AQUEOUS SYSTEMS AT HIGHTEMPERATURE
2641
Aqueous Systems at High Temperature. XVIII.
Activity Coefficient
Behavior of Calcium Hydroxide in Aqueous Sodium Nitrate to the Critical Temperature of Water'J
by LeRoy B. Yeatts and William L. Marshall Reactor Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tenneseee (Received January SO, 1967)
From very extensive measurements of the solubilities of calcium hydroxide in aqueous sodium nitrate solutions, covering essentially the entire concentration range of supporting electrolyte at nine temperatures from 0" to near the critical temperature of water, the activity coefficients of calcium hydroxide were calculated. When the solubilities were plotted against a Debye-Huckel function of the ionic strengthI, dj/(l b d d T ) , where b is a function of temperature and dielectric constant and d is the ion size, a striking, nearly linear relationship to moderately high ionic strengths was found over the entire range of temperature. The results yielded values for the mean ion size varying from 5.5 A at 0' to 3.8 A at 350'. This study, believed to be the first extensive work on a base to the extremes of temperature, shows that the salting-out effect observed routinely in electrolyte systems at normal temperatures disappears completely a t high temperatures. The explanation may lie in the formation of a complex between and the supporting electrolyte. In addition to activity coefficients, the solubility product constants and thermodynamic quantities for calcium hydroxide were obtained to 350°, the highest temperatures for previous values being in the vicinity of 25'.
+
Introduction Studies of the behavior of aqueous electrolyte solutions are for the most part limited to temperatures below loo", the boiling point of water at 1 atm. This is very evident upon contrasting the phenomenally large number of studies made below 100" with the very small number above 100" (although water still can coexist with its vapor phase to 374"). I n this laboratory, equipment has been developed that makes it possible to study solubility equilibria readily at temperatures up to the critical temperature of water. By using the solubility of calcium sulfate (and its two hydrates) as a tool, not only has it been shown3z4 of the that the behavior of the mean activity 2-2 electrolyte Calcium Sulfate in 1-1 electrolyte Sohtions follows an extended Debye-Huckel equation to very high ionic strengths (6 m) and to the highest temperature studied (350") but also that the variation
sociation of sulfuric acid follows this same linear relationship. To observe the activity coefficient behavior of other types of electrolytes, especially a base that contains a hydrogen-bonding ionic species, OH-, extensive solubility measurements on calcium hydroxide were performed at temperatures from 0 to 350", near the critical temperature of water. To cover a wide range of ionic strengths, the measurements were made in supporting electrolyte solutions of sodium nitrate from zero to nearly saturated molalities. Calcium hydroxide was chosen for study because of its low solu(1) Research sponsored by U. 9. Atomic Energy Commission under contract with the Union Carbide Corp. and performed a t Oak Ridge National Laboratory, Oak Ridge, Tenn. 37830. (2) Previous paper in series: W. L. Marshall and E. V. Jones, J . Phys* 70*4028 (1966)* (3) W. L. Marshall, R. Slusher, and E. V. Jones, J . Chem. Eng. Data, 9 . 187 (1984).
Volume 71, Number 8 July 1967
LEROYB. YEATTS AND WILLIAM L. MARSHALL
2642
bility both a t low and high temperatures that would allow short extrapolations to zero ionic strength. Sodium nitrate was selected as a supporting electrolyte for its thermal and hydrolytic stability, its noncorrosive behavior on the titanium-alloy container vessels, and its very high solubility (6-7 m) which provides high ionic strengths. Activity coefficients of calcium hydroxide in supporting electrolytes can be obtained only at 25" from the previously published solubility measurements of Johnston and Grove.5 Solubilities in water alone at 2040" are very numerous16 to 100" are considerable,' and to 250" are few6vg(one point a t 150°,6several points to 250°9). Measurements in water alone, however, do not allow the attainment of activity coefficients because the solubility product constants (at I = 0) are not available. From the measurements presented herein, values for the solubility product constants were obtained from 0 to 350" by use of an extended Debye-Hiickel b d d I ) . With these constants, function, dI/(l the mean activity coefficients of calcium hydroxide were calculated to very high ionic strengths over the entire range of temperature. The results, a discussion of their general significance with regard to ion size, salting-out effect, activity coefficients, and the contrasting behavior of this water-salt system a t low and high temperatures are presented in addition to the thermodynamic quantities that were calculated.
