SOLUTION THERMOCHEMISTRY OF POLYVALENT ELECTROLYTES
9
The Solution Thermochemistry of Polyvalent Electrolytes.
11.
Silver Sulfate
by Harry P. Hopkins, Jr., and Claus A. Wulff Department of Chemistry, Carnegk Institute of Technology, Pitteburgh, Pennsylvania (Received September 6 , 1964)
Values for the thermodynamic functions characterizing the solution of silver sulfate have been obtained by utilizing data from the literature and newly determined values for the enthalpy of solution. It has been shown that previous evaluations of these quantities are in error, partially because of nonconsideration of the “weak” second ionization step. For the change in state, AgsS04(s) = 2Ag+(aq) S04+(aq), the following values have been determined for increments in the thermodynamic state functions, a t 25’: AGO = 6740 cal./mole, AHo = 4120 cal./mole, and A S o = -8.8 cal./(mole OK.). The standard entropy of the aqueous AgS04- ion has been estimated as 33 cal./(mole OK.).
+
The solution thermochemistry of salts whose aqueous solutions contain other than univalent ions is often complicated by secondary processes concomitant with solution and ionization, ie., “weak” ionization steps and hydrolysis. The failure to account for thermal effects arising from such sources (or, indeed, even to recognize them in the case of older work) has resulted in a thermochemical literature rich with inconsistent evaluations of the standard thermodynamic functions describing the solution and ionization of complex electrolytes. In favorable cases, such as calcium hydroxide,’ it has been possible to unravel the thermodynamics of the primary and secondary processes by a careful analysis of the concentration dependence of the heats of solution. This work describes such an analysis for the solution of silver sulfate Ag~S0ds)= 2Ag+(aq)
+ SO,-z(aq)
(1)
Documentation of a “weak” second ionization step for silver sulfate AgS04-(aq)
=
Ag+(aq)
+ SOd-Yaq)
saturated solution16-y* = 0.588, lead to AGIO = -RT In 4yk3m3 = 6557 cal./mole. Determination of the activity product by Kenttamaaa and by Vosburgh and McClure’ led to values of 6510 and 6550 cal./mole, respectively, for A G I O . An extensive series of determination of the solubility of silver sulfate in solutions of various supporting electrolytes has been reported by Stoughton and Lietzke.* These authors average the extrapolated values of their measurements (to zero ionic strength) in HzS04, HNO3, and 14gSO4 as 6595 cal./mole. In all these studies the supporting electrolyte contributed hydrogen and/or sulfate ions to the solution, surpressing the second ionization step if it is “weak” or masking it with the formation of bisulfate ions. The accord shown by the four values cited permits their average, 6550 f 30 cal./mole, to
(2)
is sparse and consists of only the conductance measurements of Righellato and Davies2and the potentiometric studies of Ledena at high ionic strength. The standard Gibbs free energy of solution, AGIO, has been deterniined in several studies on the assumption (usually implicit) that silver sulfate is completely ionized. For example, the solubility quoted in SeidellJ4 0.02676 m, and the mean activity coefficient in the
(1) H. P. Hopkins, Jr., and C. A. Wulff, J . Phys. Chem., 69, 6 (1966) I
(2) E. C. Righellato and C. W. Davies, Trans. Faraday SOC.,26, 592 (1930). (3) I. Leden, Acta Chem. S c a d . , 6, 971 (1952). (4) W. F. Linke, “Seidell’s Solubilities of Inorganic and Metal Organic Compounds,” 4th Ed., D. van Nostrand Co., Inc., Princeton, N. J., 1958. (5) J. B. Chloupek and V1. Z. Danes, Collection Czech. Chem. Commun.. 4, 8 (1932). (6) J. Kenttamaa, Suomen Kemistilehti, JOB, 9 (1957); Chenz. Abatr.; 51, 10159 (1957). (7) W. C. Vosburgh and R. S. McClure, J . A m . Chem. Soc., 65, 1060 (1943). (8) R. W. Stoughton and M. R. Lietzke, J . Phys. Chem., 64, 133 (1960).
