THERMODYNAMICS OF CALCIUM SULFATE DIHYDRATE
4015
Thermodynamics of Calcium Sulfate Dihydrate in Aqueous Sodium Chloride Solutions, 0-1 10°112
by William L. Marshall and Ruth Slusher Reactor Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee
(Received June I S , 1966)
An evaluation of the extensive solubility measurements of calcium sulfate dihydrate in aqueous sodium chloride solutions obtained in this study further confirmed that the variation of the ion solubility product could be described to high ionic strengths (2 m) at temperatures from 0 to 110" by only one parameter, commonly referred to as the "ion-size parameter," d, in the extended Debye-Huckel expression. This evaluation yielded a constant value of 4.5 A for d over the entire range of temperature. At ionic strengths above 2 m and at low temperatures, the ion solubility products showed negative deviations from the one-parameter expression in contradiction to the expected behavior for the association of Ca2+or S02- with Na+ or C1- ions. The negative deviation could be described by the inclusion of two additional terms which essentially approach zero at the higher temperatures. This behavior may suggest a decrease in the structure of water as the temperature rises and thus an increase in the simplicity of aqueous solutions at high temperatures compared to their behavior at 25". From the derived solubility product constants, values for AGO, AH", AS", and AC," were determined along with the variation of thermodynamic functions with the ionic strength and temperature. At temperatures of 70-95" and at high concentrations of NaC1, a double salt of cas04 and Na2S04,in addition to CaS04.2Hz0,saturated the solution phase.
Introduction I n a previous study at this l a b ~ r a t o r yit, ~was shown that the variation of the ion solubility product for CaS04and its hydrates could be expressed to high ionic strengths (2 m) at temperatures to 200" by only one parameter, A , in the extended Debye-Huckel expresA d ) , where I is the ionic strength, sion, dT/(l A = bd, b is a function of the absolute temperature and dielectric constant, and it is the parameter commonly called the "ion-size" parameter. The questions not entirely answered were (1) whether the assumption that calcium sulfate is essentially dissociated in aqueous media is valid, (2) whether additional terms to express the ion solubility products a t ionic strengths approaching 6 m did smoothly drop out as the temperature rose above 25", (3) whether either A or d is a constant or varies with the temperature, a subject of much controversy but with little or no experimental data for support, (4) whether the standard heat of solution, AH", did indeed become zero at -30", and ( 5 ) whether
+
sufficiently accurate data for extrapolation could be obtained over a very wide temperature range to allow the calculation of meaningful values not only for AGO, AH", and AS" but also for AC," for the dissolution of CaS04-2Hz0into water solution. In view of the very few comprehensive studies originating at low temperatures and extending to temperatures above lOO", definite answers to some of the above questions would give further insight into the particular system under study, the general nature of the electrolyt,e solutions in the virgin high-temperature region, and the nature of the solvent, water. Therefore, in the present extensive ~~~
(1) Work sponsored by the Office of Saline Water, U. S.Department of the Interior, and performed at the Oak Ridge National Laboratory which is operated by the Union Carbide Corporation for the U. S. Atomic Energy Commission. Presented before the Division of Physical Chemistry at the 151st National Meeting of the American Chemical Society, Pittsburgh, Pa., March 22-31, 1966. (2) Paper No. X V I in a series, "Aqueous Systems at High Temperatures." Previous paper, W. L. Marshall and R. Slusher, J. Chem. Eng. Data, 10, 353 (1965). (3) W. L. Marshall, E. V. Jones, and R. Slusher, ibid., 9, 187 (1964).
