1346
F. H. MACDOUGALL AND SIGFRED PETERSON
EQUILIBRIA I N SILVER ACETATE SOLUTIOXS' F. H . MacDOUGALL
AND
SIGFRED PETERSOW
School of Chemistry, University o j Minnesota, Minneapolis, Minnesota Received M a y 97, 1947 INTRODUCTIOK
In previous papers from this Laboratory (13,14) studies were made of t h e effect of added electrolytes on the solubility of silver acetate in water and in mixed solvents. When the added electrolyte \vas of the uni-univalent type and contained no ion in common with silver acetate, it was found that the effect could be represented quantitatively by means of a Debye-Huckel equation with a reasonable value for the parameter which, in the theory of Debye, corresponds t o an average ionic diameter. In 1931 Larsson and hdell (10)reported that this procedure was unsuccessful when the added electrolyte was an acetate. I t seemed reasonable t o suppose that this failure could be due t o the formation in such cases of appreciable amounts of complex ions. The papers by PviacDougall and Allen (14) report the results of solubility measurements when the added electrolyte was either an acetate or a silver salt. These papers present strong evidence in favor of the existence of such complex ions as XgA; and Ag2.4+. Estimates were made of the magnitude of the dissociation constants of these complex ions; certain important results obtained in the present investigation enable one t o calculate the dissociation constant of AgA; by an independent method. To obtain additional and,, if possible, more exact information about the nature of silver acetate solutions, measurements Tvere made of the electromotive force of suitable cells. Since these measurements lead more or less directly t o a determination of the concentration of silver ion in silver acetate solutions, it becomes possible t o calculate the amount of dissolved silver which is not in the form of silwr ion. During the progress of our ivork and after our experiments had shown conclusively that a considerable fraction of dissolved silver acetate is not dissociated, n-e reteired a reprint, of a valuable paper by Leden (11),who had come t o the same conclusion. In order t o be able to make some comparison of our results with those obtained by Leden, we found it necessary to determine the solubility of silver acetate in 3 21 sodium perchlorate. M.4TERIALS USED AND METHODS O F AKALTSIS
Most of the materials used Tvere available in a sufficiently high degree of purity t o meet the standards given by Rosin (16). Sodium perchlorate was prepared from sodium carbonate and perchloric acid; silver oxide was prepared from silver nitrate and sodium hydroxide. 1 This paper gives the essential portions of the dissertation presented by Sigfred Peterson t o the Graduate Faculty of the University of Minnesota in partial fulfillment of the requirements for the degree of Doctor of Philosophy, March, 1917. 2 Du Pont Fellow in the School of Chemistry, Cniversity of Minnesota.
EQUILIBRIA IN SILVER ACETATE SOLUTIONS
1347
Solutions were analyzed for silver by the Volhard method (9). Solutions of potassium thiocyanate were standardized against n-eighed samples of fused silver nitrate. Solutions containing sodium nitrate or sodium acetate were analyzed by converting the salts t o sodium chloride, which was then xeighed. Details of the analysis were adapted from Treadwell and Hall (18). In preparing all solutions, double-distilled “conductivity” water was used. PREP.4RATION O F ELECTRODES
For the measurement of equilibria in silver acetate solutions it is necessary t o use electrodes reproducible t o closer than 0,0001 volt. Many investigators have prepared silver-silver salt (especially halide) electrodes of very high reproducibility; little is said about simple silver electrodes. Lewis (12) found electrodes prepared by the thermal decomposition of silver oxide satisfactory, and electrodes prepared by electrodeposition from cyanide solutions unsatisfactory. The precision needed in this work is greater than that reported by Lenis. For this investigation the folloiving procedure was used: Platinum wire of 0.36 mm. diameter was sealed through the end of a piece of soft-glass tubing with 5 cm. protruding, and Tvas carefully annealed. The seals \\ere tested for leaks either by immersion for 4 hr. in boiling water and inspection t o detect n-ater condensed inside the tube, or by immersion for 2 days in sodium carbonate solution with phenolphthalein indicator solution inside the tubes.3 The