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DOI: 10.1039/C6RA05337H (Paper) RSC Adv., 2016, 6, 45231-45240

A comprehensive study on the dominant formation of the dissolved Ca(OH)2(aq) in strongly alkaline solutions saturated by Ca(II)

B. Kutusad, A. Gácsiad, A. Pallagiad, I. Pálinkóbd, G. Peintlercd and P. Sipos*ad
aDepartment of Inorganic and Analytical Chemistry, University of Szeged, Dóm tér 7, Szeged, H-6720 Hungary. E-mail: sipos@chem.u-szeged.hu; Fax: +36 62 544 340; Tel: +36 62 544 054
bDepartment of Organic Chemistry, University of Szeged, Dóm tér 8, Szeged, H-6720 Hungary
cDepartment of Physical Chemistry and Materials Science, University of Szeged, Aradi vértanúk tere 1, Szeged H-6720, Hungary
dMaterials and Solution Structure Research Group, University of Szeged, Hungary

Received 29th February 2016 , Accepted 29th April 2016

First published on 2nd May 2016

Abstract

The solubility of calcium hydroxide and the aqueous speciation of Ca(II) in alkaline medium at various temperatures and background electrolyte concentrations were characterized by solubility measurements applying ICP-OES and potentiometric detection methods. Contrary to suggestions from previous literature, the (dissolved) Ca(OH)2(aq) was found to be the dominant solution species above pH ∼ 13, although the well-known CaOH+(aq) is also formed to a much smaller extent. The solubility product, as well as the formation constants for the species CaOH+ and Ca(OH)2 were found to be (8.8 ± 0.2) × 10−5 M3, (1.5 ± 0.1) M−1 and (4.7 ± 0.1) M−2, respectively, at 25 °C, at 1 M ionic strength and expressed in terms of concentrations. The most important implication of this model is that the total concentration of the dissolved calcium(II) cannot be decreased below ca. 2 × 10−4 M at any base concentration, even if this is increased to the solubility limit of the caustic. This statement was further validated via precipitation titrations. The standard enthalpies and entropies of the reactions were also calculated from temperature-dependent solubility measurements.

Introduction

The aqueous chemistry of calcium(II) in strongly alkaline solutions is of particular importance in a variety of industrial fields, e.g., hydrometallurgic processes, pulp and concrete research, scale formation, mineral solubility, etc. Among these applications, the hydrolytic processes of CaO are of significance in the field of alumina production (Bayer process), most profoundly in carbonate removal.1,2 Calcium hydroxide is also relevant to radioactive waste disposal, because of the key role of cementitious materials in long term safe storage of fission products.3 The heterogeneous and homogenous equilibrium properties of aqueous solutions saturated with portlandite, Ca(OH)2(s) have been studied by several research groups, using a variety of approaches, both in terms of experimentation and theory. In spite of these efforts, considerable uncertainty still exists about the solution species forming in aqueous medium, in addition to the unquestionable basis species, Ca2+(aq). In his early paper published in 1923, Kolthoff pointed out4 that his potentiometric measurement can only be interpreted quantitatively, if the presence of CaOH+(aq) is assumed, in addition to Ca2+(aq). After this pioneering work, several studies followed, which were aimed at determining the accurate value of the equilibrium constant for the reaction
 
Ca2+(aq) + OH−(aq) = CaOH+(aq) (1)

The corresponding equilibrium constant can be given as

 
image file: c6ra05337h-t1.tif(2)

Kolthoff's first value for the logarithm of this constant was reported to be 0.87. Later, several values for K(CaOH+(aq)) (K in the followings) were estimated for I = 0 M and at 25 °C, and the agreement between them is reasonable: from solubility,5–8 potentiometric9,10 and kinetic11,12 measurements, the value of lg[thin space (1/6-em)]K is expected to be in the range of 1.0–1.6. Stability constants (including conditional ones) were also deduced from a large number of measurements, which were performed at constant (non-zero) ionic strength and/or away from ambient temperatures.13–18 Additionally, the formation of the species CaOH+(aq) was also invoked in a number of related works19–28 (the list is far from being complete), to interpret experimental observations. The common element in the publications so far cited is that they take into consideration only the CaOH+(aq) species.

Some textbooks discuss the presence of the dissolved, neutral Ca(OH)2(aq) species,29,30 the formation of which can be given via the

 
Ca2+(aq) + 2OH−(aq) = Ca(OH)2(aq) (3)
reaction, the corresponding stepwise stability constant and the overall stability product are as follows:
 
image file: c6ra05337h-t2.tif(4)
 
image file: c6ra05337h-t3.tif(5)

Ca(OH)2(aq) was also invoked to interpret the solubility data of CaF2 in alkaline solutions at elevated temperatures.31 Apart from these, there is only one further publication, in which the formation of Ca(OH)2(aq) is supposed. Guiomar et al. developed a computer program for calculating the equilibrium concentrations and dissociation constants in solutions saturated with portlandite at room temperature.21 They concluded, that ca. 30% of the calcium ions are present as Ca(OH)2(aq) in a solution at pH = 12.454.

