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Journal of the Chilean Chemical Society
versión impresa ISSN 0717-9324versión On-line ISSN 0717-9707
J. Chil. Chem. Soc. v.48 n.3 Concepción sep. 2003
http://dx.doi.org/10.4067/S0717-97072003000300002
J. Chil. Chem. Soc., 48, N 3 (2003) ISSN 0717-9324
COCRYSTALLIZATION OF LOW AMMOUNTS OF M^{2+} IONS DURING
CoSO_{4}7H_{2}O 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 M^{2+} ions (M^{2+} = {Ni^{2+}, Mg^{2+}, Cu^{2+}, Zn^{2+}, Fe^{2+}, Mn^{2+}, Cd^{2+}, Ca^{2+}}) with CoSO_{4}7H_{2}O have been determined with the method of long-time stirring of crushed CoSO_{4}7H_{2}O crystals in their saturated solution at 20^{o}C 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 Ca^{2+} to 1.20 for Fe^{2+}. Their dependence on some physicochemical and crystal-chemical properties of both sulfate hydrates (CoSO_{4}7H_{2}O and MSO_{4}nH_{2}O) and metal M^{2+} ions has been discussed. They depend mainly on solubility in water and structure of corresponding sulfate hydrates as well as on radii of M^{2+} 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)}_{b}X_{a} with macroamounts of salt M^{(1)}_{b}X_{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: C_{01}(C_{02}) molar concentration of the saturated binary solution of the salt M^{(1)}_{b}X_{a} (M^{(2)}_{b}X_{a})^{ }, n = b + a; (g_{c01}) = [(g_{c0M(1)})^{b}(g_{c0X})^{ a}]^{1/}n mean molar activity coefficient of the salt M^{(1)}_{b}X_{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)}_{b}X_{a} in its saturated solution; C_{1} (C_{2}) molar concentrations of the salt M^{(1)}_{b}X_{a} (M^{(2)}_{b}X_{a})^{ }in the ternary solution being in equilibrium with solid solution (M^{(1)},M^{(2)})_{b}X_{ a} ; (g_{c1}) = [(g_{cM(1)})^{b}(g_{cX})^{ a}]^{1/}n- mean molar activity coefficient of the salt M^{(1)}_{b}X_{a} in this solution; (g_{c2})=[(g_{cM(2)})^{b}(g_{ cX})^{a}]^{1/}n - mean molar activity coefficient of the salt M^{(2)}_{b}X_{a} in this solution; x_{1}(x_{2}) mole fraction of M^{(1)}(M^{(2)}) ion in the solid solution (M^{(1)},M^{(2)})_{b}X_{ a} ; f_{1}(f_{2}) activity coefficient of ion M^{(1)}(M^{(2)}) in the solid solution (M^{(1)},M^{(2)})_{b}X_{ a};
the Gibbs free energy of the phase transition DG_{II-I} of the salt M^{(2)}_{b}X_{a}^{ } from its structure (II) into the structure (I) of the salt M^{(1)}_{b}X_{a}
This is because of lack of the appropriate data (g_{c01}, g_{c02}, g_{c1}, g_{c2}and particularly f_{1},_{ }f_{2} ). 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: CuSO_{4}5H_{2}O [3] and MnSO_{4}5H_{2}O at 20^{o}C [4], monoclinic: FeSO_{4}7H_{2}O at 20^{o}C [5], MnSO_{4}7H_{2}O at 2^{o}C [4] MnSO_{4}H_{2}O at 50^{o}C [6], orthorhombic: ZnSO_{4}7H_{2}O [7], NiSO_{4}7H_{2}O [8] and MgSO_{4}7H_{2}O [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 CoSO_{4}7H_{2}O.
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 M^{2+} ions was investigated only in few cases: Ni^{2+} (92-4600 ppm - D_{Ni} = 0,53) [15], (510 ppm - D_{Ni} = 0,9®1,3) [16], and Cu^{2+} (traces) , D_{Cu} = 0,91 at 20^{o}C[18], D_{Cu} = 0,87 at 25^{o}C[19], D_{Cu} = 1,33 at 5^{o}C[20].
