Comprehensive Formulation of Titration Curves for Complex Acid-Base Systems and Its Analytical Implications

Abstract

This article provides extensive and exhaustive mathematical description of titration curves related to acid-base systems with mixtures of mono- and polyprotic acids and their salts and bases involved. The related curves are presented in compact forms facilitating further operations made for particular needs. Some derivative properties of the curves, such as buffer capacity and inflection points, are also discussed. The “windowed” (B V ) buffer capacity is interrelated with “dynamic” (β V ) buffer capacity, introduced for dynamic (titration) systems. The equations useful for searching the inflection points on titration curves are derived. A kind of “homogenization” of complex acid-base systems, with polyprotic acids with defined and/or undefined (e.g., fulvic acids) composition, with use of an approach based on Simms constants principle, has been considered in context with buffer capacity and alkalinity. The new concepts of total alkalinity (TAL) and total acidity (TAC), unlike ones considered hitherto, has been introduced. The TAL is determined according to curve–fitting method with use of iterative computer program, applied to nonlinear regression equation involving Simms or Hill constants. Searching the best fit of the related function is involved with addition of consecutive hyperbolic terms.