GOLDBERG, RIDDELL,WINGARD, HOPKINS, WULFF,AND HEPLER
706
Thermochemistry of Cobalt Sulfate and Hydrates of Cobalt and Nickel Sulfates. Thermodynamic Properties of Co2+(aq) and the Cobalt Oxidation Potential
by R. N. Goldberg, R. G. Riddell,' M. R. Wingard,2 H. P. Hopkins, C. A. WuM, and L. G. Hepler Department oj Chemistry, Carnegie Inatitute of Technology, Pittsburgh, Pennsylvania
(Receiaed November 9, 1966)
Heats of solution of CoSOa(c) and several hydrates have been measured. From the results of these measurements we have calculated h H 2 9 8 = -2.48 kcal mole-' for CoS04.6H20(c) HzO(l) = CoSO4.7HzO(c); A H 2 9 8 = -12.8 kcal mole-' for CoSO4.H2O(c) 5Hz0(1) = CoS04.6HzO(c) and AH298 = -6.1 kcal mole-' for CoSO4(c) H20(1) = CoSO4.H2O(c). We also use these results in calculating eHf" = - 13.9 kcal mole-', S2"= -26.0 cal deg-' mole-', and AGfo = -13.3 kcal mole-' for Co2+(aq). This free energy leads to E" = 0.29 v for the Co/Co2+ standard oxidation potential. Heats of formation as follows have been calculated for the mono-, hexa- and heptahydrates of cobalt sulfate, respectively: AHf' = -286.4, -640.8, and -711.6 kcal mole-'. We have also calculated S O 2 9 8 = 42 cal deg-I mole-! for CoSOr.HzO(c). Heat of solution measurements lead to AH298 = -15.1 kcal mole-' for NiS04.HtO(c) -I- 5Hz0(1) = NiS04.6HzO(c) and to AHr" values of -283.9 and -640.6 kcal mole-' for the mono- and hexahydrate.
+
Recent calorimetric measurements by Adami and King3 have led them to report AHr" = -212.0 f 0.4 kcal mole-' for CoS04(c). Our measurements of the heat of solution of Cos04 to form dilute aqueous solutions were undertaken to provide a AH" value to be combined with this new heat of formation to yield a reliable AHr" value for Co2+(aq). Our further measurements of heats of solution of CoS04.7H20(c) to form dilute aqueous solutions were undertaken to provide data to be combined with the third-law entropy of CoS04.7HzO(c) recently determined by Rao and Giauque4 to yield the standard partial molal entropy of Co2+(aq). The AHf" and $2" values for Co2+(aq) lead to AGf" for this ion and thence to the standard oxidation potential for the Co/Co2" couple that has resisted accurate determination by conventional electrochemical techniques. Recent calorimetric measurements by Brodale and Giauque5 have led to AH"298 for hydration of CoSOa. 6H20(c) to CoSO4.7H2O(c). Our measurements on CoS04.6H20(c) were undertaken to permit calculation of this same AH"298, partly because the heat of hydration of Cos04 6H20 to CoSOh-7HzO calculated by Broers and Van Welie6 from their recent vapor 9
T h e Journal of Physical Chemistry
+
+
pressure measurements is not in agreement with the calorimetric measurements of Brodale and Giauque. We have also investigated CoS04.H20(c). Some similar measurements have also been made on hydrates of NiSO,.
Experimental Section The calorimeter used is patterned after one previously described,' except that a Leeds and Northrup hfueller G-2 bridge and HS galvanometer were used with a nickel wire resistance thermometer for temperature measurements. Also, the resistance thermometer (1) National Science Foundation Research Participant for High School Teachers. (2) National Science Foundation Research Participant for High School Teachers. (3) L. H. Adami and E. G. King, U. S. Bureau of Mines Report of Investigations No. 6617, Director, Mines Bureau, Pittsburgh, Pa., (1965). (4) R. V. G. Rao and W. F. Giauque, J. Phys. Chem., 69, 1272 (1965).
(5) G. E. Brodale and W. F. Giauque, ibid., 69, 1268 (1965). (6) P. M.A. Broers and 0. S. A. Van Welie, Rec. Trav. Chim., 789
(1965). (7) W. F. O'Hara, C. H. Wu, and L. G. Hepler, J . Chem. Educ., 38, 512 (1961).
