Communications to the Editor
496
Solublllty Product Constant of Calcium Fluoride Publication costs assisted by the National Science Foundation
Sir: In a paper appearing recently in this journal, Stearns and Berndtl present evidence that the classical solubility product of calcium fluoride is not a constant at a given temperature and pressure but changes as a function of the composition of the solution phase. Some thermodynamic arguments in support of this finding were offered. The implications of this conclusion are so far-reaching as to demand further consideration. Stearns and Berndt used a fluoride-selective electrode to measure the concentration of free fluoride ion in a solution containing a known stoichiometric concentration of added calcium ion and excess solid calcium fluoride. In effect, the concentration solubility product constant K',,, was calculated by vO
1.0
0.5 1 / b2
(M-'Z)
Figure 4. Plot of A&-' at 410 nm against b-*.
where AA, is the measured relaxation amplitude at 410 nm, = H D P - F ~ C L~ (~OHHH ~)~~HoD P - F ~dc ~T~=, 5.0 f 0.5 K, and T = 293 K. It was noted that a plot of AA,' against b-2 gave a straight line, as shown in Figure 4. Since AE and Keg are already known, the enthalpy could be estimated from the slope: AH = -38 f 15 kcal mol-'. This value was in agreement with the enthalpy of the aquation of free Fe(II1) ion evaluated by Bernal and F ~ w l e r . ~ Acknowledgment. We are grateful to Professor M. Fujimoto for his encouragement and to Professors K. Yagi and S. Nishida for their permission to use the apparatus. We also wish to express our thanks to Professors T. Tsuji and T. Furukawa for their valuable discussions. Supplementary Material Available: Appendices I, 11, and I11 contain the three derivations for eq 4,5, and 6 (3 pages). Ordering information is given on any current masthead page.
f '/2[F-])[F-I2
(1)
and was found to increase by a factor of 2 over a range of added calcium ion from. 0 to 0.01 M, after which it decreased to near its original value with further additions of calcium ion. Anomalies in the value of Kspderived from measurements with the fluoride-selective electrode have been reported beforeS2 We have now repeated the measurements of Stearns and Berndt (at 25 "C rather than at 20 "C) using the calcium ion-selective electrode as well as the fluoride electrode. Our measurements suggest that the activity solubility product is indeed a constant withii the experimental error inherent in the electrode system. The results suggest that the variability observed by Stearns and Berndt (and confirmed by us when the fluoride electrode alone was used) may be due to adsorption of ions on the solid CaF2. Under these circumstances, the system can no longer be defined by measurements of the fluoride ion concentration alone. The cell can be represented by F-(ISE)ICaF, (s) t Caz+(rn ) lCa2+(ISE) where rn is molality and s represents a solid phase. If both electrodes respond in Nernstian fashion, one can write for the emf E of cell A E = Eoca - EoF h log ( ~ ~ ~ z f a F - 2 ) = constant - kpK,, (2)
+
References and Notes J. H. Fendler and E: J. Fendler, "Catalysis in Micellar and Macromolecular Systems", Academic Press, New York, N.Y., 1975. M. Eigen and L. DeMaeyer in "Techniques of Organic Chemistry", Vol. VIII, 2nd ed,Part 2, S.L. Frless, E. S.Lewis, and A. Weissberger, Ed., Wiley, New York, N.Y., 1963, p 895. A. E. Harvey, Jr., and D. L. Manning, J Am. Chem. Soc., 72, 4488 (1950). T. Masui, F. Watanabe, and A. Yamagishi, submitted for publlcatlon. The apparent aggregation number of DPCI (n) in chloroform was determined by the vapor pressure depression method; 7,= 5-7 at 0.50 M DPCI. The T-jump apparatus used has a coaxial cable of 157 m length as a capacitor. The characteristlc Impedance of the cable Is 50 a. (a) F. Watanabe, Doctoral Thesis, Hokkaido Universlty, Japan, 1976. (b) It was found that discharge of electrical energy stored in the cable into the sample solution is determined substantially by the resistance of the solution. Taking into account thls finding, the rise time of the temperature was calculated. More detailed representation of the calculation will be given by F. Watanabe, T. Masui, and A. Yamagishi, to be oublished. F. Guiilain and D. Thusius, J. Am. Chem. Soc., 92, 5534 (1970); D. Thusius, ibid, 94, 356 (1972). J. D. Bernal and R. H. Fowler, J. Chem. Phys., 1, 515 (1933).
