Individual ion activity and liquid junction potential—Two interrelated, interconnected electrochemical terms

Multi-component ion equilibria and transport in ion-exchange membranes

At the interface between an ion-exchange membrane and a multi-electrolyte solution, charged species redistribute themselves to minimize the free energy of the system. In this paper, we explore the Donnan equilibrium of membranes with quaternary electrolyte (Na+/Mg2+/K+/Ca2+/Cl-) solutions, experimentally. The data was used to calculate the ion activity coefficients for six commercial cation-exchange membranes (CEMs). After setting one of the activity coefficients to an arbitrary value, we used the remaining (N-1) activity coefficients as fitting parameters to describe the equilibrium concentrations of (N) ionic species with a mean relative error of 3 %. At increasing solution ionic strengths, the equivalent ion fractions of monovalent counter-ions inside the membrane increased at the expense of the multivalent ones in alignment with the Donnan equilibrium theory. The fitted activity coefficients were employed in a transport model that simulated a Donnan dialysis experiment involving all four cations simultaneously. The arbitrary value assigned to one activity coefficient affects the calculated Donnan potential at the membrane interface. Nevertheless, this arbitrary value does not affect the prediction of the ion concentrations inside the membrane and consequently does not affect the modeled ion fluxes.

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.

How Do Liquid-Junction Potentials and Medium Polarity at Electrode Surfaces Affect Electrochemical Analyses for Charge-Transfer Systems?

The importance of electrochemical analysis for charge-transfer science cannot be overstated. Interfaces in electrochemical cells present certain challenges in the interpretation and the utility of the analysis. This publication focuses on: (1) the medium polarity that redox species experience at the electrode surfaces that is smaller than the polarity in the bulk media and (2) the liquid-junction potentials from interfacing electrolyte solutions of different organic solvents, namely, dichloromethane, benzonitrile, and acetonitrile. Electron-donor-acceptor pairs of aromatics with similar structures (i.e., 1-naphthylamine and 1-nitronaphthalene, 10-methylphenothiazine and 9-nitroanthracene, and 1-aminopyrene and 1-nitropyrene) serve as redox analytes for this study. Using the difference between the reduction potentials of the oxidized donors and the acceptors eliminates the effects of the liquid junctions on the analysis of charge-transfer thermodynamics. This analysis also offers a means for evaluating the medium polarity that the redox species experience at the surface of the working electrode and the effects of the liquid junctions on the measured reduction potentials. While the liquid-junction potentials between the dichloromethane and acetonitrile solutions amount to about 90 mV, for the benzonitrile-acetonitrile junctions, the potentials are only about 30 mV. The presented methods for analyzing the measured electrochemical characteristics of donors and acceptors illustrate a means for improved evaluation of the thermodynamics of charge-transfer systems.

Measurements and Utilization of Consistent Gibbs Energies of Transfer of Single Ions: Towards a Unified Redox Potential Scale for All Solvents

Utilizing the “ideal” ionic liquid salt bridge to measure Gibbs energies of transfer of silver ions between the solvents water, acetonitrile, propylene carbonate and dimethylformamide results in a consistent data set with a precision of 0.6 kJ mol⁻¹ over 87 measurements in 10 half‐cells. This forms the basis for a coherent experimental thermodynamic framework of ion solvation chemistry. In addition, we define the solvent independent peabsH2O ‐ and the EabsH2O values that account for the electronating potential of any redox system similar to the pHabsH2O value of a medium that accounts for its protonating potential. This EabsH2O scale is thermodynamically well‐defined enabling a straightforward comparison of the redox potentials (reducities) of all media with respect to the aqueous redox potential scale, hence unifying all conventional solvents′ redox potential scales. Thus, using the Gibbs energy of transfer of the silver ion published herein, one can convert and unify all hitherto published redox potentials measured, for example, against ferrocene, to the EabsH2O scale.

A unified pH scale for all solvents: part I – intention and reasoning (IUPAC Technical Report)

The definition of pH, its measurement and standard buffers, is well developed in aqueous solutions. Its definition in solvents other than water has been elaborated for a couple of solvents and their mixtures with water. However, the definition of a universal pH scale spanning all solvents and phases, not to mention standard procedures of measurement, is still a largely uncharted territory. UnipHied is a European collaboration and has the goal of putting the theoretical concept of an earlier introduced (2010) unified pHabs scale on a metrologically well-founded basis into practice. The pHabs scale enables the comparability of acidity between different phases. This article draws the connection of the concepts of unified acidity and secondary pH measurement.

Modeling Acid-Base by Minimizing Charge-Balance

In this study, we show that equilibrium pH can be obtained for any specified fluid with any number of buffers and dissociations. This is done by root finding in the equation for charge balance. We demonstrate that this equation is monotonic in proton concentration for conceivable buffers. We show that the total charge on any buffer is a function of only the total buffer concentration and pH, given the thermodynamic dissociation constants. Using the Davies' equation as a placeholder for single-ion activity coefficients as a function of charge and ionic strength, we develop an iterative algorithm, whereby the apparent dissociation constants are updated from the thermodynamic dissociation constants, and from this, the equilibrium is also identified in the nonideal state. We show how this algebra leads to guaranteed conservation of both thermodynamic dissociation constants and total buffer concentrations because the distribution of buffer species is fixed by the updated dissociation constants, actual pH, and total buffer concentration. Strong ions are assumed to contribute fixed charges. In order to concentrate on the process of modeling the equilibrium pH alone, this algorithm is examined against a series of theoretical results in which the Davies' equation was given the same status. However, a large sample of clinical pH measurements is also examined. To enhance the practical utility, CO₂ and albumin are present as the default condition. We developed "ABCharge", a package in R, an open source language. The main function returns pH, activity coefficients, buffer species distribution, ionic strength, and charge balance for both the ideal and nonideal cases, for any mixture of any buffers with any number of known thermodynamic dissociation constants. Our algorithm can be updated if a more reliable and practical assessment of single-ion activities becomes available. Can Stock Photo/miceking.