J. Chil. Chem. Soc., 48, N 3 (2003) ISSN 0717-9324

COCRYSTALLIZATION OF LOW AMMOUNTS OF M²⁺ IONS DURING
CoSO₄7H₂O CRYSTALLIZATION

Marek Smolik

Institute of Chemistry, Inorganic Technology and Electrochemistry
Silesian University of Technology
Gliwice, Poland
(Received: October 24, 2002 ­ Accepted: March 29, 2003)

ABSTRACT

The equilibrium cocrystallization coefficients D_M/CoSO4.7H2O of low amounts (10^-3- 10^-1%w/w) of M²⁺ ions (M²⁺ = {Ni²⁺, Mg²⁺, Cu²⁺, Zn²⁺, Fe²⁺, Mn²⁺, Cd²⁺, Ca²⁺}) with CoSO₄7H₂O have been determined with the method of long-time stirring of crushed CoSO₄7H₂O crystals in their saturated solution at 20^oC and compared with coefficients determined by means of the method of isothermal decreasing of supersaturation during 3 ­ 360 hours of stirring. This enabled the time needed to reach equilibrium to be found. It is different for different microcomponents. The determined cocrystallization coefficients are diverse: from <0.008 for Ca²⁺ to 1.20 for Fe²⁺. Their dependence on some physicochemical and crystal-chemical properties of both sulfate hydrates (CoSO₄7H₂O and MSO₄nH₂O) and metal M²⁺ ions has been discussed. They depend mainly on solubility in water and structure of corresponding sulfate hydrates as well as on radii of M²⁺ ions. It is possible to calculate cocrystallization coefficients with empirical formula based on determined relationships between some of the considered properties of macrocomponent and microcomponents and D_M/CoSO4.7H2O coefficients at the average relative error not exceeding 10%.

INTRODUCTION

Cocrystallization is one of the major factors which influence the effectiveness of crystallization as a purification process. One of the indicators of this effectiveness is the cocrystallization coefficient of the microcomponent, D_2/1 (Henderson ­ Kra_ek [1], Khlopin [2]). Knowledge of such coefficients allows to predict the applicability of crystallization for the removal of definite microcomponents from a given substance. However the literature data concerning cocrystallization of microamounts (less than 0.1%w/w) of salts M⁽²⁾_bX_a with macroamounts of salt M⁽¹⁾_bX_a are not so ample and their cocrystallization coefficients D_2/1 hardly can be calculated (particularly if these salts are not isomorphous) by means of general thermodynamic formula:

where: C₀₁(C₀₂) ­ molar concentration of the saturated binary solution of the salt M⁽¹⁾_bX_a (M⁽²⁾_bX_a) , n = b + a; (g_c01) = [(g_c0M(1))^b(g_c0X) ^a]^1/n ­mean molar activity coefficient of the salt M⁽¹⁾_bX_a in its saturated solution; (g_c02)=[(g_c0M(2))^b (g_c0X)^a]^1/n - mean molar activity coefficient of the salt M⁽²⁾_bX_a in its saturated solution; C₁ (C₂) ­ molar concentrations of the salt M⁽¹⁾_bX_a (M⁽²⁾_bX_a) in the ternary solution being in equilibrium with solid solution (M⁽¹⁾,M⁽²⁾)_bX _a ; (g_c1) = [(g_cM(1))^b(g_cX) ^a]^1/n- mean molar activity coefficient of the salt M⁽¹⁾_bX_a in this solution; (g_c2)=[(g_cM(2))^b(g _cX)^a]^1/n - mean molar activity coefficient of the salt M⁽²⁾_bX_a in this solution; x₁(x₂) ­ mole fraction of M⁽¹⁾(M⁽²⁾) ion in the solid solution (M⁽¹⁾,M⁽²⁾)_bX _a ; f₁(f₂) ­ activity coefficient of ion M⁽¹⁾(M⁽²⁾) in the solid solution (M⁽¹⁾,M⁽²⁾)_bX _a;

the Gibbs free energy of the phase transition DG_II-I of the salt M⁽²⁾_bX_a from its structure (II) into the structure (I) of the salt M⁽¹⁾_bX_a

This is because of lack of the appropriate data (g_c01, g_c02, g_c1, g_c2and particularly f₁, f₂ ). Therefore general dependence of coefficients D_2/1 on numerous physicochemical and crystal-chemical factors (such as: ionic radii, similarity of crystal structures, ability to form solid solutions as well as solubilities of corresponding salts) is searched for, which would allow to evaluate the values of coefficients D_2/1 for various crystallization systems which have not been investigated so far.