The purpose of the present investigations was to determine cocrystallization coefficients D_{M/CoSO4.7H2O} of low amounts (10^{-3}- 10^{-1}%) of M^{2+} ions (M^{2+} = {Ni^{2+}, Mg^{2+}, Cu^{2+}, Zn^{2+}, Fe^{2+}, Mn^{2+}, Cd^{2+}, Ca^{2+}}) with CoSO_{4}7H_{2}O as well as to find out the influence of physicochemical and crystal-chemical properties of both sulfate hydrates (CoSO_{4}7H_{2}O and MSO_{4}7H_{2}O) as well as M^{2+} 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 CoSO_{4} 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 CoSO_{4 }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 CoSO_{4}·7H_{2}O 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 CoSO_{4}7H_{2}O) 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) the method of isothermal decreasing of supersaturation during 3 360 hours of stirring;
b) the method of long-time stirring of crushed CoSO_{4}7H_{2}O crystals in their saturated solution.
a) Establishing the dependence of coefficients D_{M/CoSO4.7H2O}
on time of crystallization of CoSO_{4}7H_{2}O at 20^{o}C
The supersaturated cobalt(II) sulfate solutions containing different initial amounts of Fe^{2+}, Co^{2+}, Mn^{2+}, Cu^{2+}, Cd^{2+}, Mg^{2+}, Zn^{2+} and Ca^{2+} were poured into beakers with water jacket. After having the beakers covered with watch glass and their contents cooled to 20^{o}C, the solutions were stirred with magnetic stirrer (~300 rpm) at mean temperature 20±1^{o}C over 3 -360 h. The results are presented in Fig. 1 and Table 2.
Fig.1: The dependence of coefficients D_{M/CoSO4.7H2O} on time of crystallization of CoSO_{4}7H_{2}O at 20^{o}C (a'_{o})_{M} - initial concentration of microcomponent (M^{2+}) ([ppm] in relation to CoSO_{4}7H_{2}O) |
Crystallization of CoSO_{4}7H_{2}O at 20^{o}C
^{*}- Average D_{M/CoSO4.7H2O} for given range of time of crystallization; D - mean value of D_{M/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; D^{o}_{min}, D^{o}_{MAX} initial minimum and maximum values of D_{M/CoSO4.7H2O} respectively. |
b) Determination of the equilibrium distribution
coefficients D_{M/CoSO4.7H2O} at 20^{o}C.
The equilibrium was reached starting either from initial concentration ratio of a microcomponent in crystal and in solution exceeding the
á_{ko}("conta min ated" crydstal) | |
= | |
á_{ro}("purified" solution) |
expected value of its equilibrium coefficient D^{o}_{max}
á_{ro}("purified" crystal) | |||
o | | from this ratio lower than the expected value | |
á_{ko}("conta min ated" solution |
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 CoSO_{4}·7H_{2}O by the first method were taken into consideration. The experiments were carried out in the following way:
Crushed contaminated" CoSO_{4}·7H_{2}O crystals (f<0.1mm) were introduced into several beakers together with saturated purified" cobalt(II) sulfate solution. Crushed crystals of purified" CoSO_{4}·7H_{2}O (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 CoSO_{4}·7H_{2}O and helped attain equilibrium and homogeneous partition of microcomponents in crystal [27]. Its mean value was equal to 20±1^{o}C.
While stirring was continued N_{2}H_{4}.H_{2}SO_{4} 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 Fe^{2+} and Cu^{2+} 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 CoSO_{4}7H_{2}O crystals in their saturated solution. (Table 2).