In one of our previous publications18 an attempt was made to determine the solubility of Ca(OH)2(s) in aqueous NaOH solutions at various base concentrations and at 25 °C. Only the formation of the CaOH+(aq) species was assumed to interpret those data. Although, the use of linearized relations gave acceptable results, the nonlinear parameter estimation revealed some discrepancies which were not interpreted at that time. Our aim was to resolve the anomalies experienced, therefore we carried out additional measurements in a broader temperature and concentration range, and further experimental approaches were used, such as ICP-OES, potentiometry and spectrophotometry. Since this experimental work led to some significantly new consequences, the experimental work itself and the result from its evaluation are detailed in this article.

Experimental

Materials and solution preparation

Calcium oxide was prepared from CaCO3 (≥99% purity, Sigma-Aldrich product) by annealing for 1 day at 900 °C, then it was stored in a desiccator with the exclusion of CO2. The preparation was checked by powder X-ray diffractometry (XRD) measurement to detect the possible presence of carbonate traces. For this purpose, a Philips PW1710 instrument was used (at the Kα radiation of Cu) and the diffractogram attested the phase purity of CaO.

Highly concentrated NaOH stock solution was made from NaOH pellets (a. r. grade, Analar Normapur) and Millipore MilliQ water in a caustic-resistant plastic bottle. The precipitated Na2CO3 was removed by filtration under CO2-free conditions. The density of the filtered solution was measured pycnometrically. About 1 M NaOH solution was made by gravimetric dilution, and then the precise concentration was determined by acid–base titration.

NaCl (a. r. grade, Analar Normapur), Na2C2O4 (≥99.5% grade, Sigma-Aldrich) and CuSO4·5H2O (≥98%, Sigma-Aldrich) were used as received, while the water content in CaCl2·2H2O (≥99% purity, Sigma-Aldrich) was measured with complexometric titration. For NMR experiments, D2O (99.98%, Aldrich product) was used.

Solubility experiments were carried out in a multiposition magnetic stirrer with 15 stirring positions (VELP Multistirrer 15), equipped with a water-jacketed glass pot of in-house construction. The applicability of this instrument was tested by determining the solubility of calcium oxalate monohydrate, the procedure for which is described in ref. 18. The preparation of the samples was the following: alkaline solutions (made by volumetric dilution from the standardized base solution) in the range of 0–4 M NaOH were saturated with CaO and the ionic strength was adjusted with NaCl to either 1 M or 4 M for ICP-OES or potentiometric measurements. Then the samples were stirred at given temperature for one day, under N2 atmosphere. It was pointed out18 that 6 hours are sufficient to reach the solid–liquid equilibrium between CaO and the solution, as well as to complete phase transformation from CaO to Ca(OH)2. The procedure was performed at four temperatures (5, 25, 50 and 75 °C) and the stability of the thermostat was found to be ± 0.2 °C.

ICP measurements

The different samples (I = 1 M ionic strength) were filtered with 0.22 μm PTFE syringe filters. Aliquots of the supernatants were acidified to pH ∼ 1 with HCl solution (a. r. grade, Analar Normapur product) for avoiding further problems caused by the possible absorption of CO2 and concurrent carbonate formation, or the precipitation of Ca(OH)2 due to temperature changes. 0.01 g dm−3 copper(II) sulfate was added to all of the samples as internal standard, then the aliquots were diluted with known, but different ratio (varying in the range of 1–167) in order to reach optimal concentrations of calcium(II) and copper(II), as well as to decrease the ionic strength of the samples to be measured.

The total amount of Ca2+ ([Ca2+]T) was measured with a Thermo Scientific Iris Intrepid II Inductively Coupled Plasma Optical Emission spectrometer (ICP-OES) at the wavelength values of 315.8, 317.9 and 393.3 nm (with two replicate experiments). The signals corresponding to Cu2+ were also collected at two wavelengths (324.7 and 327.3 nm). The reason of applying an internal standard was that the original standard solution containing yttrium flowed in different pathway and the composition of the matrix was very different compared to that of the samples. The total calcium concentrations ([Ca2+]T) calculated by the instrument ([Ca2+]T,ICP) were multiplied with the ratio of precisely added and calculated quantity of Cu2+:

 
image file: c6ra05337h-t4.tif(6)

This correction diminished successfully the average error of Ca-determination below 3%, except the measured ones at 393.3 nm, therefore these data were omitted in further computations. Two samples were repeated in each series for checking the reproducibility of the measurements and the average deviation was within the experimental uncertainties.

Potentiometric determinations

In order to determine the solubility and the speciation scheme at higher ionic strength relevant, e.g., the Bayer process,1,2 further experiments were needed to be performed. The ICP-OES is known to be an inappropriate method in studying solutions with high background electrolyte concentrations. Therefore, potentiometry was applied. The samples were prepared by the same procedure detailed above, the ionic strength was set to 4 M with NaCl. 10 mL of the filtered liquid phase was acidified to pH ∼6 and diluted in 10/25 ratio (resulting in 1.6 M ionic strength).