THERMOCHEMISTRY OF COBALT SULFATE
and calibration heater were contained in a glass spiral filled with paraffin oil rather than wound on a silver cylinder. All of the calorimetric work reported here was carried out a t 25.0 f 0.1". The cobalt sulfate and nickel sulfate used were Baker Analyzed reagents, the assays being 99.8 and l O O . l % , respectively. Samples were recrystallized from dilute sulfuric acid. Anhydrous cobalt sulfate was prepared by heating hydrated material at -500' for periods ranging from 5 to 20 days, accompanied by periodic gentle grinding. Samples were stored with P205in a desiccator. Solubility measurements by Rohme? and vapor pressure measurements by Broers and Van Welie6 have shown that CoS04.7Hz0, CoS04.6H20, and Coso4 H 2 0 are the hydrates that are thermodynamically stable under appropriate conditions of temperature and activity of water. Naterial having approximately the composition CoS04.7H20 was obtained as the solid phase in equilibrium with saturated solution a t room temperature. After this material had been separated from the solution by filtration and pressed on the filter, it was further dried by storing in desiccators with Pz05 until the compositions of two samples corresponded to CoS04.6.994H20 and CoS04.6.075H20. Hydration numbers were obtained by drying samples (-2 g) in porcelain crucibles to constant weight by heating at -500". Careful preliminary heating at -100" was always done to avoid spattering. Several precautions were taken to ensure that the hydrates referred to above could properly be regarded as mixtures of CoS04.7H20and CoS04.6H20. During the course of drying with P205,lumps in the samples were broken by periodic gentle grinding. After samples had reached approximately the desired composition as determined by preliminary analysis, they were placed in closed bottles and allowed to stand for 2 weeks. After one last gentle grinding, analyses and heat of solution measurements were begun. Further analyses after all calorimetric sample bulbs had been filled, weighed, and sealed confirmed that the compositions had not changed. Average deviations in analyses in terms of hydration numbers were 0.002 for the "7" hydrate and 0.009 for the "6" hydrate. ,4sample of CoS01.0.833H20was prepared by heating recrystallized hydrate at -120" for 2 days, accompanied by periodic gentle grinding. Analyses and precautions were the same as described above. Average deviation in analyses in terms of hydration number was 0.003. Another sample having composition CoSOc.6.62H20 was also prepared. Solubility measurements by Chretein and Rohmerg
707
have shown that NiS04.7Hz0, NiS01.6Hz0 (two forms), and NiSO4 .H2O are the thermodynamically stable hydrates under appropriate conditions. Two samples of nickel sulfate hexahydrate (a form, blue) were prepared by allowing the recrystallized starting material to stand in desiccators with saturated solutions of nickel sulfate a t 32-34". Analyses by heating to constant weight a t -500" gave hydration numbers of 6.000 with average deviation 0.005 for both samples. A sample of NiS04~5.059H20(average deviation, 0,009) was prepared by allowing a portion of the hexahydrate to stand in a desiccator with Pz05for 1month.
Results and Discussion Heat of solution data for CoS04.6.994H20(c) and CoS04.6.075H20(c) are listed in Tables I and 11. We take the average AH = 12.0 cal g-' for the enthalpy of solution of CoS04.6.994HzO(c) to yield 0.0239 m solution. Heats of dilution mentioned later in this paper permit us to calculate from the dat8ain Table I1 (referring to 0.0300 m solution) that AH = 4.14 cal g-l for solution of CoS04.6.075Hz0(c) to form 0.0239 m solution. Considering both materials to be mixtures of CoS04.7H20 and CoS04.6H20, the measured heats of solution (represented by Ah,, given in cal g-l) can be expressed as
+ ~(Ahs)
Ahm = ~ ( A h 7 )
(1)
in which x and y represent weight fractions of each hydrate present in the solid sample and Ah7 and Aha represent heats of solution (cal g-l) of the pure hydrates. Solution of two such simultaneous equations leads to the desired heats of solution, which are AH = 3.39 kcal mole-' for CoS04.7H20 and AH = 0.91 kcal mole-' for CoS04.6H20. Both of the AH values refer to 0.0239 m solutions. Combination of these two values leads to AHzs* = -2.48 kcal mole-' for the process
+
CoS04*6HzO(~) HzO(1)
=
CoS04*7HzO(c) (2)
The uncertainty in this AH value is about fO.05 kcal mole-'. Brodale and Giauque5 have recently reported AHzs* = -2.455 f 0.010 kcal mole-' for this same hydration process. The vapor pressure measurements of Broers and Van Welie6 led them to report AHZSS= -1.75 0.11 kcal mole-' for this process. A second-law calculation based on the data of Broers and Van Welie6leads to = 33.6 cal deg-l mole-' for the process represented by
*
(8) R. Rohmer, Compt. Rend., 199,641 (1934). (9) A. Chretein and R . Rohmer, ibid., 198,92 (1934).
