Kinetic Titrimetry: Theory of Automated Linear Titrations and Application to Thermometric End Points

A conceptual and mathematical theory is presented applicable when kinetics of titration reactions are slow. In such situations the rate of addition of titrant, ρ, is effectively a competing rate process, yielding spurious “late” end points which hitherto had no analytical significance. An integrated rate equation for second order kinetics is derived, representing a rigorous solution of the relevant Ricatti Equation when ρ = const., as is generally the case in automatic titrations. End-point correction procedures are described for approximating valid stoichiometric equivalence points. With the aid of normalized graphical plots and dimensionless variables, a method has been developed for the titrimetric determination of rate constants up to a limit of 600,000 M⁻¹ sec⁻¹. This is within the range of stopped flow methods, compared to which kinetic titrimetry has important advantages of simpler implementation and broader applicability. Capabilities are documented experimentally by thermometric enthalpy titrations of dilute solutions of nitroparaffins with strong base, which involved sluggish proton abstraction processes. Precision and accuracy of 1% were attained in the quantitative determination of nitromethane, nitro-ethane, and nitropropane at millimolar concentration levels. Rate constants were measured with a precision between 1 and 3%.