Clustering in dilute solutions and Pitzer models

Here we discuss a thermodynamic model appropriate to describe effects of strong association in dilute solutions. To have a definite example, consider a dilute electrolyte solution of a salt, say M X, that in solution dissociates to produce cations M of charge qu e and anions X of charge —qx e with aq [ = bqx- The interactions between these ions are composed of short-ranged interactions and long-ranged ionic interactions screened by the dielectric response of the solvent with dielectric constant e, as with r the distance between the ions. If the 

To seek ion clusters that might form, we need an operational definition useful in identifying them. Let s direct our attention to a specific, distinguished M ion. We will presume that a rule is available to determine how many other ions, prohahly X ions, are clustered with the distinguished M ion (Lewis et al, 1961, see discussion What do we mean hy degree of dissociation , pp. 307-308). If there are k of those counter-ions clustered, we would consider this M to be the nucleus of an MX t cluster. 

This clustering idea seeks to partition our difficulties according to the numbers of ligands, k, that might be associated with a distinguished M ion. The basic equation 

To make progress with a specific term, say ( mxJ we assume that the PDT applies to this species too  

This argument is examined and supported in more detail later, in Section 7.2 p. 146. The quantities and are proposed to be factors of the canonical 

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