Volume 70,Number 3 March 1966
708
GOLDBERG, RIDDELL, WINGARD, HOPKINS,WULFF,AND HEPLER
Table I : Heats of Solution of CoS04*6.994H*O(c)a t 25.0"
Table 111: Heats of Solution of CoSOa(c) a t 28.0"
g(0)/950
ml of Hz0
6.3676 6.3547
Moles of CoSO1/ 950 ml of HzO
kcel/mole
0.005183 0.005150 0.005196 0.005152
-18.5 -18.3 -18.1 -18.3
AH,
Table 11: Heats of Solution of CoS04*6.075H~O(c)at 25.0' g(c)/950
cal/g
7,5275 7 4996 7.4964
4.30 4.25 4.22
CoS04.'7HzO(c)
Lange'O and our measurements mentioned later to calculate Ah0 = -116.8 cal g-' for the heat of solution of CoSOl to form 0.0132 m solution. Use of this value with data from Table IV in an equation like (1) leads
AH,
ml of Ha0
CoS04*6HzO(c)
Table IV: Heats of Solution of CoSO4.0.833H~O(c)a t 25.0"
+ HzO(g)
(3) The third-law data of Rao and Giauque4 lead to a considerably more reliable value of AS0298 = 35.92 cal deg-' mole-'. Since it is quite likely that the AGOzg8for reaction 3 calculated from the log p equation given by Broers and Van Welie6 is more reliable than either AS"298 or AH0298, which involve dAG/dT, we use their AGOzg8 with As02g8 from the third lawe to calculate AHo298 = 12.96 kcal mole-' for process 3. Combination of this value with the heat of vaporization of mater at 298°K leads to AH298 = -2.43 kcal mole-' for process 2. This last value, unlike the AH298 = -1.75 kea1 mole-' reported by Broers and Van Welie,'j is in satisfactory agreement with our AH298 = -2.48 kcal mole-' and AH298 = -2.455 kcal mole-' from Brodale and G i a u q ~ e . ~ Heats of solution of CoSO4(c) are listed in Table 111. The average of these results is AH = -18.3 kcal mole-', where the concentration of the final solution is 0.00546 ra. Although the final solutions in our measurements were quite dilute, heats of dilution to zero concentration are not negligible. We estimate this heat of dilution as -0.5 ( i 0 . l ) kcal mole-', based on the work of Lange'O on NiSO4 and ZnSO4. We thus obtain AH" = -18.8 kcal mole-' for the process =
CoS04(c) = Co2+(aq)
+ S042-(aq)
(4)
Combination of this heat of solution with heats of formation of CoSO4(c) from Adami and King3 and of SOd2-(aq) from Circular 500" leads to AHfO = -13.9 kcal mole-' for Co2+(aq). Heats of E,olution of CoS04.0.833HzO(c) are listed in Table IV. In order to separate the measured heats into contributions due to heats of solution of CoSOr and CoSO4.HzO, we use heat of dilution data from The Journal of Physical Chemistry
g(c)/950
ml of Hz0
2.1323 2.1293 2.1292 2,1050
to AH = -12.0 kcal mole-' for the heat of solution of CoSO4.HzO to form 0.0132 m solution. The corresponding heat of solution at infinite dilution is AH" = -12.7 kcal mole-' and that to form 0.0239 m solution is AH = -11.9 kcal mole-'. Combination of the AH" values for solution of Cos04 and COs04. HzO leads to AH298 = -6.1 kcal mole-' for the process
+
COSO~(C) HzO(1) = CoSOd.HzO(c)
(5)
Further combination of AH values for solution of CoS04,HzO and CoS04.6H20 to form 0.0239 m solutions gives AH298 = - 12.8 kcal mole-' for the process
+
C O S O ~ . H ~ O ( C jHzO(1) )
=
C O S O ~ . ~ H ~ O (6) (C)
Consideration of calorimetric uncertainties due to slow solution of CoS04.0.833HZO along with uncertainties associated with sample composition and heats of dilution leads us to estimate that our total uncertainties in AH values reported for processes represented by (5) and (6) are about *0.8 kcal mole-'. Vapor pressure measurements by Broers and Van Weliee led these workers to report AH298 = -8.68 f 0.35 kcal mole-' for the process represented by (6). -~
(10) E. Lange in "The Structure of Electrolytic Solutions," W. J . Hamer, Ed., John Wiley and Sons, Inc., New York, N. Y . , 1959; E. Lange and W. Miederer, Z.Elektroehem., 60, 34 (1956). (11) "Selected Values of Chemical Thermodynamic Properties," National Bureau of Standards Circular 500, U. S. Government Printing Office, Washington, D. C., 1952.