The potentiometric titrations were carried out with the help of a Metrohm Titrando 888 automatic instrument and a Metrohm-type, combined Ca(II)-ion selective electrode (Ca-ISE). The calibration protocol was the following: the initial solution containing 0.1 mM CaCl2 was titrated with 0.2 M CaCl2 solution; the ionic strength was adjusted to 1.6 M in both. During the titrations (including both of the calibration and the following measurements), the samples were continuously stirred and the temperature was (25.0 ± 0.2) °C.

The calibration curve showed linear relationship between the measured potential and the logarithm of [Ca2+]T (which can be assumed equal to [Ca2+], the equilibrium concentration of calcium ion) above lg[Ca2+] ∼ −3.3 value. However, the [Ca2+]T of numerous samples were estimated to be in the nonlinear range, thus, calibration by means of nonlinear regression has been chosen. For this purpose, the calibration curve was fitted by smoothing via splines with using the Spline Calculus program.32

Precipitation titrations

Five samples with analytical concentrations of NaOH concentrations of 0, 1, 2, 3 and 4 M were prepared with compositions similar to those used in the ICP and in the potentiometric measurements. 5 mL aliquots of each solutions following filtration were titrated with 0.1 M sodium oxalate solution. The precipitation of CaC2O4 was followed by recording the ‘absorbance’ with a Shimadzu 1650-PC UV-Vis spectrophotometer at the 400–700 nm wavelength range. Since high absorbance values were expected for sample with no added NaOH, it was appropriately diluted (i.e., in 0.55/100 ratio).

Although, the ‘absorbance’ was measured, the loss of intensity of the incoming light is closely related to the light scattering caused by the solid particles, thus, the spectrophotometric determination can be regarded similar to turbidimetry. For each measurement, the absorbances were averaged at the visible range by eqn (7).

 
image file: c6ra05337h-t5.tif(7)

For qualitative analysis, these mean values were used.

NMR investigations

Nuclear Magnetic Resonance (NMR) Spectra acquisition was performed using a BRUKER Avance DRX 500 MHz spectrometer equipped with a 5 mm inverse broadband probe head furnished with z oriented magnetic field gradient capability. To stabilize the magnetic field, it was locked to the 2D signal of the solvent containing 20 v/v% D2O.

The reference peak of 43Ca NMR was set to 0.000 ppm and it was obtained by collecting 4096 scans in a sample containing 8 M CaCl2. Under these conditions, the Ca2+ has six H2O molecules in its first coordination sphere at least, resulting relatively large shielding for the Ca nucleus. In the target sample with 0.1 M CaCl2 and 0.025 M NaOH, the spectrum was obtained by accumulating 64k interferograms (this means ca. two days measurement time) because of the low natural abundance of 43Ca (0.001%).

Mathematical relationships

In addition to eqn (1)–(5), which were mentioned in the introduction, the other essential chemical reactions to be considered are the hydrolysis of CaO and the dissolution of the forming Ca(OH)2(s).
 
CaO(s) + H2O(l) = Ca(OH)2(s) (8)
 
Ca(OH)2(s) = Ca2+(aq) + 2OH−(aq) (9)

In equilibrium, the last equation can be quantitatively described with the solubility product of Ca(OH)2(s), which can be expressed as:

 
L(Ca(OH)2(s)) = [Ca2+][OH−]2 (10)

In the followings, Ca(OH)2(s) always stands for the solid, while Ca(OH)2(aq) represents the dissolved (aqueous) species. All of the thermodynamic constants (K, β, L) are expressed in terms of molarities and can be regarded as stability constants.

Beside Ca2+ and OH−, the two OH-containing calcium(II) complexes were assumed to be in heterogeneous equilibrium in the studied system.

The added concentration of NaOH is accurately known, while the data measured via ICP are the total concentrations of calcium(II) for all measurements. Thus, the [Ca2+]T vs. cNaOH function must be deduced and used for the calculations. Beside the law of mass action, the mass balance equations for [OH−]T and [Ca2+]T can be written up.

 
[OH−]T = [OH−] + [CaOH+] + 2[Ca(OH)2] (11)
 
[Ca2+]T = [Ca2+] + [CaOH+] + [Ca(OH)2] (12)

The hydrolysis of CaO and the corresponding dissolution of each Ca(OH)2 result in the appearance of one Ca2+ ion and two OH− ions in the solution; accordingly, the total amount of hydroxide ions will always be higher than the analytical concentration of NaOH (cNaOH).