Volume 70.Number 12
December 1966
WILLIAML. MARSHALL AND
4016
study many additional solubilities of calcium sulfate dihydrate were measured at temperatures from 0 to 110" and to sufficiently high concentrations of sodium chloride (-6 m), where either NaCl or another solid phase was found to saturate the solutions. From these results the thermodynamic behavior of this system at saturation vapor pressure is described over its entire range of stability. Values for the solubility product constants and the variation of the ion solubility product with the ionic strength and temperature are obtained at the several temperatures from which the thermodynamic functions at zero and high ionic strengths are calculated. The interpretation of these results by means of the extended Debye-Huckel expression with the one A parameter shows that very good agreement can be obtained by assuming that CaS04 in solution completely dissociates to Ca2+and S042-ions, within the limits of detect,ionof our method. Additional terms to express the ion solubility products were essentially unnecessary at temperatures somewhat above 25" , thus strongly suggesting the assumed breakdown in the structure of water at the high temperatures. A constant value for the ion size, d, of 4.5 A was observed over the entire range of temperature. The value for AH" did reach zero at 30", and the over-all data were found to be sufficiently accurate to obtain estimates for ACpo in reasonable agreemen t with other independent estimates. The thermodynamic functions are compared with analogous values for CaS04 (anhydrite) from which the change in the transition temperature with ionic 2H20, was strength, CaS04.2H20(s)--+ CaSOr(s) calculated and compared with some literature values. The thermodynamic functions for this reaction over a range of the ionic strength and temperature were also obtained.
+
Experimental Section The reagents used and their methods of purification have been stated previously. Experimental procedures have been described before3 except that a refrigeration unit was added to the thermostat bath for use between 0 and 25". Most experimental runs at 70-110" were made in the high-pressure vessels described el~ewhere.~Samples of the liquid phase were removed periodically for calcium analysis by EDTA potentiometric titration.6 For analyses for NaCl, liquid samples were either dried and weighed, or poured through a cation-exchange resin to remove Na and Ca, and subsequently titrated for the remaining HC1 and H2S04. With either method the analyzed quantity of CaS04 was subtracted from the total quantity of CaS04 and NaCI. In one set of experiments at 70", The Journal of Physical Chemistry
RUTHSLUSHER
where various weighed quantities of Na2SOIwere added to a NaCl solution saturated with both C&O4 .2H20 and a second solid, the solution-solid mixtures were heated in a flask that was connected to a reflux condenser. A magnetic stirrer-hot plate unit was used; by adjustment of the heat output, the temperature could be held constant to k2". Solid phases were removed initially and periodically and dried rapidly by the vacuum filtration of the excess liquid phase. The solids were examined with a petrographic microscope and were identified by the comparison of the properties with those of known compounds.s
Results and Discussion SpeciJic. The solubility equilibrium under study CaS04-2H20(s)
Ca2+
+ 502- + 2H20
can be expressed by a solubility product constant Ksp"
(1)
= aCa2+%0,2aHz02
= ~ C ~ ~ + ~ S O , ~ - Y C ~ " + Y S O I ; - ~(2) HZO~
KSP(p)YCaa +YSOp4Hz02
(3)
where K,," is the solubility product constant for CaS04.2H20 at zero ionic strength, acaat, USO,;-, and a H Z 0are the activities of the several species, mcact and msora- are the analytical molalities of the ions, ycazt and ySol2- are their respective activity coefficients, and Kap(P) is a practical ion solubility product (= [Ca2+][S042-]). The ion solubility product that includes the activity of water will be considered the "true" product where and therefore we shall let K,,(T) = K,,(P)UH~O~ KBP(T)+ KSP(P)-+ K,," as the ionic strength approaches zero and a H 2 0 approaches unity. From an extended Debye-Huckel relationship and the addition of linear and quadratic terms, the ion solubility products can be expressed by log Ksp(T)
=
log Kap" 8Sfl/(l
+ + ABPdI)+ BI - C12
(4)
and logK,p(P) = log K,," 8SdI/(l
+
+ A s p d I ) + B'I
- C'P
(5)
where S is the Debye-Huckel limiting slope X d d G , I is the ionic strength (= 4 X molal solubility of CaSOl molality of NaCl), and A,,, B , B', C , and C' are adjust-
+
(4) J. s. Gill and W. L. Marshall, Rea. Sei. Instr., 32, 1060 (1961). ( 5 ) H. A. Flaschka, "EDTA Titrations," Pergamon Press Ltd., London, 1959. (6) A. E. Hill and J. H. J . ~ m Chem. . SOC., 60, 1647 (1938).
wills,
THERMODYNAMICS OF CALCIUM SULFATE DIHYDRATE
able parameters, where B' and C' account also for the variation of aH102with I. Since in our experiments mcar+= msO,,-, eq 5 for log K,,(P) reduces to logs
=
log so
+
4017
+
so and 2/?/(1 &,
