Pseudo-equilibrium equation of calcium phosphate precipitation from aqueous solution

Abstract

For a precipitation reaction involving an amorphous phase, the equilibrium equation takes the general form (middle), which converts to the conventional “reaction quotient” (left) and the “solubility product” (right) in two limit cases, respectively.

Pseudo-equilibrium equations for calcium phosphate precipitation with multi-unit particles

“…1a) is an improvement on series C n P5 investigated in our previous work ([Pi] i = 5.00 mmol L −1 and [Ca 2+ ] i = 2.50, 3.00, 3.50, 4.00, 4.50 mmol L −1 , respectively). 38 In the current series, more significant differences were observed between systems in both the ionic product and the amount of the precipitate, yielding a higher signal/noise ratio of the solution chemistry data.…”

“…2a leads to Type I pseudo-equilibrium equation (eqn (18)), providing further evidence for our previous report. 38 Whereas the negative slope in Fig. 2b leads to a Type II equation (eqn (19)), showing that the ionic product (IP) m decreased as the precipitate concentration [S m ] increased.…”

“…36 In the aqueous medium at a near-neutral pH, the dominant cluster Ca(HPO 4 ) is the main constituent of the incipient ACP. 33,[37][38][39] A recent report demonstrated the preparation of amorphous Ca(HPO 4 ) from near-neutral solutions. 40 And the precipitates with Ca/P values close to 1.0 were detected from solutions with variable Ca/P ratios.…”

“…In actuality, we have previously observed the association between the ionic product and the amount of the precipitate, 49 and later derived a pseudo-equilibrium equation that relates the ionic product to the surface proportion of a precipitate particle. 38…”

Structural Biology of Calcium Phosphate Nanoclusters Sequestered by Phosphoproteins

“…It is possible to apply equilibrium thermodynamics to a metastable supersaturated solution in a prolonged lag phase [83,84] in order to define an effective solubility product, applicable to any supersaturated solution provided it is well away from the spinodal boundary where no lag phase can exist [114]. We justify the approach because the time needed for ions to reach equilibrium with the continuous phase is likely to be short compared to the time spent in the lag phase and we restrict our application to nearly stable solutions with lag times of days or longer.…”