Investigations on cocrystallization of microcomponents in several sulfate systems (triclinic: CuSO₄5H₂O [3] and MnSO₄5H₂O at 20^oC [4], monoclinic: FeSO₄7H₂O at 20^oC [5], MnSO₄7H₂O at 2^oC [4] MnSO₄H₂O at 50^oC [6], orthorhombic: ZnSO₄7H₂O [7], NiSO₄7H₂O [8] and MgSO₄7H₂O [9]) have shown that in different crystallization systems, different factors mentioned above have predominant influence on the coefficients D_2/1 and very often these influences overlap. It was interesting how these factors influence the coefficients D_2/1 in the case of crystallization of monoclinic CoSO₄7H₂O.

Cocrystallization of hydrates of M(II) sulfates with cobalt(II) sulfate heptahydrate has been recognized to some extent [10-24]. However, those investigations concerned mainly macroamounts (more than 1% w/w) of the mentioned sulfates. Cocrystallization of microamounts (10^-3-10^-1% w/w) of M²⁺ ions was investigated only in few cases: Ni²⁺ (92-4600 ppm - D_Ni = 0,53) [15], (510 ppm - D_Ni = 0,9®1,3) [16], and Cu²⁺ (traces) , D_Cu = 0,91 at 20^oC[18], D_Cu = 0,87 at 25^oC[19], D_Cu = 1,33 at 5^oC[20].

The purpose of the present investigations was to determine cocrystallization coefficients D_M/CoSO4.7H2O of low amounts (10^-3- 10^-1%) of M²⁺ ions (M²⁺ = {Ni²⁺, Mg²⁺, Cu²⁺, Zn²⁺, Fe²⁺, Mn²⁺, Cd²⁺, Ca²⁺}) with CoSO₄7H₂O as well as to find out the influence of physicochemical and crystal-chemical properties of both sulfate hydrates (CoSO₄7H₂O and MSO₄7H₂O) as well as M²⁺ ions on D_M/CoSO4.7H2O coefficients.

EXPERIMENTAL

Reagents and solutions: Cobalt(II) sulfate heptahydrate, p.a. (POCh ­ Gliwice) was additionally purified by crystallization. Standard solutions of Fe(II), Zn(II), Cu(II), Cd(II), Mg(II), Ni(II), Mn(II) sulfates and Ca(II) nitrate were used. Ammonia solution (14 M) was obtained by saturating distilled water with ammonia gas. Sodium versenate p.a. (POCh ­ Gliwice) ­ 0.1 M water solution, hydrazinum sulfate p.a. (POCh ­ Gliwice) ­ saturated water solution and murexide ind. (POCh ­ Gliwice) were used

Apparatus: Atomic absorption spectrometer model 3300 manufactured by Perkin Elmer was applied.

Analytical methods: The macrocomponent: cobalt(II) was determined by complexometric titration with sodium versenate in ammonia acetate buffer solution in the presence of murexide[25]. The microcomponents (Fe, Ni, Cu, Zn, Cd, Mn, Mg and Ca) were determined by means of direct atomic absorption spectrometry (Perkin Elmer 3300 Atomic Absorption Spectrometer) from 0.1423 mol/L (or less) solutions of CoSO₄ in 0.02 mol/L sulfuric acid. Absorbances of the samples and of the sets of standards having the same concentrations of the matrix [cobalt(II) sulfate], were measured under the same conditions.

The method of determination of distribution coefficients D_M/CoSO4.7H20

After crystallization the crystals were separated from mother solutions by means of filtration through a Büchner funnel with a sintered glass disk, weighed, washed with saturated purified CoSO₄ solution and dissolved in water. Mother solutions were diluted with water in volumetric flask. From the cobalt(II) contents in both solutions (mother solution and solution containing dissolved crystal) the degree of CoSO₄·7H₂O crystallization b was found, as well as the volumes of these solutions were calculated, necessary to determine the microcomponents.