 
[OH−]T = cNaOH + 2[Ca2+]T (13)

Expressing the equilibrium concentrations of the species with their formation constants, equations between [OH−]T, [Ca2+]T and [OH−] will be obtained. In addition, using the term of the solubility product, gives a relation between homogenous and heterogeneous equilibria.

 
image file: c6ra05337h-t6.tif(14)
 
image file: c6ra05337h-t7.tif(15)

Combining the above equations with eqn (13), the

 
[OH−]3 − cNaOH[OH−]2 − KL[OH−] − 2L = 0 (16)
formula can be deduced. According to the Descartes' rule, there is one and only one positive real root of this equation (i.e., [OH−]), and the Newton–Raphson procedure is applicable to find it, therefore [Ca2+]T can be calculated from eqn (15). The aim was to minimize the differences between the experimental and the calculated [Ca2+]T values by finding the most probable three equilibrium constants.

Results and discussion

Quantitative ICP and potentiometric determinations

Primary measurements. Primary data for [Ca2+]T (collected at the wavelengths of 315.8 and 317.9 nm) were normalized to the intensity of the copper(II) internal standard. These corrections with respect of both wavelengths of Cu2+ resulted in the same total concentrations of calcium(II) (within experimental uncertainties), therefore the calculations with regard to the 324.7 nm of copper(II) were omitted during the further evaluation processes. The [Ca2+]T values were obtained via potentiometry at 4 M ionic strength.

Table 1 contains the measured total concentrations of Ca2+ (or their average in case of ICP measurement) against the initial analytical concentration of NaOH.

Table 1 Observed average total concentrations of Ca2+ (normalized to the Cu2+ internal standard according to eqn (6)) at the 5–75 °C temperature range and at constant ionic strength
T = 5 °C, I = 1 M T = 25 °C, I = 1 M T = 25 °C, I = 4 M T = 50 °C, I = 1 M T = 75 °C, I = 1 M
cNaOH (M) [Ca2+]T (mM) cNaOH (M) [Ca2+]T (mM) cNaOH (M) [Ca2+]T (mM) cNaOH (M) [Ca2+]T (mM) cNaOH (M) [Ca2+]T (mM)
0.0000 33.725 0.0000 30.923 0.0000 21.352 0.0000 24.207 0.0000 19.015
0.0102 30.897 0.0115 25.865 0.0099 17.850 0.0102 20.631 0.0101 16.231
0.0158 26.911 0.0158 24.854 0.0148 16.328 0.0152 19.478 0.0165 14.499
0.0252 24.955 0.0250 22.242 0.0247 13.466 0.0252 16.205 0.0249 12.599
0.0252 25.438 0.0253 21.144 0.0400 10.126 0.0257 16.060 0.0254 12.102
0.0409 21.320 0.0400 17.630 0.0750 5.116 0.0411 12.411 0.0420 8.635
0.0732 14.925 0.0711 12.471 0.0989 3.589 0.0703 7.569 0.0712 4.895
0.1009 10.805 0.0998 8.544 0.1484 2.025 0.1002 4.814 0.1060 2.891
0.1020 10.652 0.1010 8.182 0.2473 1.002 0.1018 4.776 0.1528 1.788
0.1020 10.647 0.1496 4.921 0.3998 0.615 0.1504 2.877 0.2500 0.956
0.1517 6.542 0.2498 2.460 0.7007 0.380 0.2521 1.423 0.3991 0.580
0.2498 3.289 0.4004 1.288 0.9974 0.308 0.4015 0.845 0.4038 0.559
0.3990 1.517 0.4033 1.287 2.0031 0.236 0.4016 0.825 0.7082 0.397
0.4044 1.514 0.6998 0.719 3.0005 0.277 0.7008 0.534 0.9808 0.369
0.6986 0.927 0.9836 0.683 3.9900 0.254 1.0173 0.462 0.9808 0.370
0.9797 0.701                

As it is indicated both in Table 1 and Fig. 1, at a given temperature, [Ca2+]T significantly decreases with the increasing cNaOH, and the same can be observed as the temperature increases. The latter refers to the decrease of the solubility product of Ca(OH)2(s) and the corresponding exothermic electrolytic dissolution. It can also be stated that ∼90% of the change occurs up to 0.25 M NaOH at every temperature. These findings agree well with previously published data.18,28


image file: c6ra05337h-f1.tif
Fig. 1 Measured total concentrations of Ca2+ as a function of the added concentration of NaOH at various temperatures (5–75 °C) and 1 M ionic strength.

Calculation of the solubility product and the formation constants

Data processing was performed by using the ZITA program package.33 Four models applying different aqueous species were used. These models were as follows: (a) only L was fitted (e.g., only the Ca2+ was taken into account); (b) L and K were fitted simultaneously (the additional formation of CaOH+(aq) was also considered); (c) L and β were fitted (formation of the Ca2+ and Ca(OH)2(aq) was assumed and CaOH+(aq) omitted); and (d) L, K and β were fitted together, supposing the co-existence of all possible species. These calculations were carried out independently for the various temperatures, giving the values of L, K and β at 5, 25, 50 and 75 °C.