Volume 69, Number 1 January 1966
HARRY P. HOPKINS, JR.,AXD CLAUSA. WULFF
10
be adopted for AGIO if the second ionization step is Lietzkes report 4.47 kcal./mole from the temperature not “weak.” dependence of the solubility. No attempt was made to I n their tabulation of the activity product of silver account for the effect of the second ionization step in sulfate, Stoughton and Lietzkes did not include their the derivations of these values. results utilizing KSOs as the supporting medium. This To permit a choice between the inconsistent values available for the thermodynamic functions describing lather value they report to be low by 0.103 pK unit140 cal./mole. This is perhaps the only electrolyte the solution of silver sulfate, a direct determination of the heat of solution was undertaken. in which the solubility of silver sulfate is uncomplicated by the medium. The value of A G I O , in KSOB, Experimental is then 6595 140 = 6735 cal./mole. An indeSeveral commercial samples of silver sulfate were pendent evaluation of AGIO is reported by Pan and Ling tested for suitability as experimental material and were from their thorough study of the electromotive force rejected because of slow rates of dissolution. A fresh of the Ag(s),/Ag2S04(s) electrode. Their value for sample was prepared by treating a solution of Fisher the standard free energy of solution is 6707 cal./mole certified reagent silver nitrate with a dilute solution of and is independent of any assumption about the sulfuric acid. Only the initial precipitate was collected. strength of the second ionization step. After successive washing with cold absolute ethanol and Righellato and Davies2 report the extent of the cold ether, the sample was dried under vacuum for 1 second ionization step at only two concentrations of week. Duplicate gravimetric determinations of the silver sulfate. If the concentration dependence of silver content (as silver chloride) indicated a purity of this quantity (but not its numerical value) is assumed a value comparable to the purity of the initial 99.8%; to be the same as that for T12S01arid K2S04,the degree silver nitrate. of second ionization iri the saturated solution is 0.77. Calorimetric determinations were made using the This datum leads to a silver ion concentration of 0.047 m existing apparatus, l 3 which includes a resistance and a sulfate ion concentration of 0.021 m. The satuthermometer to sense temperature increments. Samrated solution is still sufficiently dilute to permit estiples of the silver sulfate, described above, ranging bemation of the activity coefficients by -log y = 0 . 5 0 5 ~ ~ . tween 1.56 and 4.28 g. were dissolved into 950 ml. of v‘j/(l as y S g -= 0.785 and SO,-^ = 0.382. distilled water at 25.0 0.1’. The data were conThe standard free energy of solution corresponding to verted to enthalpies of solution on the basis of a gram these data is A G I O = -RT In (0.047)2(0.785)2(0.021). formula mass of 311.83. Twelve determinations, (0.382) = 6770 cal./mole. covering the concentration range m = 0.005 to 0.014, The average of the last three values cited for AGIO, were fitted, by least squares, to the straight line 6740 f 25 cal./mole, may tentatively be taken as representing the standard free energy of solution for A H o b a d = 4175 3370m”’ 40 caI./mole (3) silver sulfate on the assumption of a “weak” second where the uncertainty is the r.m.s. deviation. ionization step. The entropy of Ag2S04(s)has been determined by Discussion Latrmer, Hicks, and Schutz’o as 47.8 cal./(mole’K.). The existence of a “weak” second ionization step can The sum 2S0*,S SO^-^ has been evaluated as 39.0 be tested as follows. The observed heat of solution can cal. /mole OK.) from a consideration of the data for be represented by silver and alkali halides, nitrates, and sulfates.” The AHobsd - AHd,i = AHiO - (1 - a)AHzO (4) standard entropy increment for eq. 1 is then 39.0 47.8 = -8.8 cal. 1 (mole OK.). The standard enthalpy where A H d , , is the concentration-dependent heat of of solution, aHlO,cannow be computed as either 6550 dilution (estimated from values for the alkali sulfates) , 298.15(8.8) = 3930 cal./mole or 6740 - 298.15(8.8) = AH,’ is the standard enthalpy increment for eq. 2, and 4120 cal. /mole, representing the choices of “strong” and LY is the extent of the weak second ionization. If “weak” second ionization, respectively. A n indirect determination of the enthalpy of solution (9) K. Pan and C-L. Lin, J . Chinese Chem. Soc. (Taiwan), 6 , 1 (1959). by ‘rhomsen,12at Bo,as 4480 cal./mole for Ag2S04. (10) W. M. Latimer, J. F. G. Hicks. and P. W. Schutz, J . Chem. Phys., 1, 424 (1933). 140(IH20has been corrected by Latimer, et aZ.,1° to give (11) C. C. Stephenson, personal communication. AHI0 = 4207 cal. mole. This value is supported by the (12) J. Thomsen, “Thermochemische Untersuchungen.” Vol. 111, result of Pan and Linlg4215 cal./mole, derived from the Johann Ambrosius Barth Verlag, Leipziq, 1883. temperature dependence of the e.m.f. of the Ag(s)’ (13) C. U’u, M. M. Birky. and L. G. Hepler, J . P h y s . Chem., 6 7 , 1202 AgzS04(s) electrode. In contrast, Stoughton and (1963).