The relative concentrations of microcomponents ([ppm] in relation to CoSO₄7H₂O) in the mother solution - a'_r and in the washed crystal - a'_k determined by direct atomic absorption made it possible to calculate the homogeneous distribution coefficient ­ D_M/CoSO4.7H2O (Henderson-Kraek, Khlopin):

Conditions of determining cocrystallization coefficients

The determination of cocrystallization coefficients, D_M/CoSO4.7H2O was carried out by means of the following two methods, which enable homogeneous distribution of microcomponents during the crystallization to be achieved [26]:

a) Establishing the dependence of coefficients D_M/CoSO4.7H2O
on time of crystallization of CoSO₄7H₂O at 20^oC

The supersaturated cobalt(II) sulfate solutions containing different initial amounts of Fe²⁺, Co²⁺, Mn²⁺, Cu²⁺, Cd²⁺, Mg²⁺, Zn²⁺ and Ca²⁺ were poured into beakers with water jacket. After having the beakers covered with watch glass and their contents cooled to 20^oC, the solutions were stirred with magnetic stirrer (~300 rpm) at mean temperature 20±1^oC over 3 -360 h. The results are presented in Fig. 1 and Table 2.

Fig.1: The dependence of coefficients DM/CoSO4.7H2O on time of crystallization of CoSO47H2O at 20oC (a'o)M - initial concentration of microcomponent (M2+) ([ppm] in relation to CoSO47H2O)

Crystallization of CoSO₄7H₂O at 20^oC

*- Average DM/CoSO4.7H2O for given range of time of crystallization; D - mean value of DM/CoSO4.7H20; ta - value of Student t-test for (n-1) degrees of freedom and for the confidence level of (1-a) = 0.95; n ­ number of determinations; s ­ standard deviation; Domin, DoMAX ­ initial minimum and maximum values of DM/CoSO4.7H2O respectively.

b) Determination of the equilibrium distribution
coefficients D_M/CoSO4.7H2O at 20^oC.

The equilibrium was reached starting either from initial concentration ratio of a microcomponent in crystal and in solution exceeding the

expected value of its equilibrium coefficient D^o_max

D^o_max

When selecting values D^o_max and D^o_min the highest and the lowest values of D obtained during crystallization of CoSO₄·7H₂O by the first method were taken into consideration. The experiments were carried out in the following way:

Crushed contaminated" CoSO₄·7H₂O crystals (f<0.1mm) were introduced into several beakers together with saturated purified" cobalt(II) sulfate solution. Crushed crystals of purified" CoSO₄·7H₂O (f<0.1mm) and contaminated" saturated solution of cobalt(II) sulfate were introduced to some other beakers. Contents of the beakers were stirred for ~360 h with a magnetic stirrer in a closed room. Fluctuations of temperature facilitated recrystallization of CoSO₄·7H₂O and helped attain equilibrium and homogeneous partition of microcomponents in crystal [27]. Its mean value was equal to 20±1^oC.

While stirring was continued N₂H₄.H₂SO₄ was added in small portions (100 ml of saturated water solution) in order to avoid oxidation of iron(II). The results are given in Table 2.

* The upper limit of Dca/CoS04.7H2O. has been taken into consideration.

RESULTS AND DISCUSSION

The cocrystallization coefficients D_M/CoSO4.7H2O determined with the first method of isothermal decreasing of supersaturation during 3­360 hours of stirring (Fig. 1) vary distinctly in the initial period of crystallization (they increase for Fe²⁺ and Cu²⁺ and decrease slightly for the other microcomponents) to achieve for each microcomponent, after different period of time of crystallization, constant values (plateaus) close to equilibrium ones, determined by means of the second method of long-time stirring of crushed CoSO₄7H₂O crystals in their saturated solution. (Table 2).

The distribution coefficients of ions M²⁺{Ni²⁺, Fe²⁺, Zn²⁺, Cu²⁺, Mg²⁺ , Mn²⁺ , Cd²⁺} for two series D^o_max and D^o_min do not differ from each other essentially, which means that the equilibrium condition was reached for them, and average values for both series are equilibrium values (Table 2).

The run of the curves D_M/CoSO4.7H2O = f (time) in Fig. 1 and comparison of plateaus of these curves with corresponding values of the equilibrium distribution coefficients enable the time needed for each microcomponent to reach equilibrium to be found (Table 2).

The determined cocrystallization coefficients are diverse: from <0.008 for Ca²⁺ to 1.20 for Fe²⁺and depend on the properties of both sulfate hydrates (CoSO₄7H₂O and MSO₄nH₂O) and metal M²⁺ ions, which is discussed below.