+
Experimental Section Reagent grade calcium hydroxide (or calcium carbonate) was treated several times in boiling deionized water3 to remove any soluble impurities, filtered, and the recovered product dried a t 100". The dry calcium hydroxide was ignited a t 1150" for approximately 16 hr to convert calcium carbonate impurities to calcium oxide: the carbon dioxide content of the freshlv ignited Oxide was found to be about 250 ppm' In the experiments at 25" the apparent of calcium hydroxide in water was measured as 0.0226 m , about lo% too high On the basis Of Other experiments16 and noted also by Bates and co-workers.6 A solubility of 0.0203 m was obtained within l-hr rocking time by use of calcium hydroxide predigested a t 250" for 4 hr in a high-pressure vessel; this product therefore was used for all measurements at 0.5 and 25". Either 'lid was and for measurements a t higher temperatures. Excess solid calcium hydroxide or mixtures of talcium carbonate and calcium hydroxide were equilibrated with either deionized water or sodium nitrate (Baker Analyzed reagent) solutions prepared with deThe Journal of Physical Chemistry
ionized water. The containing vessels for the 0.5 f 0.1 and 25.0 f 0.1" experiments were 50-ml glassstoppered Pyrex bottles; the ground-glass surfaces were coated with Kel-F 800 (Spray-on Products, Inc.). The vessels and their contents were rocked in a constant-temperature bath for 2-5 hr. Previous experiments showed that 1 hr was sufficient time for equilibrium to be reached between washed calcium hydroxide and the liquid phase. The experimental equipment and the procedures used for temperatures between 50 f 1 and 350 f 1" are described in earlier p a p e r ~ . ~ - ~Normally, J~ the solutions in the highpressure vessels were sampled a t three different temperatures. The vessels and their contents were rocked a t the lowest temperature for at least 64 hr and a t each of the higher temperatures for about 22 hr. A sample of each solution was filtered during sample withdrawal, a t the temperature of the experiment, to remove suspended solids. Porous glass was used for filtering a t 0.5 and 25" while porous Teflon was used between 50 and A known volume of each solution sample was treated with excess concentrated nitric acid, evaporated to dryness at loo", and weighed rapidly as a mixture of sodium and calcium nitrates. Another portion of each sample was analyzed for the calcium ion concentration by means of a semimicro potentiometric titration" with standard EDTA (ethylenediaminetetraacetic acid) solution (-0.01 M ) . The sodium nitrate concentration in the solution was determined by the difference between these two analyses. The densities of aqueous sodium nitrate solutions12were used t o convert molarity to molality.
Results and Discussion General Results. The experimental results for the solubilities of calcium hydroxide in aqueous sodium (5) J. Johnston and C. Grove, J . Am. Chem. SOC.,53, 3976 (1931). (6) L. B. Miller and J. C. Witt, J . Phys. Chem., 32, 285 (1929); J. Johnston and C. Grove, J. Am. Chem. SOC.,53, 3976 (1931); I. M. Kolthoff and V. A. Stenger, J. Phya. Chem., 38, 639 (1934); N. Fratini, Ann. Chim. Appl., 39,616 (1949);R.G.Bates, V. E. Bower, and E. R. Smith, J . Res. Natl. Bur. Std., 56, 305 (1956). (7) A. d'Anselme, Bull. SOC.Chim., (3) 29, 936 (1903); H. Bassett and H. S. Taylor, J . Chern. SOC.,105, 1926 (1914); R. T . Haslam, G. Cdingaert, and C. M. Taylor, J. Am. Chem. SOC., 46,308 (1924); H. Barnett, J. Chem. Soc., 1270 (1934). (8) w. A. Shenstone and J. T. Cundall, J. Chem. SOC., 53, 544 (1888). (9) R. B. Peppler and L. S. Wells, J. Res. Natl. Bur. Std., 52, 75
(1954). (10) J. S. Gill and W. L. Marshall, Rev. Sci. Instr., 32, 1060 (1961). (11) H. A. Flaschka, "EDTA Titrations," Pergamon P ~ S Ltd., S London, 1959. (12) "International Critical Tables," Vol. 111, McGraw-Hill Book CO.,Inc., New York, N. Y., 1928,p 82.