Finally, all experiments carried out at different temperatures were used together in a single run, supposing that the

 
image file: c6ra05337h-t8.tif(17)
relation is valid, where X can be either L, K or β, as well as, ΔG°, ΔH° and ΔS° mean the standard Gibbs energy, the enthalpy and the entropy of a given reaction, respectively. These thermodynamic data can also be calculated from the previously fitted equilibrium constants. Since there was no noticeable difference between these two approaches of calculation, the latter one will not be detailed further.

During the fitting procedure, the sum of squares of the differences between the measured and computed lg([Ca2+]T/M) values was minimized.

The fitted curves of each model at 25 °C (based on the ICP measurements) can be seen on Fig. 2. Model (a) is not able to describe any range of the experimental changes, so supposing the [Ca2+]T = [Ca2+] relation is insufficient. Model (b) can reproduce the experimental points only in the range of 0–0.15 M cNaOH. This means that considering the sole formation of CaOH+(aq) may be acceptable only below pH = 13. In model (c), the only considered species was the Ca(OH)2(aq) instead of CaOH+(aq) (beside the calcium(II), of course). Interestingly, assuming Ca(OH)2(aq) led to much more reliable result, since the deviation between the model and the measurement is almost negligible. Only small systematic differences can be found above cNaOH = 0.7 M, suggesting the Ca(OH)2(aq) may be more important than Ca(OH)+(aq). Taking both species into account in model (d), even these small deviations disappear, the agreement between the data points and the fitted curves is within the experimental uncertainty.


image file: c6ra05337h-f2.tif
Fig. 2 The results of calculations by applying four different chemical models (detailed description is given in the text) at T = 25 °C and I = 1 M ionic strength. The inset depicts the range where the deviations of the different models are the most obvious.

Our calculations are somewhat in contradiction with previous literature data, as the most accepted monohydroxido complex of calcium(II) seems to have insignificant role in equilibrium stage. This result can be understood from Table 1 since every data series shows a much smaller decrease in [Ca2+]T as the function of the base concentration than it would be expected. (Columns 5–6 and 9–10 even show that [Ca2+]T has reached a constant value.) If only the CaOH+(aq) would form (beside the existing Ca2+(aq)), [Ca2+]T would decrease to practically zero at higher concentrations of NaOH. This follows from eqn (15), because the first two terms of the expression are valid, therefore [Ca2+]T would be proportional to [OH−]−2 and also to [OH−]−1. The second term (which corresponds to the existing CaOH+(aq)) results less steep, but still remarkable decrease of the total dissolved calcium(II) concentration. A constant factor (βL) appears in the expression of [Ca2+]T by assuming the formation of Ca(OH)2(aq). The third term shows that [Ca2+]T reaches a constant value at high concentrations of the added base. Accordingly, models (c, d) give the experimental points back quite well.

Solubility measurements at 4 M ionic strength could also be successfully interpreted by assuming both the CaOH+(aq) and Ca(OH)2(aq). Fig. 3 and Table 2 summarize the results of model (d), and ΔH° and ΔS° values in Table 3 were derived from the finally calculated equilibrium constants.


image file: c6ra05337h-f3.tif
Fig. 3 Experimental (symbols) and calculated (thin solids) lg([Ca2+]T/M) values as a function of cNaOH according to model (d) (detailed description in the text) at 5–75 °C and I = 1 (main figure) or 4 M (inset) ionic strength.
Table 2 Results of calculations with standard deviations at 5–75 °C (I = 1 M) from ICP-OES and 25 °C (I = 4 M) from potentiometric measurements
T (°C)/I (M) L (M3) K (M−1) β (M−2)
5/I = 1 (1.3 ± 0.1) × 10−4 1.2 ± 0.1 3.2 ± 0.1
25/I = 1 (8.8 ± 0.2) × 10−5 1.5 ± 0.1 4.7 ± 0.1
25/I = 4 (3.0 ± 0.2) × 10−5 2.2 ± 0.6 7.5 ± 0.4
50/I = 1 (4.1 ± 0.1) × 10−5 2.7 ± 0.2 7.2 ± 0.1
75/I = 1 (2.4 ± 0.1) × 10−5 3.0 ± 0.1 11.1 ± 0.1

Table 3 Standard enthalpy and entropy changes (left to right) calculated in this work and their comparison with literature data
  Reaction ΔH° (kJ mol−1) ΔS° (J mol−1 K−1) Reference
(a) Ca(OH)2(s) = Ca2+(aq) + 2OH−(aq) −20 ± 2 −146 ± 5 This work
−18 −160 22
−14 −145 36
−13 −142 37
(b) Ca(OH)2(s) = CaOH+(aq) + OH−(aq) −8 ± 3 −103 ± 8 This work
(c) Ca(OH)2(s) = Ca(OH)2(aq) −6 ± 2 −85 ± 5 This work
(d) Ca(OH)2(aq) = CaOH+(aq) + OH−(aq) −2 ± 2 −18 ± 6 This work
(e) Ca(OH)2(aq) = Ca2+(aq) + 2OH−(aq) −14 ± 1 −61 ± 1 This work
(f) CaOH+(aq) = Ca2+(aq) + OH−(aq) −12 ± 2 −43 ± 6 This work
−5 −44 5
−5 −47 10

