Single-ion Quantities

Consider a solution of an electrolyte solute that dissociates completely into a cation species and an anion species. Subscripts - - and — will be used to denote the cation and anion, respectively. The solute molality ms is defined as the amount of solute formula unit divided 

We first need to investigate the relation between the chemical potential of an ion species and the electric potential of the solution phase. 

The electric potential (p in the interior of a phase is called the inner electric potential, or Galvani potential. It is defined as the work needed to reversibly move an infinitesimal test charge into the phase from a position infinitely far from other charges, divided hy the value of the test charge. The electrical potential energy of a charge in the phase is the product of 4 and the charge. 

The Gibbs fundamental equation for an open system, dG = —SdT+Vdp+Yii pti d / (Eq. 9.2.34), assumes tbe electric potential is zero. From this equation and Eq. 10.1.2, the Gibbs energy change during the transfer process at constant T and p is found to depend on 

The chemical potential of the cation in a phase of electric potential (p, defined by the partial molar Gihhs energy [9G(0)/9n+]r,p, is therefore given by 

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By combining these ions with other counterions, single ion transfer activity coefficients are calculated. By these techniques transfer free energies or activity coefficients have been determined for many ions and nonelectrolytes in a wide variety of solvents.Parker has discussed the extrathermodynamic assumptions that lead to single ion quantities. 

This, of course, is always negative, and plays the same role in aqueous thermochemistry as the lattice energy does in the energetics of ionic solids. The hydration enthalpy cannot be measured directly, and many thermodynamicists frown upon this or any other single-ion quantity. For example, the enthalpy of solution of sodium chloride can be measured and subjected to the following analysis ... 

Ion solvation in polar solvents is also an important aspect of the subject matter considered here. This is traditionally studied by measuring the Gibbs energy and enthalpy of transfer of a variety of electrolytes from water to another polar solvent. Single ion quantities are then derived on the basis of the TATB assumption. Study of these quantities for simple monoatomic ions like the alkali metal cations and the halide anions leads to the conclusion that specific molecular properties, namely, Lewis acidity and basicity, are important in ion solvation. On the other hand, the dielectric permittivity, a non-specific bulk property. 

The Galvani potential difference may not be found experimentally because single ion quantities are not subject to experimental determination. However, because of the requirement of electroneutrality, the concentration of cations and anions in each phase is equal. Furthermore, in the limit of dilute solutions, the activities of these ions are equal in each phase. Thus, by equating (8.9.5) and (8.9.6), one obtains for dilute electrolyte concentrations... 

Because the partition equilibria observed at the liquid liquid interface are relevant to interfacial phenomena in specific ion electrodes and biological membranes, there is an interest in determining single ion quantities associated with transfer of an ion from water to the non-aqueous phase. This quantity can only be estimated from experimental data after making an extrathermodynamic assumption. One common assumption discussed earlier in section 4.8 is the so-called TATB assumption, according to which... 

Quantities at standard conditons as used in solution chemistry are also tubulated. Standard heats of formation of ions in aqueous solutions, Af//2°9g[Yi(aq)], include the heat of formation of the pure compound Y under standard conditions and the heat of transfer of pure compound Y from its pure state to infinite dilution in solvent S, that is, the quantity - H. The tables of single-ion quantities in aqueous solutions are based on the additional assumption that Af//°[H+(aq)] = AfG°[H+(ag)] = S°... 

Despite this drawback there is an interest in science and technology in single-ion quantities for rationalizing the discussion of electrolyte solution properties. Various methods have been developed for their estimation based on extrathermodynamic assumptions, such as the following (1) The contributions of cation and anion are set equal for a salt composed of ions of equal charge and approximately equal radii (2) the results of measurements on a series of homologous electrolytes are extrapolated with regard to ionic radii or ionic volumes to zero ion size or zero reciprocal radii (3) the differences in conventional ionic properties are used for theoretically rationalized extrapolations and (4) the properties of ions are compared with those of isoelectronic neutral molecules of similar chemical constitution and size. 

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