Factorizing of a concentration function for the mean activity coefficients of aqueous strong electrolytes into individual functions for the ionic species

Partial osmotic pressures of ions in electrolyte solutions and the Gibbs-Guggenheim uncertainty principle

The concept of the partial osmotic pressure of ions in an electrolyte solution is critically examined. In principle these can be defined by introducing a solvent-permeable wall and measuring the force per unit area which can certainly be attributed to individual ions. Here I demonstrate that although the total wall force balances the bulk osmotic pressure as required by mechanical equilibrium, the individual partial osmotic pressures are extrathermodynamic quantities dependent on the electrical structure at the wall, and as such they resemble attempts to define individual ion activity coefficients. The limiting case where the wall is a barrier to only one species of ion is also considered, and with ions on both sides the classic Gibbs-Donnan membrane equilibrium is recovered, thus providing a unifying treatment. The analysis can be extended to illustrate how the electrical state of the bulk is affected by the nature of the walls and the container handling history, thus supporting the "Gibbs-Guggenheim uncertainty principle," namely the notion that the electrical state is unmeasurable and usually accidentally determined. Since this uncertainty is conferred also onto individual ion activities, it has implications for the current (2002) IUPAC definition of pH.

Ionised concentrations in calcium and magnesium buffers: Standards and precise measurement are mandatory

In Ca(2+) and Mg(2+) buffer solutions the ionised concentrations ([X(2+)]) are either calculated or measured. Calculated values vary by up to a factor of seven due to the following four problems: 1) There is no agreement amongst the tabulated constants in the literature. These constants have usually to be corrected for ionic strength and temperature. 2) The ionic strength correction entails the calculation of the single ion activity coefficient, which involves non-thermodynamic assumptions; the data for temperature correction is not always available. 3) Measured pH is in terms of activity i.e. pHa. pHa measurements are complicated by the change in the liquid junction potentials at the reference electrode making an accurate conversion from H(+) activity to H(+) concentration uncertain. 4) Ligands such as EGTA bind water and are not 100% pure. Ligand purity has to be measured, even when the [X(2+)] are calculated. The calculated [X(2+)] in buffers are so inconsistent that calculation is not an option. Until standards are available, the [X(2+)] in the buffers must be measured. The Ligand Optimisation Method is an accurate and independently verified method of doing this (McGuigan & Stumpff, Anal. Biochem. 436, 29, 2013). Lack of standards means it is not possible to compare the published [Ca(2+)] in the nmolar range, and the apparent constant (K(/)) values for Ca(2+) and Mg(2+) binding to intracellular ligands amongst different laboratories. Standardisation of Ca(2+)/Mg(2+) buffers is now essential. The parameters to achieve this are proposed.

Meaning and Measurability of Single-Ion Activities, the Thermodynamic Foundations of pH, and the Gibbs Free Energy for the Transfer of Ions between Dissimilar Materials

Considering the relationship between concentration and vapor pressure (or the relationship between concentration and fugacity) single-ion activity coefficients are definable in purely thermodynamic terms. The measurement process involves measuring a contact potential between a solution and an external electrode. Contact potentials are measurable by using thermodynamically reversible processes. Extrapolation of an equation to zero concentration and ionic strength enables determination of single-ion activity coefficients. Single-ion activities can be defined and measured without using any extra-thermodynamic assumptions, concepts, or measurements. This method could serve as a gold standard for the validation of extra-thermodynamic methods for determining single-ion activities. Furthermore, it places the concept of pH on a thermodynamically solid foundation. Contact potential measurements can also be used to determine the Gibbs free energy for the transfer of ions between dissimilar materials.