Evaluation of Transition Points between Different Solid Phases in Aqueous Media

A uniform procedure is suggested for calculation of the pHt value(s) separating equilibrium solid phases in pH scale, at an excess of the precipitating agent. The pHt value, related to pairs of precipitates formed from the species ( ) Me OH u i i + − ( ) 1, , i p  = and H L j n j + − ( ) 1, , j q =  , fulfils the relation pH L n p F ⋅ + = , where F is a constant value involving pKso’s for solubility products ( so K ’s) of these precipitates, and the equilibrium data, related to the species composing these precipitates.


Introduction
Some species are able to form different solid phases in aqueous media whose composition depends on pH-value of these media.In particular, this was indicated for the systems obtained after introducing the ternary salts such as struvite [1] or dolomite [2] into pure water or aqueous solution of a strong base in presence/absence of CO 2 , originating e.g. from air.Full physicochemical knowledge was involved in the algorithms used for calculations made according to iterative computer programs related to redox or non-redox, mono-or two-phase systems [3]- [8].This paper concerns calculations related to two-phase systems, and made with use of Excel spreadsheets.It refers to location of different equilibrium solid phases within defined pH-intervals [9]- [11].The search of these pH-intervals is based on the simplified calculation procedure.The pH-values separating these intervals are

Formulation of the Transition Points
Let the precipitates ( ) , Me H L be two equilibrium solid phases formed in an aqueous system involving Me u + and L n − ions, together with the ( ) species resulting from hydrolytic phenomena; other (possible) soluble complexes formed between the related species are omitted (not involved) in the related balances.The numbers: a, b, c, d, u, n, k and m in (1) and ( 2) satisfy the conditions of electro neutrality of the corresponding precipitates: ( ) We assume that the Me-species are precipitated with an excess of the L-species; this excess is expressed by the molar concentration: If the protonated species do not exist, then L where and , and the equilibrium solid phases: ( ) Applying in (8) the relations (3) and (4), we have ( ) and then, by turns, where Similarly, when the relations: (2) and (10): and then In each case, pH L y n p =⋅ + is an increasing function of pH .This means, in particular, that larger y values correspond to larger pH t values.This circumstance is particularly important when arranging the equilibrium solid phases along the pH axis, when the number of possible solid phases is 3 ≥ .

Transition Point for Carbonates
Many divalent cations form sparingly soluble carbonates MeCO 3 ( ) ,11 so pK and hydroxides Me(OH) 2 ( ) ,2 so pK .In this case, we have: The curve of (see Figure 1).The pH t values found this way for different Me +2 ions are collected in Table 1.
Figure 1.Location of pH 10.85 t = value separating the pH-intervals for (ZnCO 3 , Zn(OH) 2 ) pair (see Table 1). 2 In this system, the physicochemical data related to another solid phases: Pb 5 (PO 4 ) 3 OH and Pb 4 O(PO 4 ) 2 as precipitates are also cited in literature [12] [13]; however, the solubility products for these species are formulated there in an unconventional manner.The unification of the solubility products to conventional notation will be the first, preparatory step for further considerations.The expressions for solubility products, formulated unconventionally, will be denoted as so K * (asterisked, with the corresponding subscripts, specifying their stoichiometric composition).We have: ( ) refer to the reactions: ( ) Pb PO OH , ( ) Pb O PO (see Appendix).At pH t , we assume (this assumption will be verified later) that the solubility products for PbHPO 4 . Similarly, when assuming that the solubility products for Pb 3 (PO 4 ) 2  ; the pH ti values separating pH intervals of the equilibrium solid phases are specified in the lower part of the Table 2.

Crossing the pH Scale
In some cases, the precipitate of sparingly soluble salt is characterized by a relatively small solubility product value.Consequently, the pH t value, separating the pH range of the salt and the corresponding hydroxide

Me OH OH
, where Me C is the total concentration of Me in the system, , so u K is defined by Equation (10).= as abscissa related to this y -value is much higher than 14 (see Figure 3); what is more, it is much higher than pH values of a saturated strong base.Moreover, at high pH values, Zn(OH) 2 is transformed into soluble complexes, mainly ( ) Zn OH − ( ) Another example is the system with precipitates: CaC 2 O 4 ( )

Final Comments
A simple, uniform method for determining the pH ranges of different precipitates as the equilibrium solid phases in aqueous systems with Me-and L-species is presented.The systems with two or more precipitates thus formed are discussed, together with the problem of ordering of appropriate precipitates along the pH scale.The above issues are applicable to the systems where soluble complexes of the value of expression on the right side of Equation (18), related to defined Me +2 ion, forms a straight line parallel to pH-axis (see Figure1).The abscissa of the point of intersection of this line with the curve relationship indicates the pH t value, separating the pH -intervals for MeCO 3 and Me(OH) 2 , as the equilibrium solid phases.For example, 23.78 y = calculated for the pair (ZnCO 3 , Zn(OH) 2 ) corresponds to pH 10.85 t = u as the equilibrium solid phases, is significantly higher than the pH value, practically obtainable by addition of a strong base.In other instances, Me u + ions form soluble hydroxo-complexes up to pH value of the solution is high-the hydroxide is not an equilibrium solid phase when

Figure 4 )
; this value corresponds to pH 14.69 t =, related to calculated pH value of 4.9 mol/L NaOH.The Ca(OH) 2 does not dissolve in an excess of strong base; Ca +2 forms only one hydroxo-complex, CaOH +1 ( )1 2 p = < , and then Ca(OH) 2 is not dissolved in an excess of OH −1 ions.

Figure 2
Figure 2. The curve

Figure 3 .
Figure 3.The curve 3pH S y p = + vs. pH plotted at

Figure 4
Figure 4.The curve type are not formed or are relatively weak ones.Solubility products can be defined in different ways.The lack of awareness of this fact can be a source of confusion, as results from examples taken from the literature.In particular, for the solubility product 11 soKof PbHPO 4 we find the following 11 so pK values: 11.36[14], and •••23.80[15]-bothare referred allegedly to the dissociation value, which we denote as so pK * , is significantly different from the previous ones; we can therefore assume that, in fact, it relates to dissociation reaction e., the value close to 11.36.The solubility product for Pb 5 (PO 4 ) 3 OH is also formulated improperly in[15].

Table 1 .
The pH pH t = values for the systems with MeCO 3 so pK

Table 2 .
Comparing the y-values in the first line of Table 2, we state that the PbHPO 4 on the pH -scale.Next, considering the y -values in the second line of Table 2, we state that the lowest y -value ( )

5 (PO 4 ) 3 OH is
the next precipitate on the pH-scale.Referring to the third line of Table2, we state that the lower y -value

Table 2 .
Expressions for