protruding wire was fused at the tip and bent into a helix approximately 3 mm. in diameter and approximately 8 mm. in length. X thick aqueous paste of silver oxide was packed onto the platinum spiral and dried for 45 min. at 100°C. Longer drying causes the oxide t o crumble and fall off the electrode; a briefer drying period results in eventual introduction of considerable moisture into the oxide-decomposition chamber. The dried oxide was decomposed t o porous silver metal by heating for 6 hr. at 400°C. in a Pyres tube in an electric furnace. Recombination was prevented by passing purified nitrogen (17) over the electrodes during the last half-hour of the heating and the subsequent cooling. Copper Ti-ire was inserted into the tube of the electrode and brought into electrical contact xith the platinum by either mercury or Wood’s alloy. Electrodes prepared in this manner 11ere frequently found t o differ in potential by several tenths of a millivolt nhen placed in the same solution. This disagreement often changed with time, usually increasing. An electrolytic purification method mas found t o reduce the disagreement between almost all electrodes t o 0.00002 Yolt or less. h lory current is passed through a dilute perchloric acid solution n-ith a platinum anode and the electrode to be treated as cathode. The conditions for this treatment have not been found critical; 0.5 milliamp. for 3 hr. in 0.02 ,M perchloric acid has been found satisfactory. After a period of use varying from about two weeks t o three months, silver electrodes become negative (in the external circuit) with respect t o freshly treated electrodes. A repetition of the electrolytic treatment restores the electrodes 3
Method attributed t o T. F. Young by J. E. Wertz
1348
F. H. DhCDOUGALL .UID SIGFRED PETGKSON
to agreement. The deterioration of electrodes is much more rapid in acetate solutions than in nitrate solutions. Some study was made of electrodes prepared by electrolytic deposition of silver on platinum. Electrodes formed by deposition from KAg(CN)2 solution xere not reproducible and were decidedly negative (external circuit) t o thermally deposited silver electrodes. Rapid electrolysis of 5 per cent silver nitrate solution (0.2 amp. for a fen- minutes on a 1-cm. length of platinum 0.36 mm. in diameter) gave electrodes which agreed within 0.00002 volt with treated thermal electrodes; however, the silver deposit was so loosely adherent as t o make this type of electrode impractical. To avoid the lack of reproducibility of silver electrodes, other investigators (8, 11) have used silver chloride electrodes. At the suggestion of Professor I. M. Kolthoff, silver iodide electrodes were tried. The silver electrodes described above were electrolytically oxidized for 2-4 hr. with 1.25 milliamp. in 0.05 X potassium iodide. The simple platinum cathode x a s separated from the anode solution by a sintered-glass filter crucible. Mutual agreement among the silver iodide electrodes as well as agreement between these and simple (electrolytically treated) silver electrodes was satisfactory. The iodide electrodes reached equilibrium potentials more slowly than silver electrodes, and also deteriorated n-ith use. The stability of these electrodes appeared greater than that of simple silver electrodes in acetate solution, but less in nitrate solution. The electrodes were tested by measurement of the electromotive force between them in a multiple-necked cell containing 0.01 M silver nitrate. THE EXPERIMENTAL NETHOD
Cells studied were of the type
1 AgA or i i g S o 3 (c,) i I
?;ah (cp)
$ 1.0, the curvature may well be due t o other causes (such as change in values of activity coefficients) than the existence of Agr13--. Accordingly we have confined our attentions to the curve for (A-) 5 1.0 and have used the method of least squares t o find the best straight line. In this way, we find from Leden's data: B 1
= 2.37 and B2 = 1.71
Applying these values of Bl and BZt o our data in table 3 dealing viith the solubility of silver acetate in 2.95 molar sodium perchlorate, we find c A ~ A = 0.00532, c A g + = 0.04747, cA- = 0.04729, cagA,= 0.00018. The values obtained for cAga, cAg-, and cA- are virtually independent of the value taken for Bz. From our values for K , and K I (see equations 14 and 15) it follows that in all aqueous solutions saturated a t 25OC. with silver acetate:
1356
F. H. MACDOUGALL AND SIGFRED PETERSON
TABLE 2 Molalities and the function K’ CELL
C
*z
t
m.
m.