The most important consequence of the work is not only proving the existence (formation), but also the predominance of the aqueous calcium hydroxide, Ca(OH)2(aq) above ∼0.2 M equilibrium concentration of NaOH (at 25 °C) as indicated in Fig. 4. This species is surprisingly not considered as an influential component in saturated solutions of Ca(OH)2(s) (except for the work of Guiomar et al.21). On the other hand, the formation constants of CaOH+(aq) reported in the previous publications5–18 are generally higher with one order of magnitude than the calculated value that can be found in Table 2. This significant contradiction can be partly resolved with considering that those values are extrapolations for infinite dilution. The experiments were conducted at low ionic strength and hydroxide concentration; in this caustic concentration range assuming the CaOH+(aq) only is sufficient for describing the measured points (Fig. 2). The other main reason of this difference is the omission of the dissolved Ca(OH)2. Without this species the value of K will comprise in itself the effect of the dihydroxido component – i.e., the overall change in [Ca2+]T can be described better only with higher formation constant even at higher ionic strengths.13,18 According to model (b), the constant calculated from it was found to be (9.2 ± 0.6) M−1 at 25 °C which is in excellent agreement with the previously reported (9.3 ± 0.4) M−1 value.18


image file: c6ra05337h-f4.tif
Fig. 4 Fraction of calcium(II) (left axis, thin solid line) and total concentration of calcium(II) in logarithmic units (right axis, thick dashed line) at 25 °C and 4 M ionic strength assuming heterogeneous equilibrium.

For simple evaluation process, linear approximation would be necessary, but it requires the [OH−] ≈ cNaOH simplification, as the majority of the previous literature shows. However, this approach is in contradiction with the experimental observations depicted in Fig. 5. The difference between these two quantities is significant in the range of 0–0.25 M NaOH, where most of the experiments were conducted. The deviation becomes even more pronounced with decreasing temperature. Since 90% of the change in the total concentration of the calcium(II) takes place in this range, this systematic difference between the approximation and complete chemical model may easily introduce false species or “hide” existing ones (i.e., Ca(OH)2(aq)). This means that the linear approximation is an erroneous approach and should be avoided for more accurate evaluations.


image file: c6ra05337h-f5.tif
Fig. 5 Concentration of free hydroxide ion as a function of the analytical concentration of NaOH at different temperatures and I = 1 M ionic strength.

An important consequence of the existence of Ca(OH)2(aq) is the unexpected change of [Ca2+]T (see Fig. 4), which tends to a minimum, not to zero. According to model (b), the following expression would be valid for [Ca2+]T:

 
image file: c6ra05337h-t9.tif(18)

Eqn (18) states that the total quantity of the dissolved Ca2+ decreases with increasing concentration of NaOH. The solubility at higher concentrations can be estimated using calculated constants corresponding to 4 M ionic strength. These obviously false values obtained from model (b) were found to be 4 × 10−6 M3 for L and 99 M−1 for K. Considering the maximum solubility of NaOH at 25 °C (∼20 M), [Ca2+]T would be 2 × 10−5 M. The experimentally found one is 2.5 × 10−4 M, which is higher by more than one order of magnitude. In a saturated NaOH solution, the estimated [Ca2+]T would be 2.3 × 10−4 M according to model (d) and eqn (15). The surprising consequence is that [Ca2+]T cannot decrease below 2.3 × 10−4 M with increasing total base concentration. The limit of this minimum value can be calculated from eqn (19).

 
image file: c6ra05337h-t10.tif(19)

With these equilibrium constants, other reactions can also be characterized thermodynamically, i.e., the formation of Ca(OH)+(aq) from Ca(OH)2(s), the equilibrium between the aqueous and solid Ca(OH)2 and the formation of Ca(OH)2(aq) from Ca(OH)+(aq).

 
Ca(OH)2(s) = CaOH+(aq) + OH−(aq) (20)
 
[CaOH+(aq)][OH−(aq)] = LK (21)
 
Ca(OH)2(s) = Ca(OH)2(aq) (22)
 
[Ca(OH)2(aq)] = Lβ (23)
 
CaOH+(aq) + OH−(aq) = Ca(OH)2(aq) (24)
 
image file: c6ra05337h-t11.tif(25)

According to eqn (21), (23), and (25), the constants of these reactions are calculated to be (1.32 ± 0.09) × 10−4 M2, (4.1 ± 0.1) × 10−4 M and (3.1 ± 0.2) M−1 at 25 °C and 1 M ionic strength, respectively.