THERMOCHEMISTRY OF COBALT SULFATE
709
Although our calculations already reported indicate that AGzg8for reaction 2 from the work of Broers and Van Weliee is satisfactory, it is clear that their AH298 and AS298 values derived from dAG/dT are in error for that 'reaction. The following calculations show that the same is true for their work relevant to reaction 6. The log p equation given by Broers and Van Welie6 for the CoS04.6H20-CoS04.H20-H20(g) system leads (with S O 2 9 8 values for CoS04.6H20and water from Rao and Giauque4 and Circular 50O1') to 8 ' 2 9 8 = 29 cal deg-' mole-' for CoSO4.HzO(c). This value seems much too lowv: since various estimation procedures that work well for other hydrates of Cos04 lead to 8 ' 2 9 8 values from 38 to 43 cal deg-l mole-' for this compound. On the other hand, combination of A G O 2 9 8 from Broers and Van Welie6 with our AH298 leads to 8'298 = 42 cal deg-' mole-' for CoSOI.H20(c). We use this entropy along with our AH and A G O from Broers and Van Welie6 in subsequent calculations, but do not use any heats or entropies obtained from second-law calculations based on vapor pressure data.6 Heats of solution of material having the composition CoS04.6.62H20 were carried out with samples of various size so that solutions formed ranged from 0.010 to 0.034 m. These AH data lead to integral heats of dilution nearly identical with the more precise values obtained from direct measurements'O on solutions of NSO4 and ZnSO4. Results we have already quoted may be combined with heats of formation" of HzO(1) and S02-(aq) to yield AHf" values for the hydrates of CoS04. Further combination of these AHr" values with entropies of CoSO4.7H20 and CoS04.6H20 from Rao and Giauque4 and for CoS04.H20 from this paper leads to AGf" values. Entropies of the elements are taken from Kelley and King.12 The results of these calculations are list,ed in Table V.
permits calculation of the standard partial molal entropy of Co2+(aq). The standard free energy of solution of COSO~.~HZO(C), which is the solid phase in equilibrium with saturated solution at 298"K, is calculated from AGO = -RT In s2yTt2aw7
in which s, yi, and a, represent the molal solubility, the mean activity coefficient in saturated solution, and the activity of water in the saturated solution. The solubility is given by Brodale and G i a ~ q u e . ~We estimate the desired activity coefficient from data given by Robinson and Stokes13for ?;iSO4, and similarly estimate the osmotic coefficient that permits calculation of the desired activity of water. The derived free energy of solution is AGO = 3.17 kcal mole-'. The standard heat of solution of CoSO4.7Hz0 is obtained as AH" = 2.61 kcal mole-' from our measured heats and the heat of dilution.1° The heat of solution of this compound reported by Brodale and Giauque5 combined with a less certain heat of dilution leads to AHo = 2.69 kcal mole-' for this process. Combination of our AH" with A G O leads to AS"298 = -1.9 cal deg-' mole-' for the process represented by (7). Further combination of this AS" with available e n t r o p i e ~ ~leads * ' ~ to SZo= -26.0 cal deg-' mole-' for Co2+(aq). Earlier cal~ulations'~leading to the entropy of Co2+(aq)were averaged to give 3," = -26.6 cal deg-l mole-'. Since the entropies leading to this average were partly based either on estimates or on uncertain data, the present value is considerably more reliable. Combination of AHf" and 3 2 " values leads to AGt" = -13.3 kcal mole-' for Co2+(aq). This value is necessarily consistent with our tabulated AGf" for CoS04. 7H20 and the standard free energy of solution. The above AGf"leads to the following oxidation potential Co(c)
Table V : Thermodynamic Properties (298°K) of Hydrates of Cos04
so, Compound
CoSOi. HzO(c)
CoS04.6HzO(c ) COSOa. 7Hz0( C )
4.Hfo,
4GP,
kcal/mole
kcal/mole
cal/deg mole
-286.4 -640.8 -711.6
-248.7 -533.7 -590.6
42 87. 8634 97. 04g4
Consideration of the process represented by Cos04 * 7H20(c) = Co2+(aq)
+ SO2-(aq) + 7H20(1)
(7)
(8)
=
+ 2e-
Co2+(aq)
(E" =
0.29 v)
(9)
The difficulties associated with obtaining a satisfactorily reversible Co/Co2+ electrode system are illustrated by the E o values ranging from 0.246 to 0.298 v quoted by Latimer.I5 Our thermodynamic S o = 0.29 v seems more reliable than any value presently available from electrochemical measurements. (12) K. K. Kelley and E. G. King, G. S. Bureau of Mines Bulletin 592, U. S. Government Printing Office, Washington, D. C., 1961. (13) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed, Butterworth and Co. Ltd., London, 1959. (14) H. C. KOand L. G. Hepler, J . Chem. Eng. Data, 8, 59 (1963). (15) W. M. Latimer, "The Oxidation States of the Elements and Their Potentials in Aqueous Solutions," 2nd ed, Prentice-Hall, Inc., New York, N. Y., 1952.