(Apt)
(A-)
1/K’
1 2 3‘ 4 5
0.0382 0,0506 0.0363 0.0460 0.00987
0.04388 0.05963 0.04165 0.05356 0.06212
0.04388 0.05963 0.04165 0.05356 0.01190
0.0384 0.0508 0.0365 0.0463 0.00995
0.0384 0,0538 0.0365 0.0463 0.0602
5.68 5.47 5.78 5.35 5.32
6 7 8 9 10
0.0058 0.01183 0.005511 0.02809 0.005859
0.005843 0.01253 0.03600 0.03129 0,01615
0.005943 0.01250 0.006252 0.03129 0.006246
0,0058 0.01187 0,005524 0.02819 0.005878
0,0058 0.01187 0.03527 0,02819 0.01578
5.68 5.67 5.46 5.58 5.19
11 12 13 14 15
0.05653 0.002956 0.006077 0.005353 0.05065
0.02625 0.01308 0.006253 0.05021 0.05963
0.006246 0.003126 0.006253 0.006254 0.05963
0,005671 0.002965 0,006094 0.005380 0.05092
0.02567 0.01292 0,00609 0.04934 0.05092
5.50 5.36 5.09 5.20 5.37
16 17 18 19 20
0.05057 0.00539 0.01127 0.01036 0.03666
0.05963 0.02602 0.01187 0.04176 0.04162
0,05963 0.005949 0.01187 0,01189 0,04162
0.05083 0.005411 0.01130 0.01041 0.03682
0.05083 0.02548 0.01130 0.04027 0.03682
5.43 5.43 5.66 5.35 5.30
21 22 23 24 25
0.01059 0.004629 0.00398 0.002628 0.002115
0.03194 0.1007 0.2019 0.5114 0.7229
0.01188 0.006227 0.006287 0.006367 0,006451
0.01059 0.004660 0.00402 0.002688 0.002184
0.03066 0.09912 0.1996 0.5077 0.7186
5.68 6.28 6.03 7.45 8.36
26 27 28 29 30
0.001754 0.002470 0.003995 0.003786 0.002473
0.9375 0.5176 0.7346 0.2020 0.5117
0.006506 0.006065 0.01221 0.005983 0.006063
0.001827 0.002528 0,004125 0.003825 0.002531
0.9329 0.5141 0.7265 0.1998 0,5081
9.15 7.52 8.30 6.01 7.60
31 32 33 34 35
O.OO4441 0.003751 0.001655 0.02106 0.01055
0.1007 0.2021 0.9381 0.1307 0.01109
0.005955 0.005981 0.006152 0.02985 0.01109
0.004473 0.003794 0.001724 0.02123 0.01058
0.09925 0.1999 0.9337 0.1221 0.01058
6.03 6.14 9.15 6.30 5.71
36 37 38 39 40
0.00255 0.001315 0.00814 0.001315 0.00991
1,1211 2.1749 0.1116 2.187 0.03111
0.01161 0.01212 0.01113 0.01212 0.01110
0.00268 0.00144 0.00820 0.00144 0.00995
1,109 2.159 0,1085 2.171 0.02996
10.29 15.17 6.09 15.13 5.56
EQUILIBRIA
1357
IN SILVER ACETATE SOLUTIOKS
TABLE 2-Concluded 1/K'
(As+)
CELL
41 42 43 44 45
0.00444
46 47 48 49
0.00194 0.00685 0.01057 0.00955
0.5215 1.5117 0.2130 0.01109 0.04101
0.01133 0.01180 0.01118 O.OllG?l 0.01111
0.00455 0.00207 0.00693 0.01061 0.00960
0.5147 1.498 0.2085 0.01061 0.03950
8.19 12.36 6.43 5.42 5.99
0.01018 0.00957 0.0475
0.02100 0.04088 0.05566
0.01109 0.01110 0.05566 0.01112 0.02776
0.01021 O.Oo962 0,04773 0.00913 0.02531
0.02013 0.03939 0.04773 0.0592 0.0253
5.81 5.91 5.54 5.98 5.42
50
TABLE 3 Solubilitu of silver acetate ut 66°C.