AQUEOUSSYSTEMS AT HIGH TEMPERATURE
2643
Table I: The Molal Solubilities of Ca(0H)S and Mixtures of Ca(OH)z T = 0.5OC NaNO, (m) 0 0 0
0.0487 0.219 0.412 0.882 1.24 2.73 4.87 4.87 4.87 4.87 NaN03 0
0.231 1.28 4.52
Ca(OH)2e (m) 0.0229 0.0228 0.0226 0.0252 0.0300 0.0327 0.0369 0.0377 0.0390 0.0363 0.0379 0.0280 0.0379
CaCO, a + Ca(OH)2' 0.0225 0.0284 0.0380 0.0375
NaNOJ 0.0527 0.229 0.437 0.888 1.33 2.80 4.72 NaN0, 0 0
,0.0530 0.0530 0.23 1 0.23 1 0.423 0.423 0.927 0.927 1.27 1.27 2.91 2.90 4.52 4.52
0
0.0195 0.102 0.207 0.390 0.842 2.31 4.79 NaN0, 0
0.0545 0.106 0.259 0.547 1.23 3.19 4.89
0
0.0661 0.113 0.268 0.596 1.34
CaCO, i-Ca(OH)2 0.00999 0.00999 0.0107 0.0126 0.0138 0.0148 0.0170 0.0173 0.0183 0.0185 0.0177
0.0242 0.103 0.205 0.311 0.822 0.827 2.11 2.15 4.71
CaCO, -t Ca(OH)? 0.0199 0.0199 0.0222 0.0222 0.0259 0.0259 0.0281 0.0282 0.0308 0.0306 0.0320 0.0316 0.0337 0.0323 0.0303 0.0296
NaN03 0
Ca(OW2 0.00737
NaN03 0
CaC0, Ca(OH)? 0.00733
C d W 2 0.0167 0.0181 0.0201 0.0220 0.0241 0.0260 0.0268 0.0233
+
CaC0, Ca(OH)2 0.0174 0.0191 0.0204 0.0230 0.0248 0.0271 0.0267 0.0230
T = 75OC NaN03
NaN03
0.00999 0.0103 0.0109 0.0119 0.0129 0.0129 0.0139 0.0147 0.0156 0.0164 0.0174 0.0183 0.0187 .o.o 181 0.0177 0.0170
Ca(OH)2 0.0202 0.0202 0.0224 0.0264 0.0286 0.0307 0.0320 0.0320 0.0289
T = SO°C NaN03
0.0235 0,0215
T = 100°C NaN03 0 0 0.0231 0.0549 0.104 0.116 0.212 0.286 0.416 0.542 0.834 1.35 2.33 2.79 4.71 5.57 0 0
'T = 25'C 0 0
3.18 4.95
+
Ca(OH), CaCO, 0.0138 0.0156 0.0168 0.0188 0.0209 0.0228
T = 125OC
+
T = lSO°C NaNOJ 0 0
0.0257 0.106 0.205 0.415 0.840 2.243 4.71 NaN03 0
0 0
0.0483 0.0590 0.0975 0.110 0.246 0.496 1.25 2.65 5.76
Ca(OW2 0.00543 0.00552 0.00619 0.00756 0.00856 0.00979 0.0114 0.0133 0.0139
+
CaCO, Ca(OH)? 0.00533 0.00540 0.00552 0.00670 0.00691 0.00747 0.00768 0.00878 0.0101 0.0122 0.0134 0.0137
T 5: 175'C NaN03 0 NaN03 0
0 0
0.0232 0.105
NaN03 0 0 0.0224 0.102 0.208 0.305 0.818 2.12 2.30 4.61
0 NaN03
0
+
CaCO, Ca(OH), 0.00282 0.00288 0.00334 0.00464 0.00565 0.00591 0.00768 0.00995 0.0103 0.0122
Ca(OH)2 0.00209
+
CaCO, Ca(OH)Z 0.00203
T = 2SOoC NaN03 0 0 0.0225 0.103 0.106 0.216 0.256 0.416 0.513 0.846 1.30 2.2s 2.70 4.61 6.29
WOW2 0.00146 0.00142 0.00181 0.00257 0.00265 0.00327 0.00345 0.004 12 0.00440 0.00556 0.00660 0.00852 0.00929 0.01 18 0.0139
NaN03 0 0 0 0 0.00427 0.00464 0.0119 0.0120 0.0213 0.0369 0.0720 0.0993 0.102 0.197 0.246 0.404 0.503 0.804 1.30 2.15 2.71 4.54 5.97
CaCO, Ca(OH)2 0.00136 0.00147 0.00130 0.00138 0.00143 0.00 144 0.00166 0.00160 0.00173 0.00198 0.00228 0.00241 0.00246 0.00303 0.00316 0.00377 0.00418 0.00510 0.00619 0.00794 0.00851 0.0110 0,0119
