Phosphates of divalent metals often show complex structures and great variability in chemical composition. Numerous examples were given in work by Bassett and Bedwell [1] . Their first paper in the series concerns monohydrogen phosphates as well as double salts with potassium or ammonium and from 0 to 7 mol of water of crystallization per mol of salt. An important representative is the biogenic mineral struvite, MgNH₄PO₄∙6H₂O, typically found in guano [2] [3] .

A number of years ago we studied the crystallization of phosphates of some transition metals including Co, Ni and Cu and in particular double salts with ammonium [4] [5] . In this connection we needed, among others, the solubility product of ammonium nickel phosphate hexahydrate, NH₄NiPO₄∙6H₂O:

This compound is often named Ni-struvite, because it is isomorphous with struvite. Our way of writing the solubility product has been chosen for two reasons: 1) The activity coefficient of an uncharged species like NH₃ is close to unity, and 2) is the most abundant phosphate species in neutral and weakly basic solution, its concentration being orders of magnitude higher than that of except at high pH. We then avoid involving the third dissociation constant of phosphoric acid, which is not known with so high precision as the two others.

Solubility products of simple salts comprising only one type of cation and one type of anion are often found in standard tables [6] and databases [7] , whereas data for mixed salts are much more difficult to retrieve, if they exist at all. For unknown reasons we never published any details on the value for Ni-struvite quoted in our paper on crystal habit [4] , and nobody else seems to have done so. Recent literature, however, points to a certain interest in this and related substances in different fields as examplified by spectroscopy [8] , microbiology [9] and pollution control [10] [11] , where information on solubilities seems important for understanding the mechanism of incorporation of the mineral in microbes and evaluation as fertilizer struvite obtained from Ni-containing wastewater. We therefore found it worthwhile to reconsider the data and carry out a revision using new values of equilibrium constants.

Total concentrations of ammonium and phosphate in the equilibrated solutions were calculated from initial concentrations and the amounts of Ni-struvite precipitated or dissolved, obtained from the results of nickel analyses. For each experiment the values of [NH₃], a(Ni²⁺) and a() in Equation (1) were calculated from the known total concentrations of chloride, nickel, ammonium and phosphate and literature values for the equilibrium constants, i.e. dissociation constants of phosphoric acid and ammonium as well as stability constants of complexes of nickel ion with ammonia, phosphate and chloride [7] . The resulting system of nonlinear equations was solved by a Newton-Raphson iteration using a previously described computer program [14] , which also yields pH and ionic strength I. Activity coefficients of ions were calculated from I with the Debye-Hückel equation

A and B are temperature-dependent parameters equal to 0.5115 and 0.3291, respectively, at 25˚C, and z_i is the charge and the radius of the ion in units of the electron charge and Å, respectively. Values of the latter are given in Kielland’s paper [15] ; those not found there are estimated from values for similar ions.

A total of 12 precipitation and 16 dissolution experiments were carried out. Of the latter, 3 results deviated so much from the mean that it was decided to make a statistical test for extreme deviations. The test yielded significant to highly significant deviation, so these results were not included in calculation of mean and standard deviation. One of the cases concerns the experiment with dissolution in pure water, yielding a solubility product significantly lower than the average. Probably the rate of dissolution in the absence of acidity is so low that the solution is not yet saturated at the time of sampling. Another cause could be uncertainty of the analysis, as the concentrations were very low. In the other two cases slight, but still significant deviation in the direction of higher solubility was found; this will be discussed below. In addition to the ordinary precipitation experiments we analyzed the mother liquor from Ni-struvite synthesis, so that the total adds up to 13 of each kind of experiment. In nine of the dissolution experiments only ammonium dihydrogen phosphate was added at concentrations ranging from 0.2 to 10 mM. Table 1 and Table 2 show the amounts of salts added in the ordinary precipitation experiments and in the dissolution experiments as well as equilibrium concentrations of nickel found by analyses of the saturated solutions.

In the mother liquor from the synthesis chloride concentration was 0.0504 M, and the equilibrium concentration of Ni was 2.3 µM. Ionic strength was high in this solution, I = 0.6, but otherwise the values ranged from 0.0015 to slightly below 0.1. In this range we can trust the validity of the Debye-Hückel Equation (2) for calculation of activity coefficients. Values of pK_sp = −log K_sp are plotted

against calculated pH in Figure 1. Mean value and standard deviation of the whole sample are indicated on the graph.

A remarkable fact is that the result from the mother liquor, indicated with a filled symbol, does not deviate significantly from the rest in spite of the high ionic strength. As a whole, no significant dependence on ionic strength was found; regression analysis yielded a correlation coefficient << 1. The mean value with its standard deviation was found as

Finally we notice that the mean values for each of the two series of experi- ments are very similar, being 11.036 for precipitation and 11.034 for dissolution. Thus the general criterion for equilibrium, that the same value of the equilibrium constant should be found on approach from either side, is fulfilled in this case. This is by no means trivial, as the literature has many examples of a significantly higher value of K_sp from precipitation than from dissolution.

The solubility of Ni-struvite is a little lower than that of struvite, for which we have found pK_sp = 9.94 [16] . More recent research by other investigators [17] [18] [19] [20] [21] give values in the range 9.5 - 10.3 with an overall average of 9.99, i.e. not significantly different from our result and still below the value for Ni-struvite. The standard free energy change for the transformation

equals ΔG = −6.22 kJ/mol as found from our results. Table 3 shows calculated solubilities of the two solids in pure water as well as concentrations in a solution saturated with respect to both. The dependence of solubilities on pH is shown in Figure 2; it is supposed that pH is regulated by the addition of hydrochloric acid.

From further calculations using the literature value for the solubility product of the trinickel phosphate (TNP) Ni₃(PO₄)₂∙8H₂O [7] , it turned out that a saturated solution of Ni-struvite in pure water is highly supersaturated with respect to this compound. Some of the systems of the dissolution experiments of the present study, including those yielding deviating solubility products, were supersaturated with respect to TNP as well, though not so much. Crystallization

of a new phase like TNP, which could explain deviating results for the solubility product, is more easily overlooked in dissolution than in precipitation with the procedures used in the present study.

Both metal ions, Mg²⁺ and Ni²⁺, are likely to be found as hexaquo species in both the solid phase and in solution except, for the latter, at high solution concentration of ammonia. Ni-struvite is isomorphous with struvite with all three axes a, b and c being shorter by 0.5% on the average [22] [23] . The electrostatic (Madelung) energy is thus slightly more negative for Ni-struvite, whence we should expect a lower solubility for this substance in agreement with observations. On the other hand, in view of the similarity of the structures, the possibility of mixed crystals with both Mg and Ni should not be neglected in evaluating the practical use of struvite precipitation in polluted systems [10] [11] .

The previously published value of pK_sp [4] agrees with the present one within experimental uncertainty as demonstrated by the results presented above. The solubility product may thus be useful in estimates of dissolved nickel in soil and other systems containing ammonia and phosphate. Similar studies have been attempted with the analogous cobalt salt, but the strong color of Co(II) has turned out to be a problem in the analyses, so no reliable results have yet been obtained.

The work has been supported by grants from the Danish National Scientific Research Council and the Carlsberg Foundation for purchase of microscopes.

Madsen, H.E.L. (2017) Solubility Product of Ni-Struvite, NH₄NiPO₄∙6H₂O, at 25˚C. Advances in Chemical Engineering and Science, 7, 206- 214. https://doi.org/10.4236/aces.2017.72015