I
AgA
Molality
I
Molarity
0.06699 0.06160
j
0.06654 0.05301
'
1
' ~
SaC10, Molality
I
Molarity
0. 3.4264
For the molar and molal activity coefficients, fo and yo, of unionized AgS in 2.95 Jf sodium perchlorate we obtain accordingly fo =
0.0105 om2 = 1.97
70 = 1.70
(20) (21)
From equation 10 with yo = 1.7 and S = 3, k is calculated to be about 0.077, which is the basis for our assumption that
12
= 0.07
(22)
I t is true that this value may be considerably in error. We can also find from the previously mentioned data (0.04747) (0.04729) f =
K1
= 0.00195
whence
f = 0.87
(23)
where f is the mean molar activity coefficient of Ag+ and A - in 2.95 M sodium perchlorate saturated with silver acetate. From this result, the corresponding value of y2 is 0.64 or of y is 0.80. If now we use Leden's value of 1.71 for Bz, together with f = 0.87, we find from the equation Kz = f / B z , a value of Kz
1358
F.
n.
MACDOUGALL LYD
SIGFRED PETERSON
equal to 0.51, more than twice as large as the value me have already found (see equation 14). In this connection it is to be noted, first, that the exact relation between K 2 and B2 is given by the equation:
secondly, that the rule that all univalent ions in a given solution have equal activity coefficients, though approximately valid in solutions of low or moderate ionic strength, may be greatly in error when the ionic strength is high. As an illustration, consider the values found by Jones (6) for the molal activity coefficient of sodium perchlorate in 3.5 molal sodium perchlorate and of lithium perchlorate in 3.5 molal lithium perchlorate. He finds for y in these cases 0.619 and 1.89, respectively. I t is highly probable that in a 3.5 molal solution containing both sodium perchlorate and lithium perchlorate, the activity coefficient of Li+ would be much greater than that of S a + . Similarly, in a concentrated snlution containing sodium perchlorate, sodium acetate, and silver acetate, the ratio fA- to fApA; may differ considerably from unity.
A more direct determination of Kz Gsing the relations, (&A)
(&+I ( - ~ - ) Y ~ I K , Y O
K, = 0.186 a t 25°C.; K , = 0.179 at 3470°C. log yo = 0.07 S for 25OC. and 3470°C.
and the molalities (Ag+) and (A-) given in table 2, we can calculate the molality of AgA in the acetate solution of each of the fifty cells studied. By means of the equation (AgA;) = m, - (,4g+)
-
(AgA)
(8)
we can then calculate the molality of the complex ion Ag.G in each of the acetate
solutions. S o w in all the solutions in which (Ag+) N (A-), each of these molalities is less than 0.05. Since Kz is approximately equal to 0.2, it follows from equation 2, (&A,)
= (Ag+)(A-W/Kz
that in all these solutions (AgA;) is less than 0.00040 and frequently much less. To obtain values of (AgA;) which are of any significance we must accordingly restrict ourselves to solutions in which (A-) is considerably larger than (Ag').
1359
EQUILIBRIA IN SILVER ACETATE SOLGTIONS
This means that we shall consider only cells 24 t o 28, 30,33, 34, 36 to 39, 41, 42 and 43. It may be added that when equation 8 is used to calculate (AgA;) in the acetate solutions of cells 1 to 23 inclusive, the values obtained, most of which are positive, range from -0.00011 to $0.00037. From each significant value of (AgA;), we can calculate KOby means of the equation
TABLE 4 The equilibrium constant K , at 25'C.
24 25 26 27 28 30 33 34
0.00255 0.00258 0.00252 0. W243 0.00492 0.00240 0.00238 0.00734
0.231 0.229 0.235 0.227 0.236 0.218 0.234 (0.133)
0.00113 0.00169 0.00216 0.00111 0,00316 0.00113 0.00205 0.00128 ~
~~~
~~
Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.230
TABLE 5 The equilibrium constant K1 at 94.7"C. CELL
36 37 38 39 41 42 43
I
(A&
0.00415 0.00312 0.00269 0.00312 0.00445 0.00376 0.00368
,Average. , . . . . . , . . . . . . . . . . . . . . . . .
..... ... . .