+
T = 275OC NaN03
0.00401 CaCO, Ca(OH)?
0
NaN03
Ca(OW2 0.000909
+
CaCO, Ca(OH)? 0.000872
T I 3OO0C
0.00394
WOW2 0.00287 0.00297 0.00348 0.00456
0.00518 0.00633 0.00779 0.0104 0.0124
T a 225OC NaN03
0
T=200°C NaN03
0.210 0.417 0.837 2.38 4.68
Ca(OH)2
+
+ CaCOt in Aqueous NaN03,0.5350'
NaN03 0 0
0.0218 0.0545 0,107 0.122
Ca(OH)2 0.000604 0.000641 0.000946 0.00129 0.00 155 0.00172
0.207 0.308 0.425 0.542 0.838 1.41 2.17 2.77 4.65 NaN03 0 0 0
0.0202 0.0228 0.0516 0.0995 0.104 0.106 0.133 0.203 0.210 0.262 0.399 0.423 0.530 0.815 0.848 1.34 2.21 2.53 4.44 6.24
0.00220 0.0027 1 0.00288 0.00333 0.00449 0.00565 0.00765 0.00900 0.0144 CaCO, + Ca(OH)z 0.000575 0.000548 0.00056 1 0.000765 0.000794 0.00 101 0.00147 0.00129 0.00135 0.00157 0.00176 0.00177 0.00200 0.00238 0.00248 0.00305 0.00360 0.00390 0.00540 0.00677 0.00738 0.0108 0.0142
T = 325OC NaN03
Ca(OW2
0
0.0003 17
NaN03
0
+
Ca(OH)2 CaCO, 0.000371
T = 35OoC NaN03 0 0
0.0250 0.116 0.232 0.235 0.46 1 0.549 0.875 0.878 2.27 2.34 4.81 4.91 NaN03 0 0 0 0 0
0.00484 0.0137 0.0139 0.0241 0.106 0.113 01120 0.230 0.45 1 0.541 0.826 0.856 0.954 1.37 2.18 2.43 2.80 4.62 6.26
Ca(OW2 0.000197 0.000192 0.000445 0.000923 0.00128 0.00142 0.00178 0.00235 0.0033 1 0.003 14 O.OC661 0.00733 0.0129 0.01 25 CaCO, .t- Ca(OH)2 0.0001 90 0.000177 0.000170 0.000144 o.000146 0.0001 68 0.000270 0.000276 0.000328 0.000639 0.00065 1 0.000705 0.00107 0.00173 0.00177 0.00269 0.00296 0.00331 0.0 0 3S 9 0.00619 0.00661 0.00725 0.0116 0.0144
' Saturating solid phase(s).
Volume 71, hTumber8 July 1967
LEROYB. YEATTSAND WILLIAML. MARSHALL
2644
T 350 300
40-f
250
200
("C)
450
100
75
50
25
f5'
0
5
2 (0-2 c
.2
=s E
5
N
c
g
2
0
40-3
5 AND TAYLOR (43!4)
2 d
FRATlNl (13491
io-4 1.4
1.6
4.8
2.0
2.2
2.4
2.6
2.8
'3.0
3.2
3.4
3.6
3.8
'/T(*KI (03
Figure 1. Solubility of Ca(OH), in water from 0 to 350".
nitrate at temperatures from 0.5 to 350" are presented in Table I. A comparison of the solubilities in water with those of earlier investigators is shown in Figure 1. Agreement is generally good, but with a marked difference between the present results and the two points of Peppler and WellsQat 200 and 250". Table I also includes measurements of the calcium moIality at saturation where both calcium carbonate and calcium hydroxide were the simultaneous saturating solid phases. These determinations were made over the same range of salt molality and temperature where calcium hydroxide alone was the saturating phase. Comparisons up t o 250" of the values in Table I show essentially identical results in the presence or absence of solid calcium carbonate. Therefore, the solubility curves up t o 250" shown in Figures 1 and 2 were drawn through the combined results. At 250" and above, however, the molality of calcium in sodium nitrate solutions was slightly lower when the two saturating solids were present than when calcium hydroxide alone was the saturating solid. Debye-Huckel Treatment; Ion Size. Calcium hydroxide was assumed t o ionize completely according t o the solubility equilibrium Ca(OH)&)
Ca2+(aq)
+ 20H-(aq)
(1)
The solubility product constant expression for this equilibrium is The Journal of Physical Chemistry
K,,"
=
mCar+moH-2ycan+yOH-2
(2)
where mCar+and moH- are the molalities of the ions and Y C a z t and y O H - are their respective activity coefficients. If K,, is substituted for mCsr+m0H-2, a mean activity coefficient yk used, and the logarithm of the expression taken, eq 2 becomes log K,," = log K,,
+ log y*'
(3)
An extended Debye-Huckel expression of the form log y i = -2SI"2/(1
+
- BI - C12
(4)
was used, where S is the limiting DebyeHuckel slope for a 1-1 electrolyte, I is the ionic strength in molal units (= mNsNOp and A , B, and C are constants for a given temperature. The substitution of this expression into eq 3 relates the solubility product to the ionic strength
+
log K,, = log K,,"
+
6SI1/'//(1
+ AI'/') + 3BI + 3C12
(5)
The assumed chemical equilibrium indicates that K,, = 4s3 and K,," = 4(s")3, where s is the molal solubility of calcium hydroxide a t ionic strength I, and so is the hypothetical solubility a t zero ionic strength. Use of these equalities with eq 5 leads to logs = log so
+ 2SI1"/(l + AI"*) + BI + C12
(6)
2645
AQUEOUSSYSTEMS AT HIGHTEMPERATURE
IO'
,
0
I
I
0.i
0.2
I
I
I
1
0.4
0.5
0.6 TEUPERATURE
Figure 2. Solubility of Ca(0H)t in aqueous NaNOa from 0.5 to 350'.
