2017
THERMODYNAMIC PROPERTIES OF HIGH-TEMPERATURE AQUEOUSSOLUTIONS
The Thermodynamic Properties of High-Temperature Aqueous Solutions. IX. The Standard Part,ial Molal Heat Capacities of Sodium Sulfate and Sulfuric Acid from 0 to 100"' by W. L. Gardner,2E. C. Jekel,3 and J. W. Cobble Department of Chemistry, Purdue University, Lafayette, Indiana
(Received March 5 , 1968)
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The standard partial molal heat capacities, of NazSOl(aq) and H2S04(aq) ( L e . , two hydrogen ions and a sulfate ion) have been obtained by the integral heat method between 0 and 100". At 25' the values of for NazSO4 (as) and H2S04 (as) are -46.7 and -70.6 cal mol-' deg-', respectively.
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Introduction In previous communications from this laboratory, both the practical and theoretical need for thermodynamic data on aqueous solutions above 25"have been pointed Of particular interest are the standard of electrolytes as a partial molal heat capacities, function of temperature. Such data allow the calculation of the free energy, enthalpy, and entropy changes for ions at elevated temperatures. One chemically important electrolyte is sulfuric acid, and this communication describes the method used to 20 for completely dissociated H2S04(as) determine from 0 to 100". Not only is sulfuric acid an interesting 1:2 electrolyte, but it is involved in a number of electrochemical cells. Heat capacity data enable one to test the reversibility of sulfate ion electrodes in a rigorous third-law manner,6J2and such tests are described in the communication immediately following the present one.
tion and the heat of solution of the completely dissociated electrolyte by a careful analysis of the concentration dependence of the heat of solution, such a process introduces additional errors. Finally, the heat of solution of HzS04 (or its hydrates) is sufficiently high to introduce larger errors in ( a A H : / a t ) , than desirable. For these reasons it seemed reasonable to determine for NazS04(as) , and to generate the corresponding values for HzS04(aq) from the known Na+ - H+ difference in Apparatus. The heat of solution calorimeter has been previously described elsewhere." Materials. Baker Analyzed grade Na2S04was recrystallized from water five times, retaining approximately 75% of the material on each crystallization. The hydrated salt was desiccated in a vacuum oven at 155" for 1 day, ground, and reheated at 200" for several hours in a muffle furnace.14J5 This material was stored
Experimental Section The integral heat method4 of determining the partial molal heat capacities of electrolytes at infinite dilution has provided the most accurate values of 6,; yet reported. The simplest variation of this method involves determination of the heat of solution of some reference substance at infinite dilution, AH:, as a function of temperature. The slope ( a A H , " / a t ), gives AC,," as a function of temperature. If the heat capacity of the reference substance (solid, liquid, or solution) is known over the temperature range involved, then the heat capacities of the ions formed on solution can be fixed. In principle, the heat of solution of pure HzS04 (or one of its hydrates) can be used to obtain for HzS04(aq). Unfortunately, pure HzSO4 is a difficult substance to work with directly, since the absorption of only 20 ppm of water will cause a noticeable effect on its heat of solution. Further, even a t dilutions of -0.001 m, the second dissociation is only 90% complete a t 25". While it is possible to obtain both the heat of dissocia-
(1) Supported in part by a grant from the National Science Foundation. (2) From the Ph.D. Thesis of William Lee Gardner, Purdue University, June 1968. (3) Department of Chemistry, Hope College, Holland, Mich. (4) C. M. Criss and J. W.Cobble, J. Amer. Chem. SOC.,83, 3223 (1961). (5) J. C. Ahluwalia and J. W. Cobble, ibid., 8 6 , 5377 (1964). (6) J. C. Ahluwalia and J. W. Cobble, ibid., 86, 5381 (1964). ( 7 ) 0. M.Criss and J. W. Cobble, ibid., 8 6 , 5385 (1964). ( 8 ) C. M. Criss and J. W. Cobble, ibid., 86, 5390 (1964). (9) J. W.Cobble, ibid., 86, 5394 (1964). (10) R. E. Mitchell and J. W. Cobble, ibid., 86, 5401 (1964). (11) E. C. Jekel, C. M. Criss, and J. W. Cobble, (bid., 8 6 , 5404 (1964). (12) J. W.Cobble, A n n . Rev. Phys. Chem., 17, 15 (1966). (13) Actually ??pae for HzS04(aq) has been directly determined a t 30' from the heats of solution of HZSOI.HBOa t 25 and 35O. The value obtained, -73 * 5 cal mol-1 deg-1, agrees well with that reported from the present research in Table 111 of -67.1 cal mol-1 deg-1. The direct value was obtained by J. M. Readnour in our laboratories. (14) Some heats of solution were carried out a t 25" using sodium sulfate heated to 400°. This material gave high values compared to salt heated only to 200°, presumably because of the phase transition a t 240' of the type reported by Schmidt and Sokolon.ls (15) N. E. Schmidt and V. A. Sokolon, Russ. J. Inorg. Chem., 6 , 1321 (1961).
