Enthalpy and Entropy of Complex Formation of Polyphosphate Ions with Alkaline-earth Metal Ions

Abstract

The thermodynamic quantities concerning the complex formation of polyphosphate ions (n= 6 and 8, n: the average degree of polymerization of polyphosphate) with Mg(II), Ca (II), and Sr( II ) were determined and compared with those obtained previously for pyro-, tri-, and tetra-phosphate complexes with these metal ions: (1) The thermodynamic stability constants of the complexes of the types ML, MHL, and NM. (where M, H, and Lare metal ion, hydrogen ion, and polyphosphate ion, respectively) were evaluated from pH titration data obtained at various ionic strengths at 25°C. (2) The enthalpy changes associated with the formation of the 1: 1 complexes (ML) at 25°C were determined by a direct calorimetric methed. On the basis of these values and the thermodynamic stability constants of the 1: 1 complexes, the corresponding entropy changes were calculated. As shown in Table 1, the complex formation is endothermic and the entropy change is always positive and large. The 4S° and 4H° increase with increasing average degree of polymerization of the polyphosphates (n); the rate of increase is relatively large below 4, and then becomes smaller (Fig.2). The 4S° and iiH° also increase with decresing radius of the metal cations (Fig.2). All these results are interpreted in terms of the present theories of metal chelate formation in aqueous solution.