It should be emphasized that during the solubility experiments carried out at I = 1 M, the NaCl was systematically replaced with NaOH. The mean activity coefficient (γ±) were reported to be 0.657 in 1 mol kg−1 NaCl and 0.679 in 1 mol kg−1 NaOH solutions,34 resulting in about 3% overall change under strictly constant ionic strength conditions. The molality is nearly equal to the molarity and the ionic strength. For our measurements, the contribution of Ca(II)-containing species to the ionic strength can be omitted, therefore the solubility and stability constants determined here can be regarded as concentration constants.

At 4 M ionic strength (where potentiometry was used), this change of γ± is about 22% in our NaOH/NaCl mixtures.35 Thus the 22% value should be considered as the real uncertainty of the equilibrium constants calculated. Most importantly, these considerations did not alter the chemical model derived from these experiments, i.e., the predominance of Ca(OH)2(aq) under hyperalkaline conditions.

The enthalpy and entropy changes of different reactions

The different standard enthalpy changes reported here (Table 3) for the dissociation of Ca(OH)2(s) (reaction (a)) are in good agreement with that of ref. 22, but differs from those of ref. 36 and 37. Most of the entropy values agree with each other, except for the value presented in ref. 22. The dissociation of the solid calcium hydroxide is exothermic and therefore accompanied with negative change of entropy. Taking only the dissociation into account, a positive entropy change should be expected, however, the hydration of the resulted ions increases the ordering in the system causing large negative entropy change. This observation is similar to the hypothetic formation of CaOH+(aq) from Ca(OH)2(s) (reaction (b)), but the extent of the entropy change is smaller for this reaction, indicating that smaller number of ions are produced with smaller charge number.

The direct dissolution of Ca(OH)2(s) (reaction (c)) is also exothermic, and because of the formation of the primary coordination sphere, it causes a significant decrease in disorder (ΔS° = −85 J mol−1 K−1). The dissociation reactions of the aqueous Ca(OH)2(aq) are also exothermic, while the higher order of the forming hydrated Ca2+ (reaction (e)) compared to the formation of CaOH+(aq) (reaction (d)) results in more negative ΔS° (eqn (26)). For the dissociation reaction of CaOH+(aq) (reaction (f)), the differences between the formation constants are reported here and in the literature are based upon the difference of enthalpy changes, while the entropies are practically the same. The values of ΔH° and TΔS° given in the table suggest that the reaction system examined seems to be entropy-driven process.

 
Ca(H2O)x−i(OH)i2−i(aq) + iH2O(aq) = Ca(H2O)x2+ + iOH−(aq); i = 1, 2 (26)

Precipitation titrations

From the previous measurements it was found, that the aqueous Ca(OH)2 is the main solution species, and that [Ca2+]T becomes constant at higher base concentrations of NaOH. Given, that these phenomena are in contradiction with literature data, an additional, independent method was used to further validate this surprising finding.

The concept of these experiments was the following: if the solutions to be titrated would contain different total concentration of Ca(II), the precipitation would start at different volume of the titrant. The maximum amount of the calcium oxalate precipitation would also appear at different added volume of titrant (Vmax). Since the precipitation was monitored via absorbance measurements, the peak maxima denote the Vmax values in each case.

As Fig. 6 shows, this is not the case for the solutions containing 1–4 M added NaOH, thus, the total Ca(II) concentrations do not differ from each other significantly. Much higher Ca(II) concentration – and therefore lower Vmax – is indicated in only that case when the starting solution was 4 M NaCl which is supported by Fig. 1. One consequence of the ICP measurements is that the total Ca(II) concentration became practically constant above 1 M NaOH concentration because of the significant formation of the Ca(OH)2(aq) species. The results of these spectrophotometric (or turbidimetric) titrations clearly support this statement. In case only CaOH+(aq) existed, the [Ca2+]T should be continuously decreased with increasing hydroxide concentration, and the Vmax values would shift.


image file: c6ra05337h-f6.tif
Fig. 6 Measured mean absorbances (at the visible range) as a function of added volume of sodium oxalate at T = 25 °C and I = 4 M ionic strength.

NMR investigations

Fig. 7 shows the 43Ca NMR spectrum of a solution containing 0.100 M CaCl2 and 0.025 M NaOH. The sample remained clear during the measurement (i.e., there was no precipitation). The observed chemical shift of the calcium nucleus changed from 0.000 ppm (reference peak in 8 M CaCl2 solution) to −1.116 ppm. This significant upfield shift was generally observed38 for the coordination of negatively charged O-donor containing D-gluconate. Therefore this change of the chemical shift is possibly due to the coordination of OH−, which provides higher electron density around the Ca2+ ion. At these initial concentrations of CaCl2 and NaOH, the Ca-containing species other than the aqua-ion is the CaOH+(aq). This implies that the observed change is due to the formation of CaOH+(aq). For detecting the dihydroxido species, the cNaOH should be 0.1 M at least, which would result, however, precipitation and much lower [Ca2+]T value. Under these circumstances, the NMR measurement would become even more time- and cost-consuming.
image file: c6ra05337h-f7.tif
Fig. 7 43Ca NMR spectrum of a solution containing 0.100 M CaCl2 and 0.025 M NaOH at T = 25 °C.

