Geometric-algebraic approach to aqueous solutions of diprotic acids and its buffer mixtures

Summary: A general closed-form expression for [H3O+] in weak acid solutions and buffers, as well as their titration with a strong base, has been mathematically analyzed using computer algebra systems. The expression is used to evaluate the precision and accuracy of different approximations commonly used in general chemistry and chemical analysis courses, without numerical approximations. The stability of pH when a strong base is added to a buffer solution is determined using the closed-form expression for [H3O+]. Furthermore, it is shown that the [H3O+] expressions for all systems can be obtained from a general closed-form expression using effective weak acid constants and concentrations, without any numerical or graphical methods.

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.