Polyprotic Acids and Beyond-An Algebraic Approach

For an N-protic acid-base system, the set of nonlinear equations (i.e., mass action and balance laws) provides a simple analytical solution/formula for any integer N >= 1. The approach is applicable for the general case of zwitterionic acids H(N)A(+Z) (e.g., amino acids, NTA, and EDTA), which includes (i) the ordinary acids as a special case (Z = 0) and (ii) surface complexation. Examples are presented for N = 1 to 6. The high-N perspective allows the classification of equivalence points (including isoionic and isoelectric points). Principally, there are two main approaches to N-protic acids: one from hydrochemistry and one outside inorganic hydrochemistry. They differ in many ways: the choice of the reference state (either H(N)A or A(-N)), the reaction type (dissociation or association), the type/nature of the acidity constants, and the structure of the formulas. Once the (nonlinear) conversion between the two approaches is established, we obtain a systematics of acidity constants (macroscopic, microscopic, cumulative, and Simms). Finally, 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.

Automated summary

An analytical solution/formula for N-protic acid-base system is provided through a set of nonlinear equations, which includes applications in both ordinary acids and surface complexation. The perspective of high-N allows for the classification of equivalence points and differences between isoelectric and isoionic points. Two main approaches to N-protic acids, from hydrochemistry and inorganic hydrochemistry, are discussed, along with the systematics of acidity constants that result from the conversion between these approaches. Additionally, statistical mechanics provide insights into buffer capacities and higher pH derivatives as fluctuations in the form of variance, skewness, and kurtosis.