Department of Chemistry Faculty of Science Hokkaido University K;f+ku, Sapporo, Japan or0
Kfsp= ([Ca"added]
Takeshl Masui Fumiyukl Watanabe" Aklhlko Yamaglshl
Received August 30, 1976 The Journal of Physical Chemistw, Vol 81, No. 5, 1977
where k is (RT In 10)/2F. The emf of the cell should thus be constant if the activity product is a constant. The measurements were made at an ionic strength of 1.0 mol kg-l, maintained by addition of appropriate amounts of KC1. In this way it was hoped that the liquid-junction potentials would be stabilized and that changes in the activity coefficients of Ca2+and F- would be minimized. I t was therefore possible to monitor independently the molalities (rather than the activities) of the two ions by measuring the potentials of the calcium-responsive and fluoride-responsiveelectrodes individually with respect to a saturated calomel reference electrode (SCE). By measurements in solutions of KF/KC1 and in solutions of CaC12/KC1,the standard emf values for the cells SCElISE were found to be -177.9 and 108.0 mV for the fluoride and calcium electrodes, respectively, at 25 "C. The corresponding Nernst slopes were 59.42 and 29.74 mV per decade. The salts used (KF, KC1, CaC12, and CaF2) were of reagent quality. Calcium fluoride was digested repeatedly under successive portions of boiling distilled water over a period of 2 days. Potassium fluoride was dried to constant weight, and a solution of recrystallized calcium
Communications to the
49 7
Editor
TABLE I: Equilibrium Data for Solutions of Calcium Chloride Saturated with Calcium Fluoride at 25 "C 1010- 1010Added lo4- K s p ICsp E (cell A), CaCl,, m 1O3mCaz+ m ~ -(eq 1 ) (eq 3) mV 0 0.000 431 0,001 030 0.001 997 0.003 108 0.005 279 0.009 155 0.013 27 0.023 72 0.037 96 0.055 33 0.079 30 0.100 1 0.116 8 0.130 3
0.855 1.16 1.66 2.50 3.51 5.46 9.00 12.8 22.3 35.6 52.0 75.9 96.9 115 129
6.36 5.41 4.63 3.76 3.22 2.63 1.99 1.76 1.36 1.06 0.868 0.715 0.625 0.563 0.529
2.05 2.71 2.94 3.38 3.74 3.66 4.13 4.41 4.29 4.18 4.06 3.90 3.70 3.64
3.38 3.57 3.53 3.64 3.77 3.56 3.95 4.14 4.01 3.92 3.89 3.18 3.65 3.61
4.8 4.5 5.2 4.4 5.4 5.9 5.2 6.5 7.1 6.7 6.4 6.3 5.9 5.5 5.4
chloride was standardized. An Orion 96-09 lanthanum fluoride electrode was used. The calcium ion-selective electrode made use of a membrane incorporating a neutral ligand ~ a r r i e r .The ~ electrodes were mounted, together with a commercial saturated calomel reference electrode, in the top of a water-jacketed titration cell provided with a magnetic stirrer and maintained at 25.0 OC. The cell was charged with a weighed quantity of 1 m KC1 and known excess of calcium fluoride. After the emf (measured by a Corning Model 112 pH electrometer) between each indicator electrode and the SCE had reached a constant value, successive weighed portions of a CaClZ/KClsolutions (ionic strength 1.0) were added and the measurements repeated. The ion-selective electrodes were calibrated on the molality (m) scale by emf measurements in solutions having the compositions CaC12(m),KC1 (1 3m) or KF(m), KC1 (1 - m), where m was varied over the range encountered in the reported experiments. Although as much as 12 h, with stirring, was sometimes required for equilibrium, the calibration remained essentially unchanged over the series of measurements. The results of the measurements of ion molalities in solutions of calcium chloride saturated with CaF2 are given in the first three columns of Table I. From these data, it is possible to calculate an apparent solubility product (K'Bp= mCaz+mF2)in three different ways. The first is by use of eq 1, as was done by Stearns and Berndt.l The others follow from the equations
Ktsp= rncaz+( meaSUred)rnF -'(measured)
(3)
and log K tsp = (E- Eo,
+ E°F)/k
(4) The fourth column shows that our measurements of mF confirm the variability found by Stearns and Berndt. When K' is calculated from the measured molalities of both Caz"p and F- ions, however, K'sp is more nearly constant (fifth column). The emf of cell A is listed in the last column of Table I. It is evident that the data are adequately represented by an emf of 5.5 f 1 mV, leading to a value of 3.31 X for Kip in 1 m KC1. When an estimate of y+(CaF2)by the Bransted-Guggenheim equation with interaction parameters appropriate to an ionic strength of 1.0 is applied, for the thermodynamic activity one finds 3.1 X product. This is in acceptable agreement with 4.9 X lo-", the literature value for this equilibrium ~ o n s t a n t . ~ It is noteworthy that the residual liquid-junction potentials in the measurement of the calcium and fluoride
ion molalities cancel in the calculation of log Kip by eq 4. Although the fluoride electrode is very suitable for measurements of this type, the stability and reproducibility of the calcium ion-selective electrode leave something to be desired. For this reason, an uncertainty of 1 mV does not seem unreasonable for this design of the experiment. We therefore conclude that KBpis in fact constant over a significant range of solution compositions but that the system cannot be completely defined by measurement of the fluoride ion molality alone. A possible clue to the reasons why the system defies simple definition is to be found in the results given in Table I for the first solution, which contained no added Ca2+.For this solution, one should be able to calculate K'Bp from either of the experimental parameters, mCaa+or m r , as follows:
Ktsp = 4mCa2+3 or
(5)
Ktsp = 0 . 5 m F - 3
(6)