The average value of D_M/CoSO4.7H2O for microcomponents that form sulfate heptahydrates is 1.8 times greater than that for other microcomponents. The average values of cocrystallization coefficients for microcompoents having the same number of molecules of water of crystallization (D_av) decrease with the increase of the difference of number of molecules of water of crystallization of macrocomponent and microcomponent (Dn). The correlation - r_xy of log D_av and Dn is significant at level a = 0.1 (Fig. 2).

Fig. 2. The dependence of log Dav on Dn. Dav ­ average DM/CoSO4.7H2O for microcomponents having the same nm Dn = ½nM - nm½, where nM and nm ­ number of molecules of water of crystallization of macrocomponent and microcomponents, respectively. rxy ­ correlation of log Dav and Dn

The average value of D_M/CoSO4.7H2O for microcomponents forming, as CoSO₄7H₂O, monoclinic sulfate hydrates (D_av^mon = 0.42) is very close to that of the other microcomponents (D_av^orth = 0.45), that is to say the similarity of crystal systems of macrocomponent and microcomponents does not affect directly average D_M/CoSO4.7H2O.

The coefficients D_M/CoSO4.7H2O generally increase as the solubility of MSO₄nH₂O in water decreases. Significant (at level a = 0.02), but relatively low correlation r_xy = 0.8338 goes to show that this relationship is influenced by other factors. Simple linear regression coefficient (z_xy=2.22±0,66) is close to the theoretical value for salts of AB type (z_xy=2) (Fig 3). In the case of each microcomponent the Ruff's rule is fullfiled (D_M/CoSO4.7H2O > 1, if C_CoSO47H2O/C_{MSO4 nH2O} >1 and vice versa).

Fig. 3. The relationship of log DM/CoSO4.7H2O and log (C01/C02) (C01 and C02 ­ solubilities/ mol.dm-3 in water (at 20oC) of CoSO47H2O and MSO4nH2O respectively. [28,29] rxy ­ correlation of log DM/CoSO4.7H2O and log (C01/C02)

The cocrystallization coefficients D_M/CoSO4.7H2O rises generally as the solubility of MSO₄nH₂O in the solid CoSO₄7H₂O increases. Correlation r_xy = 0.7570 is significant at level a = 0.05, but the values of (r_xy)² indicate that relatively small part of variability of D_M/CoSO4.7H2O may be explained by variability of C [mol %]. (Fig. 4.).

Fig. 4. The dependence of cocrystallization coefficients DM/CoS4.7H2O on the solubility of MSO4nH2O in the solid CoSO47H2O - CsMAX [10-12,21,24]

The cocrystallization coefficients D_M/CoSO4.7H2O of microcomponents M²⁺ depend on their ionic radii (r_M2+) (Fig. 5) The highest D_M/CoSO4.7H2O occur for these microcomponents, whose ionic radii are most close to the radius of macrocomponent (Co²⁺) (except for Zn²⁺) and they generally decrease with the increase of the difference between r_M2+ and r_co2+ For the most distant ion Ca²⁺, its value is close to zero (D<0.008).

Fig. 5. The relationship between coefficients DM/CoSO4.7H2O of microcomponents M2+ and their ionic radii

On the basis of the presented character of the run of the curve D_M/CoSO4.7H2O= f(r_M2+) linear relationships have been searched between log D_M/CoSO4.7H2O and ionic radii. It was assumed that log D_2/1 may be dependent on ionic radius (r_M2+) (absolute dimension of ion), on the converse of ionic radius (1/r_M2+) (the value proportional to Cartledge ionic potential) and on the relative difference of the radii of the mutually substituting ions ½Dr/r_Co½or (Dr/r_Co)². For these and some other dependences, for which the run was expected to be linear correlations have been calculated and compared with correlation of D_2/1 and r_M2+. The results are given in the Table 2.

For all dependences log D_M/CoSO4.7H2O = f(r_M2+) taken into consideration correlation (r_xy) is significant at level a = 0.01 and is printed in bold. The correlation of log D_2/1 and (Dr/r)² is most significant.

The coefficients D_M/CoSO4.7H2O are less closely (than in the case of ionic radii) linearly related to the difference of electronegativity of Co and other elements (De) as well as to the difference of crystal field stabilization energy of Co²⁺ and M²⁺ ions in their high spin octahedral complexes Ds = (CFSE)_MACR ­ (CFSE)_micr and are not linearly related to the difference of hardness of the ions Co²⁺ and M²⁺ (Dh).

