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.

Automated summary

This article critically examines the concept of the partial osmotic pressure of ions in an electrolyte solution. The individual partial osmotic pressures are found to be extrathermodynamic quantities dependent on the electrical structure at the wall, similar to attempts to define individual ion activity coefficients. The analysis also considers the case where the wall is a barrier to only one species of ion, recovering the classic Gibbs-Donnan membrane equilibrium and providing a unifying treatment.