David Dyrssen, Elena Ivanova' and Kerstin Aren
University of Gothenburg Gibraltargatan 5A Goteborg s, Sweden
The Solubility Curves for Calcium and Strontium Sulfates
T h e aim of this work was to devise a simple laboratory experiment which would demonstrate three points for the students. First, the effectiveness of the Bronsted saturator, or Bronsted solubility column (1-4), in saturating a liquid with a solid phase. Second, that the solubility of the sulfates of divalent metal ions is not only dependent on the solubility product, and third, how easily the total metal concentration may be determined by atomic absorption spectrophotometry.
solution has been washed out (about 5 ml are needed). The samples, which must not be chilled off, are then analyzed after suitable dilution by sucking them into the flame of an atomic absorption spectrometer (in this case a Perkin-Elmer 3030with a recorder read-out). The 4226.73 A and 4607.33 A wave-lengths were employed for calcium and strontium, respectively. Standard solutions in the range of W20 ppm in 0.2 M sodium chloride were prepared from CaCl2(HzO)z and SrC12(H20)6. Mass Balance and Equilibrium Conditions
The total sulfate concentration, [Sod2-ICt,is determined experimentally from the sum of the analytically known initial sulfate concentration and the amount of sulfate removed from the column when MS04 dissolves as M2+ SO? or MS04. [SOdtot,ero = ISOdinit [Mltot (1) Assuming that sulfate is present both as SOaZ-ions and the complex (ion-pair) MS04 then [SO,ltOt = ISOPI IMSO,] = [SO,'-] K., (2) where Kal = [MS04]for saturated solutions. With the same assumption the total metal concentration is given by [MI, = [Ma+] lMSO,I = KsoI[S0,2-l K I (3)
+
+
+
+
Figure 1.
Tho BiSnsted solubility d m n .
Procedure
The solubility column is shown in Figure 1. The inner diameter of the column is 11 mm. A layer of 5-cm solid material is sufficient in order to saturate the aqueous solution a t a flow rate of about 1/3 cm/min. I n order to minimize channeling effects, the column should be resettled now and then by back-washing. The solid material should be prepared by aging a t 60°C for two days. Finer particles are removed by washing and decanting. Solutions with different initial sulfate, [S04]i,it, concentrations to be filtered through the column are prepared by mixing 0.1 M NalSOl with 0.2 M NaC1, the sodium ion concentration thus being kept constant at 0.2 M. The temperature must be kept constant preferably aK25"C, by using an air-thermostatic room or a thermostatic bath. When changing from one initial sulfate concentration to another, all liquid above the solid column should be sucked off. Samples for the analysis of the total metal concentration. I M L are taken after the ~revious 'On leave from the Department of Chemistry, Lomonosov University of Moscow, with a grant from the Soviet Academy of Sciences.
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+
+
where K a o = [MZ+][Sop2-] is the solubility product. The formation constant 81 of MS04 is equal to the ratio Kal/K.o = [MS04]/[M2+][S042-]. The free concentration of sulfate, [SOa2-1, is eliminated in eqn. (3) with eqn. (2) (IMItot - K d ([SO?ltot- Ksl) = K a (4) To simplifythis equation the followingsymbols may be introduced: [MI,,, = Y; [Sodtot = X; K.0 = a; K.1 = b (Y
- b) ( X - b) = a
(5)
As long as no MZ+ is added to the column 2. [MI,,,, according to eqn. (I), i.e., X 2 Y. The line Y = X cuts the solubility curve at
If X o is introduced by eliminating a in eqn. (5) with eqn. (6) then (Y - b) (X - b) = (X, - b p (7) The value of b can be calculated from the value of Y = Y 1at X = 0.1 M
Table 1.
[SOFlina M
Figure 2. Solubility curves for colsium and strontium sulfates in which tho logarithm of the total metal concentration in 0.1 M Na(C1,SOd hor been plowed against the logarithm of the total rulf.te concentration. The different liner and curves ore explained in the text.
