1735
CRYSTALLIZATION AND DISSOLUT~ON OF STRONTIUM SULFATE
The Crystallization and Dissolution of Strontium Sulfate in Aqueous Solution by J. R. Campbell and G. H. Nancollas Chemistry Departments, The University, Glasgow, W . 2, Scotland, and State University of N e w York at Buffalo, Buffalo,N e w York 14314 (Received November 26, 1968)
The kinetics of crystallization and dissolution of strontium sulfate have been studied by following the change in conductivity which occurs when supersaturated or subsaturated solutions are inoculated with seed crystals. The growth of the crystals follows an equation in which the rate of crystallization is proportional to the square of the relative supersaturation in the solution. Under certain experimental conditions, this stage is preceded by an initial growth surge. Evidence, based upon the effect of adsorbates on the crystallization process, is advanced for nucleation on the surface of the crystals during this fast period. The rate of dissolution of strontium sulfate crystals into subsaturated solutions has been found to be proportional to the square of the relative subsaturation after an initial surge of short duration.
Of the common sparingly soluble bivalent metal sulfates, that of barium has been the most studied because of its importance in quantitative analysis. Much of the work on strontium sulfate, of somewhat higher solubility, has been concerned with the effects of differing conditions of precipitation upon the nature and size of the precipitated particles. l-8 It was shown that added impurities, particularly phosphates, had a marked habit modifying effect on the precipitated crystal^.^^^ The critical supersaturation and rates of spontaneous precipitation and dissolution of strontium sulfate also appear to be markedly affected by the presence of added substances capable of adsorption a t the surface of the Campbell and Cookg attempted to distinguish the successive labile or metastable states through which a supersaturated solution passes during crystallization and found that strontium sulfate began to crystallize spontaneously in 50% supersaturated solution producing rhombic crystals, up to 10 p in size. They made the remarkable observation that when the degree of supersaturation had fallen to about 4091, (a concentration of approximately 8.5 X M ) , further precipitation appeared to cease and no more crystal growth was observed even when inspected 28 days later. Since large crystals of strontium sulfate were present in the solution, this behavior was most irregular. The results of the present study show that this observation is entirely consistent with the extreme susceptibility of strontium sulfate crystal growth to the presence of minute traces of impurity. The present work is an extension of previous studies of the kinetics of crystallization of the 2-2 electrolytes magnesium oxalate'o and barium sulfate," for which characteristic induction periods and growth surges were observed. It was of interest to determine whether the growth of strontium sulfate from supersaturated solution was preceded by a growth surge similar to that observed for the barium sa1t.l' The relatively greater solubility of strontium sulfate makes it possible to
follow the growth process with greater precision, and the special features outlined above enable more detailed investigations of the effects of impurities upon the rates of crystal growth and dissolution.
Experimental Section AR salts were used, and solutions were made up by weight using conductivity water which had been prepared by one of two methods: (a) mixed-bed deionization12 and (b) double diFstillation through a nitrogenflushed fractionating column. Although the conductivity of water (b) was not as low as that of water (a), the latter contained organic impurities, probably introduced from the anion-exchange resin matrix, which had an appreciable effect upon the rates of crystal growth. Since strontium sulfate has a low-temperature coefficient of solubility, seed crystals could not be prepared from boiling saturated solutions and a precipitation technique was used. Rhombs, of average size 12-15 p (corner angle 76 lo), were prepared by dropwise additions of either strontium chloride and sodium sulfate or strontium hydroxide and sulfuric acid to water a t 70'. The seed crystals were digested for several hours, washed thoroughly with water, and allowed to age a t 25' for several weeks before use; seed suspensions con-
*