Conclusions

The formation of the aqueous Ca(OH)+(aq) ion-pair is well-known since Kolthoff4 and it was thought to be the only hydroxide-containing species in alkaline medium. In some publications,21,29–31 the possible formation of the chargeless Ca(OH)2(aq) is also mentioned, but no experimental proof was provided.

In the current study, the solubility of portlandite, Ca(OH)2(s) was studied at different temperatures (5, 25, 50 and 75 °C), at 1 M and 4 M ionic strength, and the total concentration of Ca(II) was measured via ICP-OES and potentiometry. It was found that independently from the temperature and the ionic strength, the measured data can be modelled accurately with assuming the existence of Ca2+(aq), CaOH+(aq) and Ca(OH)2(aq) species in equilibrium with Ca(OH)2(s). Our work unambiguously proved that – in contradiction with the previous results – the dominant dissolved species in concentrated alkaline medium (above pH ∼ 13) is the neutral Ca(OH)2(aq), while the contribution of Ca2+(aq) and CaOH+(aq) becomes more and more negligible as the base concentration increases. At 25.0 °C, the solubility product (L) and the formation constants (K and β) were found to be (8.8 ± 0.2) × 10−5 M3, (1.5 ± 0.1) M−1 and (4.7 ± 0.1) M−2, respectively.

The most important practical consequence of the predominance of the Ca(OH)2(aq) species is that the total concentration of calcium(II) approaches a limiting value with increasing concentration of NaOH. Therefore, contrary to the general belief, the total amount of dissolved Ca(II) cannot be removed by the addition of strong base at any concentration. The minimal concentration at 1 M ionic strength was determined to be 4.1 × 10−4 M and 2.7 × 10−4 M at 25 and 75 °C, respectively. This value is essentially equal to Lβ according to eqn (19), which is the equilibrium concentration of the aqueous Ca(OH)2(aq) and is in reasonable agreement with that observed in hyperalkaline solutions under industrial conditions (that is, at 100 °C ca. 2.2 × 10−4 M dissolved Ca2+ is present in a solution containing 4 M NaOH).1

Considering a strongly caustic solution, in which the solid calcium hydroxide is the solubility-controlling solid phase, and it also contains other Ca(II) complexes; the amount of Ca2+(aq) and CaOH+(aq) are negligible, so [Ca2+]T can be estimated applying the following relationship:

 
image file: c6ra05337h-t12.tif(27)
where k represents the kth species in the system with the βk stability product; p, q and r mean the stoichiometric coefficient of Ca2+, Az− complexing ligand and OH−.

This phenomenon was supported qualitatively by precipitation titrations coupled with UV-vis measurements. In solutions containing 1–4 M NaOH, the volume of the sodium oxalate titrant corresponding to the maximum amount of precipitation was found to be practically independent of the concentration of the base, indicating that the [Ca2+]T values were also practically identical in these solutions.

The standard enthalpy and entropy of reaction of the dissolution of Ca(OH)2(s), the dissociation of Ca(OH)+(aq) and Ca(OH)2(aq) were also calculated by the help of temperature-dependent measurements using eqn (17). These quantities were also determined for other reactions which can be derived from these three equilibria. All of these processes were found to be exothermic and mainly entropy-driven.

Finally, we would like to note here, that the second stepwise formation constant (relating to the formation of Ca(OH)2(aq) from CaOH+(aq)) according to eqn (4) is larger, than the first stepwise formation constant (formation of CaOH+(aq) from Ca2+(aq)) according to eqn (2) over the entire temperature range covered (Table 2). On the basis of statistical considerations, the opposite trend would be expected. This phenomenon is, however, not at all uncommon for the formation of chargeless solution complexes with composition identical to Ca(OH)2(aq). The most profound examples include ZnBr2(aq),39–41 PbBr2(aq),42 MnBr2(aq),43 Zn(CN)2(aq),44–46 NiCl2(aq),47 ZnCl2(aq),48–50 CdCl2(aq),51 ZnI2(aq) (ref. 52) and Zn(OH)2(aq) (ref. 53) and the list is most probably far from being complete. Several of this neutral solution complexes39–43,47–52 are weak and formed in presence of high concentration of the ligand and/or supporting electrolyte, just like Ca(OH)2(aq). Our own experience also shows, that neutral solution species have extra stability in highly concentrated, hyperalkaline solutions.26,27 When we add to this the uncertainties associated with the stepwise formation constant of Ca(OH)+(aq) due to its small degree of formation, the unusual order between the formation constants found for Ca(OH)2(aq) and CaOH+(aq) is not at all surprising.

Acknowledgements

Research leading to this contribution was supported by the National Research Fund of Hungary through OTKA K83889 and NK106234.

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