and more reproducible. In 10-cm runs all R/’s were well within f 0.05 of the reported running rates on 15-cm runs, but the separation on the latter was better. Chromagram layers are hard, flexible, and durable in contrast to coated plates. The application devices may touch the layer on sheets repeatedly without leaving perforation marks. The lesser absorptivity of the thinner layer and the necessity of applying smaller aliquots prolonged the application time. The omission of any handling of finely powdered silica gel may be considered safer. Both types of Chromagram sheets were resistant to solvents used in chromatography. Water-rich solvent systems did not cause peeling or softening of the layers. Aggressive spray reagents (concentrated acids) and exposure to chlorine gas in tanks (up to 30 minutes) had no detrimental effects.
ACKNOWLEDGMENT
The author is indebted to Henry C. Freimuth for his advice and critical review of the manuscript, and acknowledges the help of James C. Schlaffer in the experimental work.
RECEIVED for review December 19, 1966. Accepted May 8, 1967. Part of this study was presented at the 746th Meeting 01 the ACS Washington Section, conducted jointly with the ACS Maryland Section, May 6th, 1966, at the University of Maryland, College Park, Md. Work supported by funds from Grant GM-11699 of the National Institutes of Health, U. S. Public Health Service, to the Maryland Medical-Legal Foundation, Inc., Baltimore, Md.
Calcium Electrode Method for Measuring Dissociation and Solubility of Calcium Sulfate Dihydrate F. S. Nakayama and B. A. Rasnick U.S. Water Conservation Laboratory, Phoenix, Ariz. 85040 MANYCA SALTS form both undissociated and dissociated species in solution. For example, when CaS04.2Hz0dissolves in water, three distinct species are present: the Ca+z and SOa-2 ions and undissociated calcium sulfate, CaS04; in sulfuric acid the complex Ca(HS04)+1is also present. The usual chemical techniques for Ca analysis give the total solution Ca and not the individual species. Thus, in order to study the dissociation of Ca salts, indirect methods involving either colligative or electrical properties are used, which require involved instrumentation and theoretical assumptions. Recently, Ca membrane electrodes became available, which provided an opportunity to measure Ca ion activity in solutions at various ionic strengths and made possible the estimation of the dissociation and solubility parameters based on the activity of the dissociated ion rather than on the total concentration. A successful determination of Ca activity in sea water was reported by Thompson and Ross ( I ) . Ross has also described the operational theory of the Ca electrode (2).
Calibration curves of CaC1, were run in water and in different concentrations of NaCl to simulate the ionic conditions anticipated for the CaS04-NaCl and CaS04-NanS04. The electrode was calibrated empirically to avoid any uncertainty in the value of Eoca in the Nernstian equation. Linear calibration curves were obtained for the plot of emf us. the log of the Ca activity. Triplicate measurements at 25” f 1” C were made for the saturated CaS04 solutions for each of the ionic strengths used. The computation of the various solution parameters for CaS04 from the Ca activity measurements is as follows. The Ca electrode measures the activity of the Ca+2in solution and is not responsive to the undissociated and complexed Ca in solution. For a completely dissociated Ca salt (Ca+*) = yca+z [Ca+r] where ( ) refers to the activity, [ 3 denotes the concentration, and yca+z is the ionic activity coefficient of Ca. For a partially dissociated Ca salt, however, the relation must be modified as follows: (Ca+2) =
EXPERIMENTAL Apparatus. Ca activity (Ca+3 was measured with the Orion Ca membrane electrode in conjunction with a saturated KCI, Hg-Hg2Clz reference electrode and a Corning Model 12 pH-millivoltmeter Solutions. Saturated solutions of CaSOa were prepared by dissolving CaS04.2H20in deionized distilled water and in NaCl and NatS04 solutions of various concentrations up to 0.1M. Procedure. The Ca electrode was calibrated with standard CaC12 solutions, as CaClz is completely dissociated (3). (1) M. E. Thompson and J. W. Ross, Jr., Science, 154, 1643
(1966). (2) J. W. Ross,Jr., Science, in press (1967). (3) W. J. Hamer, Ed., “The Structure of Electrolyte Solutions,” Wiley, New York, 1959, p. 26.