(1) B.Lambert and W. Hume-Rotherx, J . Chem. Soc., 2637 (1926). (2) S.Otani, Bull. Chem. Soc. Jap., 33, 1543 (1960). (3) S. Otani, ibid., 33, 1549 (1960). (4) M. Miura, S. Otani, Y. Abe, and C. Fukumura, ibid., 36, 1091 (1963). (5) M. Miura and H. Naono, ibid., 38, 80 (1965). (6) H. Naono and M. Miura, ibid., 38, 492 (1965). (7) M. Miura, H. Naono, and M. Hara, ibid., 39, 344 (1966). (8) H. Naono, ibid.,40,1104 (1967). (9) A. N. Campbell and E. J. R. Cook, J. Amer. Chem. Soc., 57, 387 (1935). (10) G.H. Nancollas and N. Purdie, Trans. Faraday SOC.,57, 2272 (1961). (11) G.H.Nancollas and N. Purdie, ibid., 59,735 (1963). (12) C.W.Davies and G. H. Nancollas, Chem. I n d . (London), 7, 129 (1950). Volume 73, Number 6
J u n e 1969
J. R. CAMPBELL AND G. H. NANCOLLAS
1736 tained from 3 to 50 mg of crystals/ml. Suspensions a, b, and c were prepared using deionized water, while double-distilled water was used for suspensions f and g. Supersaturated solutions were prepared in a conductivity cell by the slow mixing of solutions containing strontium chloride and sodium sulfate. All experiments were conducted in a nitrogen atmosphere. In order to reduce the ionic strength resulting from the presence of the supporting electrolyte, sodium chloride, a number of crystallization experiments were made with strontium hydroxide and sulfuric acid. Stable supersaturated solutions containing a t least twice the solubility concentration of strontium sulfate could be prepared and a supersaturation of about 25-30% was usually used in the crystallization experiments. Crystal growth was induced by the addition of seed crystals to stable supersaturated solutions and resistance measurements were made at 25 f 0.005’ with the Jones and Joseph screened ac bridge described previously. l3 Dissolution experiments were made by adding seed crystals either to water or to subsaturated strontium sulfate solutions contained in the conductivity cell.
Results and Discussion The relatively higher concentrations of the strontium sulfate crystallization experiments as compared with the barium sulfate studies make it necessary to take into account the formation of ion pairs, SrS04,for a detailed kinetic analysis of the process. No data are available for the equilibrium constant of the reaction
Sr2+
K
=
+
5042-
__
SrSOl
Table I: Crystallization of Strontium Sulfate. Experiments in Deionized Water
[SrS04]/[Sr2+][ S 0 4 2 - ] f 2 2
where square brackets represent molar concentrations and fi is the activity coefficient of a z-valent ion. For magnesium and calcium sulfate, the corresponding association constants are 179 mol-‘ l 4 and 200 mol-l,15 respectively, and a value of 150 mol-’ has been used in the present study for strontium sulfate. Concentrations of ionic species in the supersaturated solutions were calculated in the usual manner16 from the mass balance and electroneutrality expressions by successive approximations for 1,the ionic strength, and using a CDC 6400 electronic computer. Activity coefficients were obtained from the extended form of the DebyeHuckel equation proposed by Davies” -logf,
sulfate crystals since the solubility depends upon the minimum crystal size.19 I n the present study, the solubility of the seed crystals, determined by allowing growth experiments to proceed to equilibrium and expressed as a total stoichiometric concentration of strontium sulfate, was 6.440 X mol 1.-’. The corresponding thermodynamic activity product, 2.158 X lo-’ mol2 1.-2, was used to calculate the solubility values a t the ionic strengths in each experiment. I n the initial experiments, the supersaturated solutions and seed suspensions were prepared from conductivity water, type a. Some crystallization experiments with equivalent ionic concentrations of strontium and sulfate ions, m, are summarized in Table I in which mi is the initial and m, the final ionic concentrations (after 48 hr). Typical curves of (resistance) -l against time are shown in Figure 1. After a comparatively rapid start, the rate of crystallization was very slow and after about 30 hr crystal growth had ceased with less than 25% of the reaction completed. The equilibrium conductivity values corresponded to effective solubilities considerably greater than the value given above. Dissolution experiments with these seed crystals also failed to proceed to an equilibrium value corresponding to the solubility; the final concentrations were larger, the smaller the initial subsaturation. These results indicate that adsorption was occurring on the surface of the seed crystals inhibiting both crystal
=
Az2{I1’’/(1
+ I”’) - 0.311
which has satisfactorily interpreted the activity data in many other systems.le Values in the literature for the solubility of strontium sulfate range from 5.3 x to more than 8 X mol I.-’. Kohlrauschl8 and Enustun and Turkevitchlg obtained a value of 6.22 x mol 1.-l and several results about 7% greater have been reported.20,21 Many of the discrepancies in these values can be attributed to the different conditions of preparation of the strontium The Journal of Physical Chemistry
Expt no.