The distribution coefficients of ions M^{2+}{Ni^{2+}, Fe^{2+}, Zn^{2+}, Cu^{2+}, Mg^{2+} , Mn^{2+} , Cd^{2+}} 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 Ca^{2+} to 1.20 for Fe^{2+}and depend on the properties of both sulfate hydrates (CoSO_{4}7H_{2}O and MSO_{4}nH_{2}O) and metal M^{2+} 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 D_{av} on Dn. D_{av} average D_{M/CoSO4.7H2O} for microcomponents having the same n_{m }Dn = ½n_{M} - n_{m}½, where n_{M} and n_{m} number of molecules of water of |
The average value of D_{M/CoSO4.7H2O} for microcomponents forming, as CoSO_{4}7H_{2}O, 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 MSO_{4}nH_{2}O 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_{CoSO4}_{7H2O}/C_{MSO4}_{ nH2O} >1 and vice versa).
Fig. 3. The relationship of log D_{M/CoSO4.7H2O} and log (C_{01}/C_{02}) |
The cocrystallization coefficients D_{M/CoSO4.7H2O} rises generally as the solubility of MSO_{4}nH_{2}O in the solid CoSO_{4}7H_{2}O 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 D_{M/CoS4.7H2O} |
The cocrystallization coefficients D_{M/CoSO4.7H2O} of microcomponents M^{2+} 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 (Co^{2+}) (except for Zn^{2+}) and they generally decrease with the increase of the difference between r_{M2+} and r_{co2+ }For the most distant ion Ca^{2+}, its value is close to zero (D<0.008).
Fig. 5. The relationship between coefficients D_{M/CoSO4.7H2O} of microcomponents M^{2+} 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_{Co}½or (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 Co^{2+} and M^{2+} 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 Co^{2+} and M^{2+} (Dh).
The cocrystallization coefficients depend generally on electronic configuration of M^{2+} ions. The average values of D_{M/CoSO4.7H2O} for open shell M^{2+} ions (similar in this respect to the ion of macrocomponent Co^{2+}) are nearly four times greater than those for closed shell M^{2+} 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 M^{2+} ions most influence their values. Calculation of these coefficients by means of the simplest formula D_{M/CoSO4.7H2O} (C_{01}/C_{02})^{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 M^{2+} ions with CoSO_{4}7H_{2}O 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 CoSO_{4}7H_{2}O, as: 837 J/mol (for orthorhombic ZnSO_{4}7H_{2}O, NiSO_{4}7H_{2}O and MgSO_{4}7H_{2}O) and 2510 J/mol (triclinic CuSO_{4}5H_{2}O) [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 Ca^{2+}) during the crystallization of CoSO_{4}7H_{2}O at 20^{o}C is shown in the same table.
Comparison of calculated (D_{cal.}) and experimental (D_{exp.}) values of cocrystallization coefficients of microcomponents M^{2+} during the crystallization of CoSO_{4}7H_{2}O at 20^{o}C
CONCLUSIONS
The equilibrium distribution coefficients D_{M/CoSO4.7H2O} of low amounts (10^{-3}- 10^{-1}%) of M^{2+} ions (M^{2+} = {Ni^{2+}, Mg^{2+}, Cu^{2+}, Zn^{2+}, Fe^{2+}, Mn^{2+}, Cd^{2+}}) with CoSO_{4}7H_{2}O have been determined by means of the method of long-time stirring of crushed CoSO_{4}7H_{2}O crystals in their saturated solution at 20^{o}C. 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 Ca^{2+} to 1,20 for Fe^{2+} and depend on some of the physicochemical and crystal-chemical properties of both sulfate hydrates (CoSO_{4}7H_{2}O and MSO_{4}nH_{2}O) and metal M^{2+} ions.
D_{M/CSO4.7H2O} values generally get greater as the difference of number of molecules of water of crystallization of CoSO_{4}7H_{2}O and MSO_{4}nH_{2}O decrease and the similarity of electronic configuration of Co^{2+} and M^{2+} increases.
Cocrystallization coefficients decrease in general as the solubilities of corresponding sulfate hydrates in water increase and as their solubilities in solid CoSO_{4}7H_{2}O decrease. They depend as well on radii (r) of M^{2+} 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 M^{2+} 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 M^{2+} ions.
Knowing solubilities (mol/L) in water of CoSO_{4}7H_{2}O and MSO_{4}nH_{2}O as well radii of Co^{2+} and M^{2+} 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 CoSO_{4}7H_{2}O, 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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