Use of Dicalcium Phosphate Dihydrate as a Probe in an Approach for Accurate Calculations of Solution Equilibria in Buffered Calcium Phosphate Systems

Abstract

Both synthetic and biological carbonated apatites have been shown to possess metastable equilibrium solubility (MES) distributions. Investigation of their MES behavior requires accurate knowledge of the activities of the relevant ions over a range of solution compositions. This in turn requires that the activity coefficients for these ions and the stability constants for the various solution complexes be accurately known. Since the solubility of dicalcium phosphate dihydrate (DCPD) can be easily determined, it can be used as a probe to study the appropriateness of proposed sets of stability constants and activity coefficients. In the present study, the solubility of DCPD was determined in acetate buffer solutions at pHs ranging from 4.5 to 6.5 and this allowed for the determination and evaluation of the stability constants of the NaHPO−4, CaHPO04, CaH2PO+4, and CaAc+ complexes. The activity coefficients were calculated by a modification of the extended Debye–Hückel method and also by Bockris and Reddy's method, in which the activity of water and the hydration numbers of ions are also considered. The solution conditions were controlled to simulate the dissolution media used for the determination of MES distributions of apatites in our laboratory. Both methods of activity coefficient determination gave very consistent DCPD solubility product (KDCPD) values, and values for the stability constants of the relevant complexes determined using the two methods were close to each other. This approach of determining the stability constants under a set of conditions similar to those in apatite dissolution studies offers an effective set of parameters which, though not necessarily always exactly correct in absolute terms, are internally consistent and should allow for the quantitative characterization of the MES behavior of apatites.