X 104, -Am X 104, m, X 104, mol/l. mol/l. mol/l.
mi
9.990 9.003 6.570 6.352 6.600 6.523 7.500 7.294 6.600 6.533
0.530 0.280 0.047 0.021 0.072 0.043 0.191 0.272 0.062 0.053
9.460 8.723 6.523 6.331 6.529 6.480 7.309 7.022 6.538 6.480
Seed
Duration of expt,
suspn
hr
a
38 40 30 30 36 34 36 36 36 30
a b b b b b b b a
(13) J. R.Howard and G. H. Nancollas, Trans. Faraday SOC.,53,1449 (1957). (14) V. S. K. Nair and G. H. Nancollas, J. Chem. SOC.,3706 (1958). (15) R. P. Bell and J. H. B. George, Trans. Faraday SOC.,49, 619 (1953). (16) G. H. Nancollas, “Interactions in Electrolyte Solutions,” Else vier Publishing Co., Amsterdam, 1966. (17) C. W.Davies, “Ion Association,” Butterworth and Co., Ltd., London, 1962. (18) F. Kohlrausch, 2.Phys. Chem., 64, 129 (1908). (19) B. V. Enustun and J. Turkevitch, J. Amer. Chem. SOC., 82,4502 (1960). (20) F. C. Collins and J. P. Leinweber, J. Phys. Chem., 60, 389 (1956). (21) A.Holleman, Z . Phys. Chem., 12, 125 (1893).
1737
CRYSTALLIZATION AND DISSOLUTION OF STRONTIUM SULFATE
Expt 18b
5.0
** Q X
3 5.7
5.6
Time, min.
Figure 1. Plots of A(resistance)-l against time. Experiments 4, 9, and 18 were made with deionized water; experiment 38, with doubly distilled water.
growth and dissolution processes. This can be seen from the results of experiments 18, 19, and 20 in which two successive additions of seed crystals were made. After the first inoculation, designated by (a), the crystallization was allowed to reach an equilibrium where it remained steady for 25 hr. On the addition of more seed suspension, represented by (b), crystal growth recommenced and a second equilibrium was reached after several hours, the conductivity again remaining steady for a t least 30 hr. The final concentrations were considerably higher than the true solubility value and increased with increasing initial supersaturation as can be seen from Table I. In order to eliminate the possible effect of chloride ions, which are well known to be occluded by crystals of barium sulfate.22~2a a number of experiments were made in which both the seed crystals and supersaturated solutions were prepared using (i) strontium nitrate and sodium sulfate and (ii) strontium hydroxide and sulfuric acid. The results obtained using deionized water were similar to those described above ; crystallization again stopped while the solution was substantially supersaturated. It became clear that the source of the inhibiting impurity was the resin matrix itself and a t this stage, the deionized conductivity water was replaced by the doubly distilled water. Some crystallization experiments are summarized in Table I1 and conductivitytime relationships are given in Figures 1 (experiment 38) and 2 . The effect of the change of water is clearly seen in Figure 1 in which experiment 38 was done in
12
6 9 Time, hr.
3
Figure 2. Plots of A(resistance)-' against time. Stoichiometric strontium: sulfate concentration ratios are 1 :1 (experiments 33 and 35), 1:2 (experiment 41), and 2 : l (experiment 43).
Table I1 : Crystallization of Strontium Sulfate. Experiments in Distilled Water [Sr'li
no.
x 104, mol/l.
33 35 37 38 41 42 43 48
7.500 7.700 7 500 10.000 5.382 10.606 IO. 606 7.500
Expt
I
[so41-]i x 104, mol/l.
