Acid-base Reactions from a (somewhat) Broader Perspective

The subject of acid-base reactions encompasses a large body of literature, with most emphasis on mono- and diprotic acids, which is the entry point to understanding pH and chemical equilibrium reactions per se. The UIT review extends this viewpoint to N-protic acids for any integer N > 1. The corresponding nonlinear algebraic system is solved, which provides easy-to-handle analytical formulas to calculate titration functions, buffer capacities, and buffer intensities.

The analytical approach is applied to different acid-base system, starting with carbonic and phosphoric acid, amino acids and EDTA and ending with surface complexation on clay minerals. In fact, the scope is much broader when we enter the terrain of org/bio/med chemistry (with fulvic/humic acids, nucleic acids, and other chimeras).

Besides: The high-N perspective allows a natural but strict classification of the 2N+1 equivalence points (including isoionic and isoelectric points).

Once you have an analytical formula (explicit function), it can be “modified” according to all rules of mathematics: (i) you can differentiate/integrate the function, (ii) you can form superpositions (mixtures), and (iii) you can invert the function. This is exploited and leads to surprising insights:

• From the viewpoint of statistical mechanics (canonical isothermal-isobaric ensemble), buffer capacities, buffer intensities, and higher pH derivatives are actually fluctuations in the form of variance, skewness, and kurtosis.
• By factorizing the partition function, each N-protic acid can be represented as a sum/superposition of N monoprotic acids.

With the last point we build a bridge to theoretical physics, where interacting particles/systems are often described by means of non-interacting "quasiparticles" (phonons, magnetons, excitons). Also noteworthy is the similarity of the ionization fraction (of monoprotic acids) with the Fermi-Dirac distribution and the sigmoidal logistic function.

Back to practice. Although the above considerations extend our understanding of acid-base systems (and the underlying equilibrium thermodynamics), in UIT we primarily use numerical models (PhreeqC, aquaC, TRN) to simulate "real systems". This finding is summarized in the very last paragraph of our 55-page report:

"Final Remark. The mathematical framework is based on three assumptions: (i) activities are replaced by concentrations, (ii) no aqueous complex formation, and (iii) no density effects (molality = molarity). These are the limits of the analytical model. Although the current approach deepens our understanding of the acid-base system, it can never replace numerical models such as PhreeqC, which are capable of handling real-world problems more accurately (including activity corrections, an arbitrary number of species and phases, and complex formation)."