This equation was used t o obtain the best leastsquares fit13for all the experimental values given in Table I. The values of the A , B, and C parameters, unsmoothed with respect t o temperature, obtained by this method are plotted as a function of temperature in Figure 3. The limiting slopes, 8,for use with molal units2 are listed in Table I1 along with the smoothed values for Kspo,A , B, and C. The A parameter is equivalent to the bd factor14 frequently used in the Debye-Huckel equation. Calculated values for b15 were used with the corresponding A parameters to obtain values for d of 4.6, 5.0, 5.4, 5.3, and 4.8 A at 0.5, 25, 100, 200, and 300", respectively. These "ion sizes" are quite reasonable." The B and C parameters at 0.5 and 25" for calcium hydroxide in sodium chloride solutions (see Figure 3) differ somewhat from those in sodium nitrate and were calculated from experimental solubilities given in Table 111. The magnitudes of the last two terms in eq 6 are important only a t the highest ionic strengths. This is shown by a plot of log s vs. I'Ia/(l AI'"), which produces a straight line a t low ionic strengths (Figure 2). At temperatures up to 150" the straight-line relationship holds at ionic strengths as high as 0.5. Above 150" the solubility curves approach a straight line only
+
('Cl
Figure 3. Variations of the A, B, and C parameters with temperature for the description of the mean activity coefficient of Ca(OH)2 in aqueous NaNOa solutions, 0-350".
Table 11: The Parameters for the Extended Debye-Huckel Expression and the Solubility Product Constant for Ca(OH)*at Different Temperatures T, OC
s
A
B
0 25 50 75 100 150 200 250 300 350
0.4875 0.5080 0.5337 0.5648 0.6006 0.6899 0.8097 0.9848 1.287 1.984
1.48 1.63 1.74 1.83 1.90 2.03 2.10 2.14 2.16 2.16
-0.021 -0.027 -0.027 -0.020 0.010 0.053 0.015 0.160 0.218
C
O.OO0
-0.0040 -0.0029 -0.0019 -0.0011 -0.0008 -0.0028 -0.0056 -0.0088 -0.0125 -0,0164
Ksp'
1.32 X 9.37 X 5.68 X 3.05 X 1.47 X 2.68 X 3.74 X 4.27 X 4.13 A 3.51
Calculated by extrapolation of eq 11 to 350'; from eq 6, K,," for 350" = 1.08 X
loe6 lo4 lo4 lo-' lo-' lo-'
lo-'
lo-' lo-''
using so
(13) M. H. Lietake, AEC Report ORNG3259, April 1962. (14) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed (rev), Butterworth and Go., Ltd., London, 1965, pp 230-238. (15) H. S. Harned an$ B. B. Owen, "The Physical Chemistry of Electrolytic Solutions, Reinhold Publishing Corp., New York, N. Y., 1958, pp 164-166.
Volume 71,Number 8 July 1967
LEROYB. YEATTSAND WILLIAM L. MARSHALL
2646
Table I11 : The Molality of Calcium a t Saturation from CaCOs and Ca(OH)2Mixtures in Aqueous NaCl a t 0.5 and 25"
+ Cs(0H)P
-CsCOa5
NaC1,
Cas+, m
m
0.05
--
0.02
-I
T
0.0224 0.0247 0.0283 0.0305 0.0321 0.0333 0.0316 0.0268
0 0.0480 0.201 0.407 0.829 1.77 2.66 4.39
T
&
z
0.04 0.40
(u
c
- 0.05 I
0
0.02
= 25"
0 0.0480 0.201 0.407 0.829 1.77 2.66 4.39 a
a
= 0.5"
0.01
0.0200 0.0219 0.0251 0.0270 0.0287 0.0289 0.0272 0.0222
Saturating solid phases.