The values of mcaz+and mF- determined experimentally for this saturated solution are in fact 8.55 X and 6.36 X mol kg-', respectively, far removed from the anticipated stoichiometric ratio of 1:2, so that eq 5 and 6 would lead to highly disparate values for K' . The product mCa2+mF2is nonetheless in reasonable accorBwith the main body of data, indicating that there is no serious experimental error. This observation suggests that F- is being adsorbed on the surface of the solid phase. Another illustration of this same effect is given by an experiment in which CaF2was added to a solution already in equilibrium with a known amount of the solid phase. In the absence of any surface effects, one would expect no change in the composition of the aqueous phase. Nevertheless, a rapid significant increase in mcaz+,with a compensating decrease in mp, was found, consistent with further surface adsorption of fluoride ions. The possibility that inclusion of soluble calcium in the CaFz was responsible for this result was minimized by repeated extraction and digestion of the CaF2 added. Anion adsorption would explain an initially low apparent KBp calculated from a measurement of the free fluoride ion concentration alone but cannot account for the decrease observed at higher molalities of calcium ion. At the pH of our solutions (about 6.0), ion pairing between H+ and F- is negligible and, furthermore, is relevant only to those calculations based on mF- alone. Stearns and Berndt controlled both the ionic strength and the pH with an acetate buffer, thus introducing the further complication of Ca2+-Ac- ion pairing. This may be expected to reduce their calcium ion concentrations by a factor of 5 but probably did not alter their conclusions. In both their study and ours, the existence of Ca2+-F- ion pairs has been ignored. Again this simplification is irrelevant when both mcaz+and mF- are measured independently. Although this equilibrium would alter the mass balance considerations necessary to the Sterns and Berndt method of calculating Kip, the effect is not serious. Finally, Stearns and Berndt' give as their criterion for saturation equilibrium the relations PCa2+,aq - PCa2+,s (7)
where p is the chemical potential. We believe that these equalities apply only to the electrochemical potential or The Journal of Physlcal Chemistv, Vol. 81, No. 5, 1977
498
Additions and Corrections
when the potential difference between the two phases is zero. In the words of Guggenheim? “For the distribution of ionic species i between two phases a, 0 of different chemical composition the equilibrium condition is equality of the electrochemical potential...”. On the other hand, the classical definition of the solubility equilibrium PCa2+,aq -k P F - = PCaF, ,s
(9)
is valid for both the chemical and electrochemical potentials. Furthermore, it is well established that activities of electrolytes derived from the emf of cells containing electrodes of the second kind (as, for example, AglAgCl or PblPbSOJ agree with those calculated from vapor pressure measurements or other colligative properties. If the Gibbs energy of the solid varied appreciably with the ionic concentration of the solution, agreement would not be found. Equation 9 does not lend support to the idea that ucaF2,+ varies with the solution composition or that the activity product is merely an approximation to the true constant. The study of Stearns and Berndt draws attention to the need for complete characterization of systems containing finely divided solids. Surface adsorption of ions in the calcium fluoride system, a function of both specific surface area and the ionic strength of the solution in equilibrium with the solid phase, can account for the apparent variability of the solubility product constant. Note Added in Proof. Since this communication was
submitted, we have been able to make surface area measurements on the digested CaFz used in these experiments. The specific surface area was 5 m2 g-l, or probably large enough for surface energies to influence solubility and adsorption properties. Furthermore, electrophoresis measurements on colloidal CaFz suspensions with and without added Ca2+and F- showed the particles to be carrying significant charge. The authors are grateful to John Horn and James Adair of the Department of Materials Science and Engineering for cooperation in these measurements.
Acknowledgment. This work was supported in part by the National Science Foundation under Grant CHE7305019 A02. References and Notes (1) R. 1. Stearns and A. F. Berndt, J. Phys. Chem., 80, 1060 (1976). (2) J. J. Lingane, Anal. Chem., 39, 881 (1967). (3) W. E. Mod,D. Ammann, E. Pretsch, and W. Simon, Pure Appl Chem, 36,421 (1973). (4) J. Bjerrum, G. Schwarzenbach, and L. G. Sillen, “Stability Constants of Metal Complexes”, Part 11, The Chemical Society, London, 1958. (5) E. A. Guggenheim, “Thermodynamics”, North Holland Publishing Co., Amsterdam, 1949, p 332.
Department of Chemistry University.of Florlda Gainesville, Florlda 326 1 I Received October 12, 1976
ADDITIONS AND CORRECTIONS 1977, Volume 81
R. A. Orwoll, R. H. Rhyne, Jr., S. D. Christesen,and S. N. Young: Volume Changes of Mixing for the System p,p’-Di-n-heptyloxyazoxybenzene + Xylene. Page 181. The title on this page incorrectly mentions p,p’-Di-n-hexyloxyazoxybenzene, whereas the article is concerned only with p,p-Di-n’-heptyloxyazoxybenzene. The same error occurred in the table of contents for the issue.-R. A. Orwoll
The Journal of Physical Chemistry, Vol. SI, No. 5, 1977
J. B. Macaskill Roger 0. Bates”
