Association weak electrolyte

The conductivity of a solution containing such molecular ions may be small compared with the value that would result from complete dissociation into atomic ions. In this way, in the absence of neutral molecules, we can have a weak electrolyte. The association constant for (29) has a value that is, of course, the reciprocal of the dissociation constant for the molecular ion (PbCl)+ the logarithms of the two equilibrium constants have the same numerical value, but opposite sign. 

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. 

A study of the concentration dependence of the molar conductivity, carried out by a number of authors, primarily F. W. G. Kohlrausch and W. Ostwald, revealed that these dependences are of two types (see Fig. 2.5) and thus, apparently, there are two types of electrolytes. Those that are fully dissociated so that their molecules are not present in the solution are called strong electrolytes, while those that dissociate incompletely are weak electrolytes. Ions as well as molecules are present in solution of a weak electrolyte at finite dilution. However, this distinction is not very accurate as, at higher concentration, the strong electrolytes associate forming ion pairs (see Section 1.2.4). 

Molar Conductivity and Association Constants of Symmetrical Weak Electrolytes... 

In a similar manner, standard states can be chosen for electrolytes that take into account molecular association. We call this the weak electrolyte standard state, and some method must be employed to determine the extent of association. As an example, we usually treat nitric acid HNO3 as a strong electrolyte so that in solution... 

In Section 11.7 of Chapter 11, we summarized equations that can be used with electrochemical cell measurements to determine Ka and Kw for the dissociation (reverse of association) of an acid and of water, assuming a weak electrolyte standard state. If care is taken to obtain reversible conditions, this method, which does involve thermodynamic measurements, is a good one for determining K. Another method often employed involves using conductance measurements. The assumption is made that a, the degree of ionization or dissociation of an electrolyte is given by the ratio A/A. That is,... 

We turn our attention in this chapter to systems in which chemical reactions occur. We are concerned not only with the equilibrium conditions for the reactions themselves, but also the effect of such reactions on phase equilibria and, conversely, the possible determination of chemical equilibria from known thermodynamic properties of solutions. Various expressions for the equilibrium constants are first developed from the basic condition of equilibrium. We then discuss successively the experimental determination of the values of the equilibrium constants, the dependence of the equilibrium constants on the temperature and on the pressure, and the standard changes of the Gibbs energy of formation. Equilibria involving the ionization of weak electrolytes and the determination of equilibrium constants for association and complex formation in solutions are also discussed. 

Figure 11. Observed and predicted aqueous solubilities of nonelectrolytes (o) and weak electrolytes ( ). The solid line is the theoretical line described by Equation 22. The dashed line is the regression line of the experimental data. (Reproduced with permission from Ref. 38. Copyright 1983 American Pharmaceutical Association.)...

Ion association — A solution of a weak electrolyte such as acetic acid shows a molar -> conductance considerably lower than that expected for a strong electrolyte. This is due to the ion association, that is, ion-pair formation of the electrolyte ions M+ and X- ... 

At infinite dilution a weak electrolyte will be completely dissociated. Thus the conductance A0 at infinite dilution can be associated with complete dissociation and a = 1. Assuming that the decrease of Aeq(Aeq = A/z) with increasing concentration is caused mostly by the decrease of the degree of dissociation, a can be defined as... 

In the case of a dissociating (or associating) solute, the molality given by Eq. (10-11) or (10-20) is ideally the tofaf effective molality—the number of moles of all solute species present, whether ionic or molecular, per 1 kg of solvent. As we shall see, ionic solute species at moderate concentrations do not form ideal solutions and, therefore, do not obey these equations. However, for a weak electrolyte, the ionic concentration is often sufficiently low to permit treatment of the solution as ideal. 

