Unified Approximations: A New Approach for Monoprotic Weak Acid-Base Equilibria.

This article describes a new approach to approximate calculations for monoprotic acid–base equilibria in otherwise pure water. The new approach, identified herein as unified approximations, uses a simple decision criterion to select between situations that should be treated as deprotonation and protonation reactions. The remaining treatment takes account of changes in concentrations of conjugate acid–base pairs for all situations and ignores autoprotolysis only for situations for which the analytical concentration of either the conjugate acid or conjugate base will always be larger than zero. The net result is a process that leads to two similar quadratic equations that give approximation errors of 5% or less for a range of situations for which 10 different sets of decisions, simplifying assumptions, procedures, and mathematical relationships are needed using classical or graphical methods.