1022
ANALYTICAL CHEMISTRY
ayca+z [Ca+%
(2)
where a is the degree of dissociation of the dissolved salt; [&+ZIT is the total calcium in solution as determined by the versenate, or equivalent, method; (Caf2) is the activity of the salt in solution as measured by the Ca electrode. The product ayc.+z can be calculated from experimentally determined values of (Ca+2) and [Ca+2]~.a and ycS+z are not independent of one another, being related to the ionic strength via the concentration of ions in solution. In the calculation procedure a! and 7 C . t z were determined by an iterative process from measured values of (Ca+2) and [Ca+2]~.An arbitrary value between 0 and 1 was selected for yca+z and a was estimated using Equation 2. From the calculated a,the concentration [Ca+*] was determined using the relation [Ca+Z] = a[Ca+2IT. Subsequently, the ionic strength, p = Zzi2 ci/2, and the activity coefficient, ycn+_2, from the relation log yca+z = - A z 2 d i / ( l B a d d , were calculated, The necessary constants were taken from
+
Table I. Dissociation and Solubility Product Constants of Cas04 at Saturated CaSOI (Ca+z x 103) /l x lo2 [Ca+% X 102 plus the following 4.21 1.47 5.4 (Sat’d CaS04only) 4.17 1.47 5.2 + O , 001 M NaCl 5.44 1.59 5.3 + O . 01M NaCl 7.43 1.69 5.5 +O. 025M NaCl 10.58 1.86 5.6 f O .050M NaCl 13.80 2.00 5.7 +O, 075M NaCl 16.80 2.13 5.9 + O . 1 M NaCl 4.24 1.45 5.0 +0.001M Na2S04 5.59 1.23 3.5 +0.01M Na2S04 7.74 1.08 2.6 +O .025M Na2S04 17.28 1.01 2.0 +O. 050M Na2S04
tabulated values of Klatz (4). From the new value of ycS+z another value of a was estimated and the process was repeated until the values of yca+z and a remained constant. The apparent dissociation constant KO’ was determined by the relation
The activity coefficient of the undissociated CaSO, was taken as unity. In the sulfate concentration, corrections for the undissociated S 0 4 - 2 as NaS04- were made using &.so4= 0.19 (5). The formation of HS04- was also considered, but under the experimental conditions, the amount of HS04- present was calculated to be negligible compared to the SO4+ concentration, and thus was not included in the final computation. The apparent solubility product was calculated from
K,’ = ([Ca+21~ X aX
yca+2)
([S04-21T X
CY
X y~0,-2) (4)
Molar, instead of molal, concentration was used throughout, because the dflermces between the two concentration systems are insignificacl at the low concentrations reported here. RESULT’S AND DISCUSSION
The apparent dissocizition and solubility product constants of CaS04 at the different ionic strengths are listed in Table I, together with their respective degree of dissociation. An element of doubt exists for the singular determinations of these constants, because we had to assume the validity of the Debye-Huckel theory for the system described. Ca activities and concentrations in unsaturated CaS04 solutions and in saturated solutions containing combinations of NaCl and (4) I. M. Klotz, “Chemical Thermodynamics,” Prentice-Hall, New York, 1950, p. 330. (5) J. L. Jenkins and C. B. Monk, J. Am. Chem. Soc., 72, 2695 (1950).
Various Solution Compositions ff
KD’x 103
0.76 0.69 0.70 0.73 0.75 0.78 0.80 0.68 0.61 0.56 0.57
6.37 5.60 5.12 5.83 5.38 5.83 5.90 5.17 5.08 6.16 6.56
Ks’ X 106 2.67 2.55 2.44 2.66 2.50 2.56 2.51 2.40 2.44 2.92 2.85
Na2S04were also determined. The experimental errors for the diluted samples became large because of the limitations in the chemical and electrode analyses and thus were not used in the calculation of K D ’ . The apparent linear and logarithmic solubility product varied with the ionic strength as Ks’ = 2.50 X 6.27 X p, and log Ks’ = - 4.60 0.163 p , respectively. If the Debye-Huckel theory and the ion-pair concept described the system entirely, a line of zero slope would have been obtained, but this does not seem to be the case with the data presented. However, on extrapolation to zero ionic strength, the resulting value should be independent of the assumption used for the calculation of y. Ks at zero ionic strength is (2.50 =t 0.10) X compared to a KS of 2.45 X reported recently by Moreno and Osborn (6). The apparent linear and logarithmic dissociation constants followed the relation KD’ = 5.32 X 4.78 X 10-3 p, and log K D’= - 2.28 0.363 p , respectively. K D at infinite dilution is (5.32 A 0.37) X compared to values of 4.9 X and 5.3 X obtained by solubility and conductometric methods (7). The irregularity of KD was greater than that of Ks because the values of the former were accentuated by the use of both factors a and (1 - a). The good agreement between the K D and Ks values obtained for the CaS04, CaS04-NaC1, and CaS04-Na2S04 systems with the Ca electrode and that derived from other independent techniques gives assurance that the electrode is measuring the activity of the Ca ions.
+
+
+
+
RECEIVED for review March 16, 1967. Accepted May 8, 1967. Trade names and company names, when included, are for the convenience of the reader and do not imply preferential endorsement of a particular product or company over others. (6) E. C. Moreno and G. Osborn, Soil Sei. SOC.Am. Proc., 27, 614 (1963). (7) R. P. Bell and J. H. B. George, Trans. Faraday SOC.,49, 619 (1953).
VOL. 39, NO. 8, JULY 1967
1023