It can be seen that the added complexity of ion association is likely to make any simple model of ion-ion interactions very difficult to apply without a number of ad hoc assumptions concerning ionic radii. This is particularly true for ionic strengths in excess of 0.01 M or for low-dielectric-constant media. However, a further difficulty is raised by the problem of the nature of an ion pair. If we consider the simple case of univalent ions A+ B forming an ion pair, it is possible to picture the pair as varying in character from one in which the charges remain separated by the sum of the ionic radii of A+ + B to a molecule in which A and B form a covalent bond, not necessarily even polar in character. Nor is it necessarily true that a given species will behave the same in different solvents. If there is a tendency to covalent bond formation, then it is quite possible that the polarity of the A—B bond will depend on the dielectric constant of the solvent. Covalently bound molecules which ionize are considered as weak electrolytes, and they are not treated by the methods of Bjerrum, which are meant for strong electrolytes. The differences may not always be clear, but the important interactions for the weak electrolyte are with the solvent, and these we shall consider next. 

Charged particles in weak electrolytes have associated with them an electrical double layer. When these particles settle under gravity the double layer is distorted with the result that an electrical field is set up that opposes motion. This effect was first noted by Dorn [74] and was studied extensively by Elton et. al. [75-78] and later by Booth [79,80]. 

Derivation of the thermodynamic equations for an electrolyte system with ion pairing follows the same procedure given for a weak electrolyte. However, in the following the ion pairing equilibrium is defined in terms of an association process. For a 1-1 electrolyte, ion pairing is described as... 

In recent years much work has been carried out, particularly by H. S. Harned and his associates, on concentration cells without liquid junction for the purpose of obtaining ionization constants of weak electrolytes. The principle involved in these investigations is as follows. Galvanic cells are set up of the form ... 

The explanation of these results proposed by Kraus and Fuoss21 in a series of papers, is based on two assumptions. The first of these is that electrolytes that are completely dissociated in water or any other solvents of high dielectric constant will be more or less associated into ion pairs in solvents of low dielectric constants. Ion pairs, AB, are considered to form entirely by electrostatic forces from the charged ions A+ and B , and the complexes are assumed to take no part in the conduction. Though no sharp division has been made experimentally these ion pairs are considered to differ from the undissociated portion of a weak electrolyte in that no electron shift has occurred in their formation. The second assumption is that, as the concentration of the ion pairs increases, a proportion of them will combine with ions by electrostatic forces, to form triple ions. ... 

For low-molecular weak electrolytes the concentration dependence of conductance is more complex, as in addition to the interionic friction effect it is strongly influenced by the association-dissociation reactions taking place in the solutions. However, as these in general follow the mass action law and thus, in simpler cases, the van t Hoff dilution law, their conductivity behavior is predictable. As a rule their equivalent conductivity steeply increases on dilution due to the increased dissociation of the electrolyte. 

For electrolytes which are not fully dissociated highly accurate data should be able to detect the onset of ion pair formation and, as the concentration increases, significant association is expected. The higher the charge type the lower the concentration at which association will be observed. Ion association results in Aobsvd values being lower than expected. For solutions of weak electrolytes where undissociated molecules are present similar behaviour is observed, viz. Aobsvd values will approach the limiting law slope from below. 

The 1957 Fuoss-Onsager equation can be adapted to take account of association of ions to form ion pairs and to account for incomplete dissociation of weak electrolytes. Chemically these are two different types of situation, but physically they are the same, viz. some of the ions are removed from solution by formation of ion pairs, or by formation of undissociated molecular species. The physical manifestation is that not all of the solute will be able to conduct the current, and so the observed conductance will be lower than that predicted by the... 

Thus, at high concentration we can formally associate 1 — a with an activity coefficient. Equation (12-57) is an expression for the chemical potential of weak electrolyte HA using the nonelectrolyte convention of Eq. (12-36). An alternative expression for //ha in zero approximation can be obtained from Eq. (12-39) in the form... 

Thus it is useful to associate a with an activity coefficient at low concentrations. At low concentrations, it is useful to represent Pha by Eq. (12-59). Equation (12-59) is similar to Eq. (12-30) which expresses //ha in terms of strong-electrolyte conventions. This completes our discussion of weak-electrolyte solutions. [More details concerning computations involving Eq. (12-56) can be found in F. H. MacDougall, Thermodynamics and Chemistry, chap. XV, 3d ed., John Wiley, Sons, Inc., New York, 1939.]... 

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