+
+ d),
*
+
+
T h e Journal of Physical Chemistry
*
THERMODYNAMIC CONSIDERATIONS IN METAL-METAL SALTSOLUTIONS
values of 01 are chosen (as described previously for the saturated solution) at selected concentrations in the range covered by our measurements and the quantity (1 - a) is plotted against the left-hand side of eq. 4, a straight line can be fitted through the points. The intercept, 4140 h 50 cal./mole, and slope, -1.5 f 0.3 kcal./mole, correspond to AHl’ and AH1’, respectively. The accord between the experimental value for AHIO and that estimated previously on the assumption of a “weak” second ionization step is excellent and substantiates that assumption. Additional evidence that a second process occurs concomitantly with solution and ionization of silver sulfate is the over-all concentration dependence of the heat of solution. When compared to ‘hormal” electrolytes of the same valence type (alkali sulfates and alkaline earth halides) the slope of A H o h s d against 4% is nearly twice as steep for silver sulfate as for the others.
11
The estimated equilibrium constant for eq. 2 is 0.05, from the work of Righellato and Davies.? The standard free energy is then AGzo = -RT In 0.05 = 1.8 kcal./mole, and the standard entropy increment for eq. 2 is (-1.5 - 1.8)/0.298 = -11 cal./(mole O K . ) . This last datum combined with the ionic entropies for the aqueous silver and sulfate ions can be used to estimate the entropy of the aqueous AgSOi- ion as 33 cal./ (mole OK.). This value is consistent with those of other univalent oxy anions. Acknowledgment.-The authors are grateful to Professor Loren G. Hepler for the use of his laboratory and its facilities and to Professor Clark C. Stephenson, of the Massachusetts Institute of Technology, for his helpful discussion. The partial financial support of the Xational Science Foundation is gratefully acknowledged.
Thermodynamic Considerations in Molten Metal-Metal Salt Solutions’”
by L. E. Topollb Atomics International, A Division of North American Aviation, Canoga Park, California (Received September 16, 1963)
The standard free energies of solution of isolated metal atoms with the molten chloride of that metal were calculated from vapor pressure and solubility data for 34 systems. Based on the values of these standard free energies of dissolution, a useful correlation is obtained. This correlation allows one to classify systems in terms of the magnitude of the energies and to estimate solubilities in some systems where experimental data are not available.
Introduction Solutions of various metals in their respective molten salts have been tjhe subject of numerous investigations.2 It is the purpose Of this paper to the standard free energies of dissolutiorl iIlvolved in the equilibrium between isolated g&SeOUSnletal atollls and nletal atoms dissolved in molten salts from solubility and vapor pressure data and t o correlate these values. The results of this study suggest that the dissolution energy
may be employed as a measure of the interaction energy of isolated metal atoms with the solvent. A classi(1) (a) This work was supported by the Research Division of the It has been presented before the Division of Physical Chemistry a t the 145th National Meeting of the Ameficarl Chemical Society, New York, N. T.,sept. 1963. (b) North American Aviation Science Center, Thousand Oaks, Calif. (2) See, for example, M. Bredig in “Molten Salt Chemistry,” M. Blander, Ed., Interscience Publishers, Inc., New York, N T., 1964,p. 367.
E. S. Atomic Energy Commission.
Volume 69,.Vumber 1
.7anuary 1965