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Volume Y.% Number 6 June i869
W. L. GARDNER,E. C. JEKEL, AND J. W. COBBLE
2018 Table I:
Heats
No.of determinations
M
x
Solution a n d
108
D
AHm cal mol-'
Values for
NanSOd
~AHW", cal mol-]
1933 1979 1960
4.53O 1475 f 16 75 1495f4 97 1489f19 106 1513 f 24 118 AH." = 1419 f 10 oal mol-'
1400 1398 1383 1395
12.54" 613 96 600 f 11 113 615 f 2 132 637 f 8 157 661 169 646 181 AH." = 507 f 3 cal mol-'
517 487 483 480 492 465
1.67 2.42 3.92
3 2 3 2
2.21 3.69 4.50 5.74
1 2 2 3 1 1
2.71 3.85 5.39 7.88 9.30 10.77
2 2 2 1 2 1
0.978 5.00 10.01 13.29 18.33 22.97
2 2 3 2 2 1
2.09 2.39 3.66 4.70 5.49 9.60
2 1 1 1
4.67 5.76 10.27 11.06
2 2 1 1 1 1
3.30 4.72 6.07 7.24 7.69 9.01 11.11
25.00' -534 f 23 71 - 4 5 7 f 17 152 -420 f 17 212 -451 240 -404f8 277 -370 303 AH," = -582 f 5 oal mol-'
40.09" -1511 f 34 128 -1497 f 17 136 -1495 f 14 167 -1463f3 187 20 1 -1454f 1 -1401 259 AH: = -1635 f 5 cal mol-'
60.28' -2647f4 244 -2634 269 -2537 348 -2533 360 AH," = -2889 f 6 cal mol-' 85.17" -4100 f 38 286 -4056k4 337 -4013 378 -3983 410 -4008 423 -3951 453 -3877 497 AH," = -4395 f 5 cal mol-'
95.00' 2.50 -4773 f 23 285 5.00 -4661 f 26 394 540 9.93 -4513 f 38 16.34 -4371 f 19 671 AH," = -5064 f 6 cal mol-'
3 2 2 2
P#
cal mol- 1
0.81" 2055 62 2053 f 19" 74 2053 93 AH: = 1995 f 25b cal mol-'