7.500 7.700 7.500 IO. 000 10.685 5.302 5.303 7.500
Seed
ks, 1. mol-1 Initial min-l/ fast
Seed orystals, suspn g C C
f f g g
g
1.140 0.945 0.700 0.076 0.220 0.120 0.440 0.485
g
g of
seed period, rnin
crystals
3.7 330 3 . 3 390 15 63 200 44 64 12 61 25 10 66 12 48
doubly distilled water; the calculated equilibrium concentration of strontium sulfate was within 1% of the solubility value. Repeated distillations of the water used to prepare the seed suspensions and the solutions had no further effect upon the rate of crystal growth. The curves for crystal growth in 1 : l solutions in Figure 2 are characterized by an initial fast period followed by a smooth fall in conductivity with time in which the rate of crystallization would be expected to follow an equation of the form22 (22) G. H. Nancollas and N. Purdie, Quart. Rev. (London), 18, 1 (1964). (23) I. M. Dawson and M. McGaffney, Proceedings of the 4th International Conference on Electron Microscopy, Berlin, Germany, Sept 1958.
volume '7.9- Number 6 June 1969
1738
J. R. CAMPBELL AND G. H. NANCOLLAS
-dTM ~-
- ks(m - mo)n
dt in which TM represents the total concentration of strontium sulfate, m (= [Sr2+]= [SO,2-]) is the ionic concentration, mo is the ionic solubility value, and s is the surface area. A typical plot of log (-dTM/dt) against log (m - mo) is shown in Figure 3, and it is seen that after an initial surge for which n = 13, the rate of crystal growth varies linearly with the square of the reIative supersaturation with n = 2 in eq 1. I n the regions following the characteristic initial surges, is the linearity of plots of drM/dt against (m illustrated in Figure 4 for a number of experiments which were made with various preparations of seed crystals. Changes in surface area of the crystals during the experiments usually amounted to 2-10'3, of the total weight of crystals present and could thus be neglected. I n Table 11, values of the slopes of the straight lines are expressed as ICs per gram of seed crystals used for inoculation. Changes of ionic strength introduced by using Sr(0H)z H2S04 in place of SrC12 Na2S04 for the preparation of the supersaturated solutions were without effect on the subsequent growth rates. In a test for diffusion, the rate of crystallization was found to be independent of stirring conditions and the observed dependence of the rate upon the square of the relative supersaturation is consistent with the theory of Davies and Jones.24 The rate of growth is controlled by an interface process involving the formation of an adsorbed surface layer of hydrated strontium and sulfate ions. Essentially the same form of eq 1 with a value of n = 2 is obtained if the concentrations of ions adsorbed on the crystal surface are expressed in terms of a simple Temkin isotherm.25 Walton considered that the implicit premise of this isotherm of a linear change of heat of adsorption with surface coverage was preferable to the assumption made by Davies and Jones2* that the concentrations of adsorbed ions are directly proportional to their bulk concentrations in the solution. The results of some experiments with nonequivalent ionic concentrations of strontium and sulfate are included in Table 11. It can be seen in Figure 5 that, after the characteristic initial surge, the rate of crystallization follows the equation
+
+
7.2
-
1
5 2 7.0 d I
6.8
-
6.6
-
Y
cn
3 I
6.2 6.41
I
\ I
3.6
I
3.7
I
I
I
I
3.8 3.9 - Log ( m -mol
4.0
I
4.1
-
Figure 3. Plot of log (-dTM/dt) against log ( m mo) for experiment 38. Values of the slopes are n = 13 (first part) and n = 2.0 (second part).
3.0
5 x
2.0
1.0
( m - mo)* x
lo',
-
~ Figure 4. Plots of -dTy/dt against (m m ~for) equivalent ionic concentrations: v, experiment 35; m, experiment 38; 0, experiment 37.
The results of the experiments using different water illustrates the remarkable sensitivity of the - dT,/dt = k's( [Sr2+]1'z[S042-]1/* - K s P ' / ~ / ~ z ) ~ preparations crystallization process to the presence of minute traces which is consistent with the model proposed above.24 of impurities. In order to investigate this effect further, In this equation, K S p is the thermodynamic solubility a number of experiments were made in which the crysproduct and f 2 is the activity coefficient of the divalent tallization was followed in the presence of sodium ions, It is of interest to note in Table I1 that for pyrophosphate and sodium trimetaphosphate ; some of strontium sulfate, the rate constants for nonequivalent the results are summarized in Table 111. ionic concentrations, k', are the same, within experi(24) C. W. Davies and A. L. Jones, Trans. Faraday SOC.,51, 812 mental uncertainty, as those for equivalent concentrations, k. For both barium sulfate" and silver chloride,26 (1955). (25) A. G.Walton, J . Phys. Chem., 67, 1920 (1963). the k' values were smaller than k and depended upon (26) C. W. Davies and G. H. Nancollas, Trans. Faraday SOC.,51, which of the lattice ions was in excess. 823 (1955). The Journal of Physical Chemistry
1739
CRYSTALLIZATION AND DISSOLUTION OF STRONTIUM SULFATE
5.42
5.38
-5 *
5.34
5.30
( W + l ' n ISO:-I"*
-
x io8.
