Unsymmetrical electrolytes

Klotz (1964) points out that these definitions of activity for unsymmetrical salts imply new and rather strange standard states for these electrolytes. If we insist on having, for example, 

This means that we cannot say, as before ( 17.2.2), that 

This is all quite confusing on the first run-through, but is quite logical. See Klotz (1964) for additional discussion. Table 17.3 contains a summary of these relationships. 

Example From Robinson and Stokes (1968, p. 478) we find that in a 2.0m solution, 7 ,caci2 125°C is 0.792. Therefore 

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So far we have considered only symmetrical 1 1 electrolytes such as HC1, K.CI, or MgS04. For unsymmetrical electrolytes, the limiting law takes a different form, and different relationships between activity, molality and activity coefficient are obtained. For example, for the 2 1 electrolyte, Na SO,, the dissociation reaction is... 

This theory of the diffuse layer is satisfactory up to a symmetrical electrolyte concentration of 0.1 mol dm-3, as the Poisson-Boltzmann equation is valid only for dilute solutions. Similarly to the theory of strong electrolytes, the Gouy-Chapman theory of the diffuse layer is more readily applicable to symmetrical rather than unsymmetrical electrolytes. 

For a 1-1 electrolyte the double layer thickness is, therefore, about 1 nm for a 101-1 mol dm-3 solution and about 10 nm for a 1Q 3 mol dm-3 solution. For unsymmetrical electrolytes the double layer thickness can be calculated by taking z to be the counter-ion charge number. 

Unsymmetrical inert electrolyte binding leads to semantic problems even at pristine conditions PZC becomes ionic strength dependent, the surface potential is not equal to zero at the PZC. etc., cf. Eqs. (3.2) and (3.3). Fortunately such problems are encountered in modeling exercises with unsymmetrical electrolyte binding, but not in reality. Anyway, this modification is not recommended. Ultimately a TLM with seven adjustable parameters (equilibrium constants of reactions (5.32), (5.33), (5.46), and (5.47) are unrelated) can be used to model raw titration data (the charging curves were not shifted to produce PZC = CIP) [66], but physical meaning of such model exercises is questionable. 

Care must be taken when dealing with unsymmetrical electrolytes. For instance, if the solubility in water for CaF2(s) is s, then s mol dm of CaF2(s) gives rise to s mol dm of... 

Section 8.22 and Worked Problems 8.13 and 8.14 derive the expressions for the mean activity coefficient exphcitly for specific electrolytes. This is preferable to simply fitting into a generalised expression which is often quoted for unsymmetrical electrolytes as it makes quite clear exactly what the thermodynamic argument actually is. The generalised expressions are ... 

When the equation is restricted to these three terms only, the final expression will be different for symmetrical electrolytes and unsymmetrical electrolytes. 

The general form of the Poisson-Boltzmann equation truncated to two terms only is accurate to three terms for symmetrical electrolytes since the third term equals zero, but is only accurate to two terms for unsymmetrical electrolytes, the third term being non-zero. In the form truncated to two terms ... 

The expression for a symmetrical electrolyte can be deduced from Equation (10.65) describing the unsymmetrical electrolyte. 

For symmetrical electrolytes, association will produce an ion pair of zero charge and to a first approximation for the ion pair is unity. For unsymmetrical electrolytes, association... 

Note well the concentration appearing in Equations (11.35) to (11.39) relates to the ionic concentrations, while that in Equation (11.40) is the stoichiometric concentration of the electrolyte. It is important to distinguish between these, especially for unsymmetrical electrolytes, see below. 

In Sections 11.12 and 11.16 it was shown that for a unsymmetrical electrolyte, ionising... 

For the unsymmetrical electrolyte the final relations are the same, but the argument is more complex, see Section 11.19.3. 

The argument given above for the symmetrical electrolyte, KCl(aq), will hold for an unsymmetrical electrolyte provided c+ refers to the concentration of the cation and not to the overall concentration of the electrolyte, e.g. 

Fuoss has stressed that his equations can only be legitimately applied for concentration ranges where kci < 0.2. This corresponds to approximately 4 x 10 moldm for 1-1 electrolytes, 1 X 10 moldm for 2-2 electrolytes and 4 x 10 moldm for 3-3 electrolytes. The theory also only applies to symmetrical electrolytes, though later workers were able to obtain expressions for unsymmetrical electrolytes. These are much more complex than that of Fuoss and Onsager. 

The MS approximation for the RPM, i.e. charged hard spheres of the same size in a continuum dielectric, was solved by Waisman and Lebowitz [46] using Laplace transforms. The solutions can also be obtained [47] by an extension of Baxter s method to solve the PY approximation for hard spheres and sticky hard spheres. The method can be further extended to solve the MS approximation for unsymmetrical electrolytes (with hard cores of unequal size) and weak electrolytes, in which chemical bonding is mimicked by a delta function interaction. We discuss the solution to the MS approximation for the symmetrically charged RPM electrolyte. 

At concentrations greater than 0.001 mol kg equation A2.4.61 becomes progressively less and less accurate, particularly for unsymmetrical electrolytes. It is also clear, from table A2.4.3. that even the properties of electrolytes of the same charge type are no longer independent of the chemical identity of the electrolyte itself, and our neglect of the factor kgq in the derivation of A2.4.61 is also not valid. As indicated above, a partial improvement in the DH theory may be made by including the effect of finite size of the central ion alone. This leads to the expression... 

For unsymmetrical electrolytes there is no complete treatment of the conductance. In some cases eqn. 5.2.31 has been employed to evaluate the conductance of unassociated unsymmetrical electrolytes and the a values obtained are reasonable. When unsymmetrical electrolytes undergo association the ion pairs formed are charged and will contribute to the conductance of the solution. Fuoss and Edelson derived a semi-empirical equation which may be employed in this case. 

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