we mix these two aqueous solutions, we immediately get a white precipitate, a cloudy, finely divided solid deposit. Analysis shows that the precipitate is silver chloride, AgCl, an insoluble white solid (Fig. 1.6). The colorless solution remaining above the precipitate in our example contains hydrated Na+ cations and hydrated N03 anions. These ions remain in solution because sodium nitrate, NaNO is soluble in water. 

Data collected with membranes of this type played an important part in the formulation of present-day solution theory—so much so that the authors have used this theory without hesitation to compute osmotic pressures of solutions whose osmotic pressures have never been precisely measured. Such a solution is sea water. The copper ferrocyanide membrane is leaky to solutions of strong electrolytes. Some data have been obtained on weak solutions of strong electrolytes by the Townend method (16), but no one has made precise measurements on the osmotic pressure of sea water. 

E. A. Guggenheim, Specific Thermodynamic Properties of Aqueous Solutions of Strong Electrolytes , Phil. Mag., 19, 588-643 (1935). 

G. Jones and M. Dole, The viscosity of aqueous solutions of strong electrolytes with spedal reference to barium chloride,... 

Debye-Huckel-Onsager theory — (- Onsager equation) Plotting the equivalent conductivity Aeq of solutions of strong electrolytes as a function of the square root of concentration (c1/2) gives straight lines according to the - Kohlrausch law... 

Ionic melts possess electrical conductivities roughly a factor ten larger than those of concentrated aqueous solutions of strong electrolytes (ionophores). 

Calculate the concentration of all ions present in each of the following solutions of strong electrolytes. 

For simplicity, the assumption is now made that the electrolyte is completely dissociatedj that is to say, a is assumed to be unity this, as will be evident shortly, is true for solutions of strong electrolytes at quite appreciable concentrations. Equation (31) can then be put in the form... 

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