1 2 I
1
0
of
-605 -609 -632 -691
-681
-673 - 1639 - 1633 - 1662 1650 -1655 - 1660
-
-2891 -2903 -2885 2893
-
-4386 -4393 -4391 -4393 -4431 -4404 -4374
-5058 -5055 -5052 -5042
0 Average deviation of individual measurements from the average. Estimated probable error.
The Journal
OJ'
Physical Chemistry
in a vacuum oven at 155" between weighings. Samples of a few hundred milligrams were weighed into thinwalled bulbs blown from 7-mm Pyrex tubing and sealed under vacuum (-0.1 mm) by sealing the neck of the bulb with a microtorch. Water used in these measurements was prepared by passing distilled water through two acid-base ionexchange columns to remove possible trace contaminants. The specific conductance of such water was 9.9 X lo-' ohm-' cm-I at room temperature. Under the conditions of usage in the calorimeter the water was saturated with air. Procedure. Over the temperature range involved in this research the heat of solution of Na2S04varies from about 2 kcal endothermic near 0" to 5 kcal exothermic near 100". The "cross-over" temperature, where the heat of solution is approximately zero, occurs a t approximately 18". In the exothermic temperature region two or more electrical calibrations were carried out before and after dissolving of the sample. From these calibrations the average electrical energy equivalence of the calorimeter could be fixed and the heat of solution determined in a normal manner. In the endothermic region a different procedure was used. During the dissolving of the salt an equivalent amount of electrical heat was added so as to operate the calorimeter under nearly isothermal conditions. hlthough it was rarely possible to exactly compensate the chemical heat in this manner, the net temperature change seldom exceeded 1 X deg. The measurements near 0" were complicated because of extremely long dissolving times. Apparently the anhydrous salt crystals first formed hydrates which then stuck together to form conglomerates. These larger masses were found to dissolve rather slowly. The difficulty could be somewhat alleviated by increasing the rate of stirring in the calorimeter, but this increased the noise levels in the temperature sensing bridge. For these reasons the heat values below 10" are subject to larger than normal errors.16 Two additional possible complications could result from the formation of HSOd- from dissolved C02 and formation of the NaS04- complex ion. In the case of COz, the upproximate heat can be calculated for the reaction COz(aq)
+ HzO + Sod2-= HS04- + HC03-
The C02 solubility and carbonic acid dissociat'ion constants have been tabulated," and the dissociation con(le) This problem could be avoided by using flnely ground NaaSOa. However, the heat of solution of the decahydrate is approximately 20 kcal and such a large heat would introduce additional errors in (aAH.O/dt),. (17) H. 9. Harned and B . B. Owen, "The Physical Chemistry of Electrolytic Solutions," 3rd ed., Reinhold Publishing Gorp., New York, N. Y., 1958, p 692. lOHaO near O0 instead of NazSO4.
THERMODYNAMIC PROPERTIES OF
HIGH-TEMPERATURE AQUEOUS SOLUTIONS
stant of HS04- as a function of temperature is known.18 The largest correction factor amounted to -7 cal/mol for the heat of solution at 95'. This small change in the heat of solution resulted in an almost negligible change in Cpzosince the corrections are small and vary smoothly with temperature. The heat and free energy of formation of NaS04from Na+ and SO? are not well known, but fortunately, little of this species is formed a t the dilutions involved in this research. Further, in the extrapolation procedure to obtain AH,", such ion pairs are automatically accounted for since their concentration diminishes rapidly and smoothly as the concentration of the electrolyte approaches infinite di1uti0n.l~ Fundamental Constants LTsed. The following values of the fundamental constants were used: 1 cal = 4.1840 abs J, 0°C = 273.15'K. Atomic weights are based on the revised carbon-12 scale.
Experimental Data Table I summarizes the results of 69 heat of solution measurements for sodium sulfate. The number of determinations at each concentration, the heats of solution, the extrapolated heat of solution at infinite dilution, and the parameters used in extrapolation are indicated a t each temperature. The heats of solution a t infinite dilution were obtained by use of a two term Debye-Hiickel type of e~trapolation.~JOIf the heat of dilution can be expressed as @L =
~ V A1 HZ+Z-
I /'/'[
(1
+ 11/')-'- Q (cI*"]
2019
Table 11: Heat Capacities of Aqueous and Crystalline Sodium Sulfate" A GPO
tav
2.67 8.54 18.77 32.54 50.18 72.72 90.08 a
Cm
-154.7 -113.8 -87.5 -69.8 -62.1 -60.5 -68.0
CPID
29.5 29.8 30.2 30.8 31.6 32.6 33.3
-125.2 -84.0 -57.3 -39.0 -30.5 -27.9 -34.7
Units in cal mol-' deg-1.
Table 111: Smoothed Values of the Partial Molal Heat Heat Capacity for Aqueous Sodium Sulfate and Sulfuric Acida Temp, OC
NaaSOr
Ob 5 10 20 25 30 40 50 60 70
80 90 1006 Units in cal mol-' deg-I.
-E,,.
H&OL
145 100.3 79.7 55.4 46.7 40.9 34.3 30.0 27.5 27.1 29.0 34.3 42.8 Ir
-zpao
176.4 114.7 91.5 75.5 70.6 67.1 63.3 61.3 60.8 63.3 69.5 80.6 96.8
Extrapolated values.
- 2.3O3RT2(dB/dt)mv+v- ( 2 ) then the first term of this equation can be subtracted from the observed heat of solution at a given concentration m and ionic strength I . AH is the Debye-Hiickel limiting slope20 and dB/dt is an empirical constant. u (I1/')is a purely numerical term and values have been recorded elsewhere.'l h function, p , is defined as
I Z+Z- 1 AHI%
(3)
= ( ( 1 + I l / 2 ) - 1 - +[.(I"')]]
(4)
p =
AH, -
$V
where a!