-
Figure 5. Plots of -dTor/dt against ([Sr*+]'/2[SOP]'I2 K8p'/l/f2)2 for nonequivalent ionic concentrations: a, experiment 41; 0, experiment 43.
Table I11 : Crystallization of Strontium Sulfate in the Presence of Adsorbates Expt no.
45 46 47 48 49
Conon of
Seed
adsorbate, M
auspn
mg/ml
3.30 x 4.30 x 10-'a 4.91 X 0.00 1.00 x 10-ob
g g g g g
202 200 178 91 248
mi X 104,
mol/l.
7.500 7.500 7.500 7.500 7.500
Sodium pyrophosphate.
b
Seed concn,
Sodium trimetaphosphate.
The striking effect of the additives upon crystal growth is seen in Figure 6 in which conductance is plotted as a function of time. At concentrations of sodium pyrophosphate as low as 4 X lo-' M, crystal growth is almost completely inhibited (experiment 46). It should be noted, however, that in each case the characteristic growth surge upon inoculation of the supersaturated solutions is still in evidence. The amount of observed crystal growth, even with the lowest attainable concentration of additive, is so small that it is not possible to make a quantitative kinetic analysis of the growth curves in Figure 6 . The condensed phosphate anions have also been found to have a marked effect on the stabilization of supersaturated solutions of strontium ~ u l f a t e . ~ - A ~ # concentration ~ of sodium M is sufficient to inhibit triphosphate as low as 3 X completely the nucleation of strontium sulfate in 0.02 M solution, considerably larger than the solubility valuee8 The effect could not be attributed to the complex formation between strontium and triphosphate ions because of the low molar ratio of P80106-:Sr2+= 1:670 in the solution.a Adsorption of the phosphate ions a t the crystal surfaces was confirmed radiochemical1y.a The characteristics of the initial surge observed upon
50
100 150 Time, min.
200
250
Figure 6. Plots of A(resistance)-l against time. Crystallization in the presence of adsorbates: experiments 45 and 46, sodium pyrophosphate; experiments 47 and 49, sodium trimetaphosphate.
the addition of seed crystals to the supersaturated strontium sulfate solutions supports the suggestion of a two-dimensional nucleation used to explain a similar phenomenon observed in the growth of barium sulfate crystals from their supersaturated solutions." Thus an increase in the initial supersaturation and the use of smaller amounts of seed crystals increase the duration of the initial surge. This is seen from the results of experiments 37 and 38 in Table 11; an increase in the initial supersaturation and the use of a smaller amount of seed crystals in experiment 38 increased the duration of the initial surge by a factor of 10. In the nonequivalent experiments the same initial supersaturation was used and, as is seen from the results of experiments 41 and 42, the duration of the initial surge increased with decreasing amount of seed crystals. For a given seed preparation, the agreement between the ks values, expressed in 1. mol-' min-' (g of seed crystals)-', is very good. Seed suspension c, which in contrast to the others had been prepared from deionized water solutions, produced considerably lower rate constants in experiments 33 and 35 but with an increased initial surge. The reduction in the number of available growth sites effected by the adsorption of the impurity reduced the over-all rate of crystallization but increased the need for surface nucleation. The results are consistent with the suggestion of Sears2' that the impurity reduces the critical free energy for two-dimensional nucleation, causing an increase in surface nucleation. The persistence of the initial surge in the presence of the phosphate additives is further evidence in support of (27) G. W. Sears in "Growth and Perfection of Crystals," R. H. Doremus, B. W. Roberta, and D. Turnbull, Ed., John W-iley & Sons, Ino., New York, N. Y . ,1958.
Volume 73, Number 6 June 1969
J. R. CAMPBELL AND G. H. NANCOLLAS
1740
4.4
4.2
4.0
1
I
I
I
50
150
.I
250
Time, min.