When b = Kalhas been calculated in this way, then a = K., can be obtained from eqn. (6). The full solubility curve according to eqn. (4) or (5) can then be calculated (5) and plotted in a logarithmic representation as shown in Figure 2. If the points with values of X other than Xo and 0.1 M fit to the calculated curve, then the assumptions underlying eqns. (1)-(3).may be assumed to be correct and no other complex is formed in this range of [SO4ltOt.A least squares treatment (6) of all data would give still better values of Keo and K.1.
Results of S o m e Experiments
The results ohtained from measurements of the solubility of CaSOa(H20)zand SrSOn at 25'C in 0.2 M Na(CI,S04) are shown in Table 1, and they have been plotted as log [MItot.against log [S041ct in Figure 2. The values in Table 2 have been obtained from eqn. (9) and the point where log Y = log X (dashed line) cuts the curve (eqn. (6) ). It is obvious that the equation Log Y
=
log K.o - log X
(10)
(dotted lines in Figure 2) does not fit to the experimental data. The MSOl complex (ion-pair) thus cannot be neglected. The mirror image part of the solubility curve above the dashed line log Y = log X can only be obtained by running a solution with M2+ (e.g., 0.2 M (M,Na)Cl) through the column and measuring the total sulfate concentration (X). The limiting value of Y is given by the asymptote log Y = log b (thin horizontal lines). Chemically the lines represent the case in which [M2+] may be neglected in comparison with [MS04].At the intersection of the dotted lines of slope - 1 (XY = a, eqn. (10) ) with the horizontal lines (Y = b) log X = log a - log b
Solubility Data for Calcium Strontium Sulfates"
-CaSO1---SrSO,log[Caltot log [ S O h log [Srltot
log l S O h t
"The values of [Mlm represent an average of four runs or more. Tho ionic medium was 0.2 M Ns(CI,SO,) and the temperature was 25.0 0.3"C.
Table 2. Values of log Kso, log KSI, and log 81 for Calcium and Strontium Sulfates a t 25°C Ianio medium log K.o log K.1 log PI log K.o log K.L log 81
0.2 M 0.2 0.2 0 0 0
Ca ~ 3 . 7 7 ~ ~ 2 . 2 4 ~ 1.52. -4.63 to -5.92' -2.32 to -3.61 2.31'
-5.554 -4.14. 1.40s -6.19 to -6.55'
.. ..
"Values taken for comparison from L. G. S I L L ~ AND N A. E. MARTELL "Stability Constants of Mctsl-Ion Complexes," S ec Puhl. No. 17, The Chemical Society, London, 1964. ~ c c o r i i n g to reference (5) the activity coefficients for Mg+ and S O P will account for a difference of 1.02 in loe K.o and loe- 41 between 0.2 and 0 M ionic media. ~~
= log 8,. A value for the complex formation (ionpairing) constant of MS04 may thus be ohtained. These constants are not very different for calcium (log 81 = 1.53) and strontium (log 81 = 1.41), and the difference in the K., values is due to the forces in the solid state, this difference being reflected in the values of K.1.
Literature Cited (1) BRSNSTED,J. N., AND PEDERSEN, K. J., Z. physik. Chem., 103.307 (1923). (2) B R ~ N ~ E J D., N:, AND LA MER, V. K., J. Am. Chem. SO&, 46,555 (1924). D., AND TYRRELL, V., A d a Chem. Scand. 15, 393 (3) DYRSSEN, (1961). (4) NANC~LLAS, G. H., "Interactions in Electrolyte Solutions," Elsevier, Amsterdsm, 1966. (5) DYRSSEN,D., JAGNER,D. AND WENGELIN,F.,"Computer
Calculations of Ionic Equilibrium and Titration Procedures," Almqvist & Wiksell, Stockholm, 1968. (6) INGRI,N., AND SILLBN,L. G., Arkiv Kemi, 23,97 (1964).
Volume 46, Number 4, April 1969
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