Stability Constants of Complexes - Experimental Methods

Experimental Methods

The method developed by Bjerrum is still the main method in use today, though the precision of the measurements has greatly increased. Most commonly, a solution containing the metal ion and the ligand in a medium of high ionic strength is first acidified to the point where the ligand is fully protonated. This solution is then titrated, often by means of a computer-controlled auto-titrator, with a solution of CO₂-free base. The concentration, or activity, of the hydrogen ion is monitored by means of a glass electrode. The data set used for the calculation has three components: a statement defining the nature of the chemical species that will be present, called the model of the system, details concerning the concentrations of the reagents used in the titration, and finally the experimental measurements in the form of titre and pH (or emf) pairs.

It is not always possible to use a glass electrode. If that is the case, the titration can be monitored by other types of measurement. Absorbance spectra, fluorescence spectra and NMR spectra are the most commonly used alternatives. Current practice is to take absorbance or fluorescence measurements at a range of wavelengths and to fit these data simultaneously. Various NMR chemical shifts can also be fitted together.

The chemical model will include values of the protonation constants of the ligand, which will have been determined in separate experiments, a value for log K_w and estimates of the unknown stability constants of the complexes formed. These estimates are necessary because the calculation uses a non-linear least-squares algorithm. The estimates are usually obtained by reference to a chemically similar system. The stability constant databases can be very useful in finding published stability constant values for related complexes.

In some simple cases the calculations can be done in a spreadsheet. Otherwise, the calculations are performed with the aid of a general-purpose computer programs. The most frequently used programs are:

• Potentiometric and/or spectrophotometric data: HYPERQUAD, PSEQUAD
• Potentiometric data: BEST
• Spectrophotometric data: SQUAD, SPECFIT,
• NMR data HypNMR, EQNMR

In biochemistry, formation constants of adducts may be obtained from Isothermal titration calorimetry (ITC) measurements. This technique yields both the stability constant and the standard enthalpy change for the equilibrium. It is mostly limited, by availability of software, to complexes of 1:1 stoichiometry.