Figure 7. Dissolution experiments; plots of (resistance)-’ against time. Experiment 6 , mi = 5.00 X M , 400 mg of seed suspension a, deionized water. Experiments 39 (mi = 5.00 X M , 420 mg of seed) and 40 (mi = 5.60 X M , 55 mg of seed) made with suspension g in double-distilled water.
this suggestion. A seeded growth experiment in the presence of sodium triphosphate and described by Kaonos also shows the characteristic initial surge before growth is completely inhibited. I n the spontaneous precipitation of strontium sulfate, the mechanism for the inhibiting action of polyphosphates has been investigated by a number of worker^^^^^^ but no satisfactory explanation has been proposed. The question as to whether nucleation is inhibited completely or whether the polyphosphate ions are adsorbed on the surface of crystal nuclei formed in the solutions remains an open one. The results of the present work in seeded systems appear to favor the latter suggestion, since even in the presence of adsorbates the addition of seed crystals to the supersaturated solutions is always accompanied by an initial concentration change. A number of experiments were made in which seed crystals were allowed to dissolve into subsaturated solutions of strontium sulfate and the rate of dissolution was followed conductometrically. Typical plots of conductance as a function of time are shown in Figure 7 for experiment 6, which was made using deionized water, and experiments 39 and 40 in double-distilled water. The effect of impurity is again seen as a striking reduction in the extent of reaction. After approximately 150 min, the reaction in experiment 6 is completely inhibited a t only 15% completion. After an initial fast portion, the dissolution follows a quadratic equation similar to that observed for crystal growth, namely
The Journal of Physical Chemistry
The change in surface area during the experiments amounted to less than 1% of the total seed crystals added. Under similar conditions, the dissolutions of silver chloride and silver chromate have been shown to be first order in relative subsaturation, indicating a diff usion-controlled p r o c e ~ s . ~Moreover, ~,~~ the effect of the presence of added surface-active substances upon the dissolution of silver chloride was very small.30 It therefore appears that the dissolution of strontium sulfate is controlled by a process other than film diffusion a t the crystal surface. A similar quadratic dependence upon relative subsaturation was also noted for the dissolution of lead ~ u l f a t e . ~ ’Further evidence in support of this suggestion is given by the results of dissolution experiments in the presence of condensed phosphate ion^^,^ in which considerable retardation of the rate is observed. Parallel radiotracer experiments indicated adsorption of the phosphate ions at the crystal surfaces. Such adsorption would be expected to occur a t sites of local high energy, such as dislocations, on the crystal faces. The dissolution of a perfect crystal is considered to commence by the creation of unit pits, one molecule deep, which grow by a stepwise prQcessacross the crystal surface. Since s w h pits are likely to form a t dislocations, the lowering of the energy of such dislocations by the presence of adsorbate would reduce the formation of unit pits. The quadratic dependence upon relative subsaturation of the dissolution of the 2-2 electrolytes indicates a slow step in the process of removal of a pair of oppositely charged ions from the crystal lattice, separation against mutual attraction, and subsequent hydration. Lattice energies of the bivalent metal sulfates are more than twice that of the 1-1 salt silver chloride, for which a film diffusion rate-determining step is found. The initial surge may be attributed to rapid dissolution a t sites of high localized energy such as the centers of dislocations which for a divalent salt will carry a relatively high charge. The numbers of such dislocations would be expected to be larger for strontium sulfate seed crystals prepared by precipitation than for silver chloride prepared by a slow recrystallization method. 30
Acknowledgment. The computational work for this paper was done at the State University of New York at Buffalo under the support of the Office of Saline Water, United States Department of the Interior (Grant No. 14-01-0001-944). We gratefully acknowledge this support. The authors also wish to thank R. W. PIlarshall for his assistance in this part of the work. (28) R. F. Reitemeire and A. D. Ayers, J. Amer. Chem. SOC.,69, 2759 (1947). (29) B. Raistrick, Discussions Faraday Soc., 5,234 (1949). (30) C. W. Davies and G. H. Nancollas, Trans. Faraday Soc., 51, 823 (1955). (31) A. L. Jones, {bid.,59, 2355 (1963).