a t low ionic strengths. The increased solubility with increase in ionic strength is striking at higher temperatures. The hypothetical solubility a t zero ionic strength (so) for each temperature is the intercept determined by the least-squares calculations. Figure 4 shows comparative plots of the solubilities at 0.5 and 25" in both sodium chloride and sodium nitrate solutions. Divergences in the comparative curves occur a t ionic strengths above 0.03 m, with the solubilities in sodium chloride solution becoming less than in sodium nitrate. The results of Johnston and Grove5 a t 25" are nearly identical with the present measurements. Solubility Product Constants. The variation of the solubility product for calcium hydroxide with temperature is shown in Figure 5 for two cases, (1) in water and (2) a t an ionic strength of zero. The curves represent the best least-squares fit to the experimental data. Results at 350" are not included since they fit the curves poorly, probably because the temperature is near the critical temperature for water of 374". Since the solubility, hence the ionic strength, decreases with increase in temperature, K,, in water approaches K,," a t high temperatures. Table I1 includes a tabulation of the K,," values. Greenberg and Copeland16 calculated a pK,," of 5.10 from the data a t 25" of Johnston and Grove5 and a value of 5.03 from other solubility data, The Journal of Physieal Chemistry
'
0
I
I
I
I
I
0.I
0.2
0.3
0.4
0.5
I
?/(,
+AI
0.6.
%)
Figure 4. Comparison of the Ca(OH)*solubilities in aqueous NaN03 and NaCl at 0.5 and 25'.
weighing heavily the measurements of Bates,6 et aE. The latter result agrees with the value 5.03 a t 25" found in this work. Activity Coeficients; General Significance. With eq 4 and the values of S , A , B, and C given in Table 11, the mean activity coefficients of calcium hydroxide can be calculated at any temperature from zero t o near the critical temperature of water. Figure 6 shows representative plots of the logarithms of the activity coefficients obtained from the separate measurements compared with the calculated curves a t several temperatures. The rise (reversal in slope) in activity coeffcients with increasing, very high ionic strengths at low temperatures, commonly designated the saltingout effect, disappears completely at temperatures above 100". This behavior is strikingly evident in Figure 7 where the logarithm of the mean activity coefficient, multiplied by S25/STt o normalize the behavior t o that a t 25", is plotted against d / ( l A 2 / 1 ) . Further, this normalized plot shows a reversal in direction of deviation from the theoretical slope at high temperatures as contrasted to temperatures of 100" and below. This reverse behavior may essentially be attributed t o the formation of complexes with the supporting electrolyte, for example, CaN03+ or NaOHO, although at present there is not sufficient information to provide unequivocal proof. At 0.5 and 25", the mean activity coefficients of calcium hydroxide are larger in sodium chloride than
+
~
~
~
~~
(16) S. A. Greenberg and L. E. Copeland, J . Phys. Chem., 64, 1057
(1960).
AQUEOUSSYSTEMS AT HIGHTEMPERATURE
2647
TEMPERATURE (‘C) 10‘~
1o
-~
10-6
19-7
a IO-8
id9
1d‘O
IO-”
Figure 5. Solubility product of Ca(OH)2 in water and a t I = 0 from 0 to 300”.
in sodium nitrate solutions of the same ionic strength (Figure 6). This is consistent with Johnston and Grove’s5 finding that calcium hydroxide has a higher activity coefficient in a solution of the salt having the higher activity coefficient when salts with a common cation are compared. Harned and James,” however, found the opposite effect on the activity coefficient of the 1-1 electrolyte potassium hydroxide in solutions of the potassium halides.
Guggenheim-Brewer-Pitxer
Deviation
Parameter.
Some years ago Guggenheirnls proposed letting the A parameter, eq 4,equal unity and having one term linear in concentration, BI,account for deviations with change in ionic strength. Pitzer and BrewerIg write B as B then term it as a deviation function, and show it as a function of I for several 1-1 electrolytes. The data from this laboratory3p4for calcium sulfate, a 2-2 electrolyte, and the present results for calcium hydroxide, a 2-1 electrolyte, at 25” were treated in this manner to produce the additional curves in Figure 8. The deviation functions for calcium sulfate and calcium hydroxide are more markedly affected than those for e ,
o
r
,
,
#
I
,
3
1
3
4
5
6
7
-0.3 -0.5
n
(
2
I. IONIC STRENGTH
Figure 6. Logarithm of the mean activity coefficient for Ca(OH)2 as a function of ionic strength in aqueous NsNOJ and NaCl a t several temperatures.
(17) H. S. Harned and G. M. James, J . Phys. Chem., 30,1060 (1926). (18) E. A. Guggenheim, Phil. Mag., 19, 588 (1935). (19) G. N. Lewis and M. Randall, “Thermodynamics,” 2nd ed, rev by K. S. Pitzer and L. Brewer, hlcGraw-Hill Book CO., Inc., New York, N. Y., 1961, p 327.