- 2.303RT2(dB/dt)v+v-m
Calculations The standard partial molal heat capacity of Na2S04 (as) was determined from the relationship d ( A H , O ) / a t = AC,"
From eq 2 and 3, it follows that p = AH,"
This requirement helps fix a more accurate value of AH,' at a given temperature by use of the data at neighboring temperatures than is usually possible from concentration studies a t single temperatures.
(3
Consequently, a linear relationship should result when p , determined from eq 3, is plotted against m, and the value of p at tn = 0 should be AH,". These linear relationships were verified at each temperature over the concentration ranges studied in this research (50.02 m). In making these linear plots, it was usually possible to improve the extrapolations by requiring that the slope of the p us. m plot at one temperature be smoothly related to the slopes at neighboring temperatures.
=
Cp: - C,,
(6) where C,, represents the heat capacity of the solid salt. AH," was determined over sufficiently small temperature intervals so that a A H o / a t and A ( AH,') / A T are not significantly different. The values of C,, for NazS04(c)were taken from the (18) E. C. Jekel and J. W. Cobble, unpublished data. See E. C. Jeksl, Ph.D. Thesis, Purdue University, 1964. (19) We have tested this assumption by deliberately adding excess Na+ (as NaCl) in some heat of solution measurements. While the absolute value of the heat of solution of NazSOr in such solutions is changed, the extrapolated value of the heat a t infinite dilution is the same as in water. (20) G. N. Lewis and M. Randall, "Thermodynamics," 2nd ed, revised by K . S. Pitzer and L. Brewer, McGraw-Hill Book Do., Inc., New York, N. Y . , 1961, p 640. (21) H. S. Harned and B. B. Owen, ref 17, Table 5-2-6.
Volume 79, Number 6 June 1069
W. L. GARDNER, E. C. JEXEL, AND J. W. COBBLE
2020 data of Pitzer and Coulter22and Schmidt and Sok01on.l~ Both sets were used in drawing a smooth curve of C, against temperature from which a "best" value could be read. Table I1 summarizes the experimental heat capacities, and Table I11 lists smooth values of at regular temperature intervals between 0 and 100". The heat capacities of aqueous sulfuric acid can be obtained from the corresponding data on NazSOl(aq)
cP:
1
I
li
-7 -180' 0
I
20
40
60 Temperature PC)
ao
J
100
Figure 1. The partial molal heat capacities of sulfate ion systems compared to other typical electrolytes (see text for references).
The Journal of Physical Chemistry
and the previously determined heat capacity differences between H+(as) and Na+ (as) .5 These values are also given in Table 111. The probable errors in the values for c,," for both electrolytes are estimated at f l cal mold1 deg-l above 15" and about two or three times that large near 0".
Discussion The heat capacities for both sulfate ion systems show remarkable changes between 0 and 100' as can be seen from Figure 1, which summarizes similar data on other electrolytes obtained in these l a b o r a t ~ r i s . ~ - ~ , 'For ~J~ example, 6,; for H2S04(aq) changes from -176cal mol-' deg-l at 0" to -61 cal mol-' deg-l a t SO", a change of over 100 heat capacity units over a 50" temperature interval! Na2S04(as) shows even a greater change. Clearly this effect is due to the behavior of S0d2-(aq) and its solvent environment near 0". A t higher temperatures a typical 3:l electrolyte such as GdCL (as) shows greater solvent interaction than Na2S04(aq) inasmuch as this is related to more negative heat capacities. Consequently, there must be some special geometrical significance to Sod2- which can cause a greater rate of change of the ice-like structure of hydration water with tempeature near 0" than other ions do, including the somewhat larger ReOr-. These very rapidly changing negative heat capacities will have a special effect on the temperature behavior of the free energy of any SO?- system. In the following paper, the temperature coefficients of supposedly reversible sulfate ion electrode systems will be examined.
Acknowledgment. The authors are indebted to Dr. John Brand for his aid in the determination of the heats of solution a t 60.28". (22) K. (1938).
Pitzer and L.
V.
Coulter. J. Amer. Chem.
Soc., 60, 1310
