Objective:
pH is generally thought to be a function of the activity of the hydrogen ion when the solvent is water. This can be difficult to understand when:
- The solvent is not water
- The model does not present the hydrogen ion (H+), as is the case with the Mixed-Solvent Electrolyte thermodynamic framework.
This article explains how we calculate pH in the absence of hydrogen ions and in solvents other than water.
A Question:
A user inquired about extending the OLI pH equation for the mixed solvent electrolyte (MSE) model to multiple solvents. This question addresses a significant challenge in thermodynamics and electrochemistry. The detailed treatment of pH in mixed-solvent-electrolyte systems is extensively discussed in the paper by Kosinski et al. (2007), available at Fluid Phase Equilibria, Volume 256, Issues 1–2, 2007.
Key Insights from the Paper:
This paper's critical equation (13) forms the basis for calculating pH in mixed-solvent systems.
Understanding the Limitations of this Equation:
- No Universal pH Scale: No universal pH scale applies to all protic solvents. IUPAC recommends separate scales for each solvent due to the unique interfacial reactions at the electrode-solution boundary for different protonated species. This variability means formal thermodynamics does not provide a one-size-fits-all solution.
- Electrode Response Variability: Different protonated species (e.g., hydronium ions in water or protonated forms of other solvents) interact differently with the electrode interface, leading to distinct electrode responses. This results in the necessity for separate pH scales for different solvents.
Empirical Approach:
Given these limitations, OLI Systems adopted an empirical method:
- Hypothesis on Proton Carriers: It was hypothesized that all small enough protonated species capable of crossing the electrode interface should contribute to the electrode response. This hypothesis was validated in systems containing H₂O₂, leading to a breakthrough in understanding and measurement.
- Concentration Summation: By summing the concentrations of all protonated species (e.g., hydronium ions and protonated H₂O₂ for a H₂O₂ system), a practical method for estimating pH was developed. This method was extended to MEG (monoethylene glycol) systems, where the concentrations of hydronium ions and protonated MEG were summed. However, this method cannot account for activity coefficients, as activities are not additive.
Current State of the Art of modeling pH (including OLI)
- Single Solvent (Water): For water as the sole solvent, equation (13) provides a rigorous method for pH calculation.
- Multiple Solvents: A universally rigorous method does not exist for systems with multiple solvents. However, the empirical method based on the summation of protonated species concentrations has been shown to align well with experimental data for specific mixtures like H₂O₂ and MEG.
In summary, while the OLI pH equation for the MSE model can be approximated for multiple solvents through empirical methods, a universally rigorous approach still needs to be attainable due to the inherent variability in electrode responses across different solvent systems.
References:
- Kosinski, J. J., Wang, P., Springer, R. D., & Anderko, A. (2007). Modeling acid–base equilibria and phase behavior in mixed-solvent electrolyte systems. Fluid Phase Equilibria, 256, 34-41
- Wang, P., Anderko, A., & Young, R. D. (2002). A speciation-based model for mixed-solvent electrolyte systems. Fluid Phase Equilibria, 203, 141-176.