Volume 71. Number 8 July 1867
LEROYB. YEAITSAND WILLIAM L. MARSHALL
2648
i
3OOOC I m I
0.6
I
0,2
0
0
0,t
Figure 7. Normalized -log y f as a function of Z'/*/(l
0.2
CaOH+(aq)
+ OH-(aq)
=
aT ibT2/2
where a, b, and c are constants. The Journal of Phyaical Chemistry
+c
0,6
log y+ -4 SIV2/(C
+r%
FROM PITZER AND BREWER'S TEXT MARSHALL AND SLUSHER (4967)
0.4
0.3
(7)
However, the data at all temperatures, plotted similarly to those in Figure 2, showed a much better leastsquares fit with the 2-1 electrolyte assumption. Nevertheless, the magnitude of the second ionization constant for calcium hydroxidem at 25O, i.e., 0.05-0.07, is such that the precision of our analytical procedures may not have been sensitive enough to perceive some small amount of association to Ca(0H) +. Although greater association might be expected at the higher temperatures, hence, more readily detected, the solubility of calcium hydroxide is lower at these temperatures and the chemical analyses less precise. Therefore, although there is a relatively good fit to the behavior of a 2-1 electrolyte, the data do not preclude the existence of CaOH+ ions in solution. Thermodynamics of Calcium Hydroxide, &S50°. With the assumption that the change in molal heat capacity, AC,", for the dissolving of calcium hydroxide in water (at I = 0) could be expressed by a linear function of temperature (OK), the change in standard enthalpy is then
AH'
0,5
+ AZ1'2) for Ca(OH)*in aqueous NaNOa, 0.5-300"
1-1 electrolytes by changes in ionic strength over the entire range of I , but are greatly different from B * for 1-1 electrolytes only at low ionic strengths. Behavior as a 1-1 Electrolyte. The experimental results were also treated as though calcium hydroxide were a 1-1 electrolyte Ca(OH)2(s)
0,4
0.3
0.2
8-
0.4
0
-0.1
--0
4
2
3
4
5
IONIC STRENGTH
Figure 8. Comparison of the deviation function B . for Ca(OH)* and for CaSOd with those for 1-1 electrolytes at 25".
could have been assumed a constant, a much better fit to the experimental data was found by using a linear function.) Equation 8 was substituted into the van% Hoff equation
(8)
(Although ACpo
(20) R. G. Bates, V. E. Bower, R. G. Canham, and J. E. Prue, Trans. Faraday Soc., 55,2062 (1959).
AQUEOUSSYSTEMS AT HIGHTEMPERATURE
2649
20 0
3 3J b
a
-20 -40 -60
-80 -100
-I20
I50 IO0
5-
iJ
'50 0
-50
-$ -100 -150 -200
/. IONIC STRENGTH
Figure 9. Thermodynamic functions for the solubility of Ca(OH), in NaN03-Hz0 solutions, 0-7 m,0-350".
d In K,,"/d(l/T) = -AH"/R
~
(9)
which was integrated to give log Kspo= a'
+ b' log T + (c'/T) + e'T
(10)
The four parameters a', b', c', and e' were calculated from log K,," values derived from eq 5 and given in Table 11. With the evaluated parameters, eq 10 becomes log K,," = -25.7085
+ 12.9722 log T (530.49/T)
- 0.03233102'
(11)
which, when substituted into the van%Hoff expression, produces
A H " (cal mole-') = 2427
Table IV : Thermodynamic Functions for the Dissolution Equilibrium Ca(OH),( s) e Ca2+(aq) 20H -( aq)
+
AH', koa1 mole-1
ASo, os1 mole-1
OC
kcal mole-1
deg-1
ea1 mole-1 deg-1
0 25 50 75 100 150 200 250 300 350
6.09 6.86 7.76 8.79 9.96 12.7 16.1 20.0 24.6 29.8
-1.57 -3.04 -4.69 -6.53 -8.55 -13.2 -18.5 -24.6 -31.4 -39.0
-28.1 -33.2 -38.5 -44.0 -49.6 -61.2 -73.1 -85.3 -97.7 -110
-55.0 -62.4 -69.8 -77.2 -84.6 -99.4 - 114 - 129 - 144 159
AGO,
T,
~
+ 25.774T - 0.147912T2
(12)
Values for AC,", equal to ( ~ A H " / ~ T )were , , calculated from the differentiated eq 12. From values for K,," and AH", the free energy changes, AGO, and entropy changes, AS", were obtained from the standard equations, A G O = -RT In Kspo and AS" = (AH" AG")/T. All values are listed in Table IV. At 25", Greenberg and Copelandl'j report AGO = 6.81 kcal mole-', AH" = -3.29 kea1 mole-', and A S " = -34.0 cal mole-' deg-'. Agreement is good between these and our own results. However, the values in Table IV differ markedly from those of Hopkins and Wulff , 2 1 who consider the second ionization step of calcium hydroxide t o be a significant factor. Their values a t 25" are AGO = 7.10 kcal mole-', AH" = -4.29 kcal mole-', and AS" = - 38.2 cal mole-' deg-'. The use of Kelley's expression22for the heat capacity of solid calcium hydroxide and Criss and Cobble's average ionic heat capacities23 for Ca2+
AC,O,
-
~~