Volume 70,Number 9 March 1966
7 10
GOLDBERG, RIDDELL,WINGARD, HOPKINS,WULFF,AND HEPLER
Heat of solution measurements were made with two separate batches of NiS04.6.000H20. The results are listed in Table VI. Integral heats of dilution that are calculated from differences in these measured heats of solution are in good agreement with the more accurate values that were directly determined. lo The standard heat of solution is AH" = 1.15 kcal mole-'.
NiS04.HzO(c)
+ 5Hz0(1) = NiS04.6HzO(c)
(10) Combination of the above heat of solution with the heat of dilutionlo leads to AHo = -14.0 kcal mole-' for the standard heat of solution of NiS04.Hz0. Table VI1 : Heats of Solution of NiSOd.5.059Hz0 a t 25.0' g(c)/950
ml of Hz0
Table VI: Heats of Solution of NiSOa*GHaO(c)a t 25.0' g ( c ) /950
ml
2.4778 3.3921 3.7680 4.2365 4.5971 4.9620 5,5785 5.737'5 6.4688 7.2230 8.2510 9.3048 10,1374 12.7062
5.2218 5.1900
AH, "it
0.0996 0.1165 0.1230 0.1304 0.1357 0,1410 0.1497 0,1518 0.1612 0.1703 0.1820 0.1933 0.2018 0.2259
kcal/mole
1.77 1.84 1.85 1.89 1.89 1.89 1.90 1.89 1.94 1.94 1.98 1.99 2.00 2.04
Heats of solution of solid samples having composition XS04.5.059HzO are listed in Table VII. Combination of these results with the heat of solution from Table VI corresponding to the same solution concentration leads by means of an equation like (1) to AH = -13.2 kcal mole-' for dissolving NiS04.HzO(c) to form a solution with concentration m = 0.0224. Combination of this AH with the appropriate AH from Table VI leads to AHzss = -15.1 kcal mole-' for the process represented by
The Journal of Phy8tcal Chemiatrtry
It has been assumed in the preceding calculations that the material we worked with was a mixture of the stable hydrates NiSO4 6Hz0and NiSO4 H2O. Samples containing a significantly larger fraction of the monohydrate were found to dissolve too slowly to permit accurate calorimetric investigation. The slowness of solution of NiS04 also prevented our measuring its heat of solution, which would have given us a new path to AGf" of Ni2+(aq)and thence a variety of compounds of Ni(I1). The best available heat of formation of Ni2+(aq) appears to be AHr" = -12.7 kcal mole-' (ref 14), which is combined with AH" = 1.15 kcal mole-' for solution of NiS04.6Hz0 and AH" = -14.0 kcal mole-' for solution of KiS04.Hz0 to yield AHfo = -640.6 kcal mole-' and aHfo = -283.9 kcal mole-' for these compounds, respectively.
-
Acknowledgments. We are indebted to the National Science Foundation for support of this research in the form of NSF-GP-1947 and Research Participation Grants for R. G. R. and M. R. W. We also thank Dr. Gary Bertrand for his help with calorimetric measurements and for keeping the calorimetric apparatus in working order.