The cocrystallization coefficients depend generally on electronic configuration of M²⁺ ions. The average values of D_M/CoSO4.7H2O for open shell M²⁺ ions (similar in this respect to the ion of macrocomponent Co²⁺) are nearly four times greater than those for closed shell M²⁺ ions

The analysis of the influence of different chemical, physicochemical and crystal-chemical factors on D_M/CoSO4.7H2O coefficients shows, that solubility in water of sulfates hydrates as well as radii of M²⁺ ions most influence their values. Calculation of these coefficients by means of the simplest formula D_M/CoSO4.7H2O (C₀₁/C₀₂)² [, (which was used in calculating D_2/1 during cocrystallization of two salts forming ideal aqueous and solid solutions) leads in the case of cocrystallization of M²⁺ ions with CoSO₄7H₂O to considerable deviations from experimental values and the average relative error amounts to 172%. After taking into consideration the Gibbs free energy of phase transition DG_II®_I of the trace component from its structure II into the monoclinic structure I of CoSO₄7H₂O, as: 837 J/mol (for orthorhombic ZnSO₄7H₂O, NiSO₄7H₂O and MgSO₄7H₂O) and 2510 J/mol (triclinic CuSO₄5H₂O) [31], it is possible to decrease the deviations and the average relative error is lowered to 124%. However the correlation of the differences between experimental and estimated in such a way cocrystallization coefficients and relative difference of ionic radii of macrocomponent (r_Co2+) and microcomponents (r_M2+): [(r_Co2+ - r_M2+)/r_Co2+]² is rather high (r_xy =- 0,9856). This enables calculating D_M/CoSO4.7H2O coefficients with the equation given in the table 3. Comparison of calculated and experimental values of cocrystallization coefficients for each considered microcomponent (except Ca²⁺) during the crystallization of CoSO₄7H₂O at 20^oC is shown in the same table.

Comparison of calculated (D_cal.) and experimental (D_exp.) values of cocrystallization coefficients of microcomponents M²⁺ during the crystallization of CoSO₄7H₂O at 20^oC

CONCLUSIONS

The equilibrium distribution coefficients D_M/CoSO4.7H2O of low amounts (10^-3- 10^-1%) of M²⁺ ions (M²⁺ = {Ni²⁺, Mg²⁺, Cu²⁺, Zn²⁺, Fe²⁺, Mn²⁺, Cd²⁺}) with CoSO₄7H₂O have been determined by means of the method of long-time stirring of crushed CoSO₄7H₂O crystals in their saturated solution at 20^oC. Comparison of these coefficients with those, determined with the method of isothermal decreasing of supersaturation during 3 ­ 360 hours of stirring enabled the time needed to reach equilibrium to be found. It was different for different microcomponents.

The determined cocrystallization coefficients are diverse: from <0,008 for Ca²⁺ to 1,20 for Fe²⁺ and depend on some of the physicochemical and crystal-chemical properties of both sulfate hydrates (CoSO₄7H₂O and MSO₄nH₂O) and metal M²⁺ ions.

D_M/CSO4.7H2O values generally get greater as the difference of number of molecules of water of crystallization of CoSO₄7H₂O and MSO₄nH₂O decrease and the similarity of electronic configuration of Co²⁺ and M²⁺ increases.

Cocrystallization coefficients decrease in general as the solubilities of corresponding sulfate hydrates in water increase and as their solubilities in solid CoSO₄7H₂O decrease. They depend as well on radii (r) of M²⁺ ions (the dependence of log D on [(r_Co2+ - r_M2+)/r_Co2+]² is linear with the correlation coefficient r_xy = -0,9350). These dependences are disturbed by the structure of sulfate hydrates.

The effect of electronegativity of M elements as well as crystal field stabilization energy and hardness of M²⁺ ions on D_M/CoSO4.7H2O coefficients is rather small. They depend mainly on solubility and structure of corresponding sulfate hydrates as well as radii of M²⁺ ions.

Knowing solubilities (mol/L) in water of CoSO₄7H₂O and MSO₄nH₂O as well radii of Co²⁺ and M²⁺ ions and taking the Gibbs free energy of the phase transition DG_II-I of the trace component from its structure II into the monoclinic structure I of CoSO₄7H₂O, as: 836,8 J/mol (for orthorhombic to monoclinic) and 2510 J/mol (for triclinic to monoclinic) it is possible to estimate D coefficients at the average relative error not exceeding 10%.

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