and OH- ions yields values for AC,", the mean heat capacity for the dissolution reaction, of -82, -80, and -88 cal mole-' deg-' a t 25, 25-100, and 25200", respectively. These correspond to values of -62, -74, and -88 cal mole-' deg-' for AC," found in this work. Although the agreement of these average values is good, our separate values for AC," in Table IV show considerable dependence on temperature. Greenberg and Copelandl'j suggest that the large decrease in entropy for the reaction is probably due to the increased order of the water molecules in the vicinity of the ions. The further decrease in A S " as (21) H.P. Hopkirls and C. A. Wulff, J . Phya. Chem., 69, 6 (1965). (22) K.K.Kelley, "Contributions to the Data on Theoretical Metallurgy," Part XIII, Bulletin 584, U. s. Bureau of Mines, U. s.Government Printing Office, Washington, D. C., 1960, p 37. (23) C. M. Criss and J. W. Cobble, J. Am. Chem. SOC.,86, 5390 (1964).
Volume 71, Number 8 July 1967
I. CRIVELLIAND F. DANON
2650
the temperature increases (see Table IV) indicates, then, an increase in the relative order of the water molecules upon leaving the environment of other solvent molecules and entering the electrostatic fields of the ions. The curves in Figure 9 were constructed from results calculated by using eq 5 to evaluate log K,, a t several constant ionic strengths up to 6 m and a t temperatures up to 300". These solubility products, each at constant I , were considered to show the same temperature dependence as In K,," in eq 10. After sets of the four parameters for several given ionic strengths were determined, values for AGfJ AH', AS', and AC,' (which correspond to the changes in the thermodynamic
quantities when 1 mole of calcium hydroxide solid dissolves in a solution of ionic strength I ) were calculated in the same manner used in the calculation of the thermodynamic quantities for the standard state (zero ionic strength). The curves a t 350" represent extrapolated results since the experimental results a t this temperature appear inconsistent with those a t the lower temperatures. The dashed curve for the average Actp from 0 to 350")shown in Figure 9, is the arithmetic mean for this temperature range. Acknowledgment. The authors express their gratitude to Professors John E. Ricci, New York University, and James W. Cobble, Purdue University, for their helpful discussions.
The Reduced Equation of State of Argon and Xenon
by I. Crivelli and F. Danonl Facultad de Ciencias Exactas y Naturales, University of Buenos Aires, Buenos Aires, Argentina (Received January 81, 1967)
A comparison of the compressibility factors of argon and xenon reduced in terms of the Kihara intermolecular core model potential is presented. It is found that correspondingstates behavior is better obeyed by using the Kihara rather than the Lennard-Jones potential. The results of this paper indicate that the assumption of the pairwise additivity of the potential seems to be valid within the range covered by the presently available experimental data.
In a recent articleJ2we showed that the second virial coefficient and the viscosity coefficient a t low pressures of argon, krypton, and xenon can be correlated on a corresponding states basis by the use of the Kihara core model intermolecular potential as given by
+
Q =
€ . [ ( ; ) "
-2(9]
where eK is the minimum of the potential which occurs at po. The intermolecular separation p is defined as the shortest distance between the outer surface of the cores. This equation is valid for p 2 d where d is the diameter of the spherical core. For smaller values The Journal of Physical Chemistry
+
of pJ = m . Results obtained by using eq 1 are much more satisfactory than those obtained by using the (12-6) Lennard-Jones (L-J) function. Levelt3 has made a careful study of the compressibility factor of argon and xenon and has shown that the PVIRT isotherms of argon may be transformed into the compressibility isotherms of xenon by multiplying by scale factors, which are ratios of potential param(1) T o whom correspondence and requests for reprints should be sent at the Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Mass. 02139. (2) F. Danon and J. C. Rossi, J . Phys. Chem., 70, 942 (1966). (3) J. M.H. Levelt, Physiea, 26, 361 (1960).