I
(AgAa-1
0.00478 0.00756 0.00024 O.OOi56 0.00233 0.00597 0.00057 .. . . .
,
, , ,
K2
0.205 0.219 0.221 0.221 0.191 0.212 0.249 , , , ,
.
1
0.217
The results of these calculations are tabulated in tables 4 and 5 . It is naturally very satisfactory to obtain a series of values of KO which agree so yell among themselves, at each of the two temperatures. Because of the many assumptions made in the theoretical development of our equations, it is difficult to estimate the uncertainty in the average values obtained for KO. However, the values K O = 0.230 at 25°C. and K O = 0.217 at 34.70"C. are probably more accurate than those given in equation 16, v u . , K O= 0.20 f0.04 a t 25°C. and KZ= 0.19 f 0.4 at 34.70%
1360
F. H. M A C D O U G W AND SIGFRED PETERSON SUMMARY
1. w e have measured the E.M.F. a t 25°C. and at 34.7"C. of cells in which one of the solutions contained sodium acetate i n d either silver acetate or silver nitrate. 2. We have determined the solubility of silver acetate at 25°C. in 2.95 M sodium perchlorate. 3. In the discussion and interpretation of our results we have made use of previous studies on the solubility of silver acetate in water in the presence of added electrolytes. We have also availed ourselves of a recent investigation of Leden on the E.M.F. of certain cells. 4. The most important result of our work is the determination of the ionization constant, K,, of silver acetate. For example, in 0.06 molal silver acetate in aqueous solution the degree of ionization is about 85 per cent. 5 . We confirmed the existence of the complex ion, AgA;, and determined its dissociation constant, K1. 6. Our results enabled us to correct previous estimates of the true activity product, K,, of Ag+ and A- in saturated aqueous solutions. 7 . We give here a list of equilibrium constants expressed in terms of molal activities and the result obtained in a determination of solubility: (a)
For the reaction AgA = Ag+
Ki
= 0.186 a t 25°C.;
+ -4-,
Ki = 0.179 a t 34.7"C.
( b ) For the reaction AgA; = Ag'
+ 2A-,
K2 = 0.230 at 25°C.; K Z = 0.217 a t 34.7"C. (c)
For the equilibria AgA(s) = AgA = Ag'
K1 =
aAgiaA-
=
+ A-,
0.00195 a t 25°C.
( d ) For the molality, m, and molarity, c , of silver acetate a t 25OC. in 2.95 molar sodium perchlorate, sat,urated with silver acetate, m = 0.06160 and c = 0.05304. REFEItEXCES (1) H ~ R N E D H., S.,ANU OWES, B. B.: The Physical Chemistrv of Electrolytic Solutions, pp. 397-405. lteinhold Publishing Corporation, New York (1943). (2) HEIFDERSON, P . : %. physik. Cheni. 69, 118 (1907); 63, 325 (1903). (3) HILL,A . E . , AND S I ~ I M O NJ. S ,D . : J. Am. Cnem. Sot. 91, 821 (1909). (4) IRVISG,GEORGEW'., J R . ,AND S.UITH,Iu. I t . : I n d . Eng.Chern., Anal. Ed. 6, 480 (1934). ( 5 ) J . ~ Q L E S ,ARTHUR:Trans. Faraday SOC.6, 235 (1910). ( 6 ) J o N E ~ J~., H . : J . Phys. Colloid Cheni. 61, 516-21 (1947). (7) KNOX,JOSEPH,ANI) WILL, H . K . : J . Chein. Sor:. 116, 853 (1919). (8) KOLTHOFF, I . M . , A R D BOSCH,W.:J. P h y s . Chern. 36, 1702 (1932). (9) KOLTHOFF, I . M., ASD SARDELL, E.B.:Y'eztbook o j Quantitative Inoryunic A n a l y s i s , Chap. XXXV. The Rfacmillan Company, Xew York (1937). (10) LARSSON, M . , ASD ADELL,R . : L. anorg. allgem. Chern. 196, 354 (1931). (11) LEUEN,100: Svensk Kem. Tid. 68, 129 (1946).
EQUILIBRIUM COOLING CURVES
1361
(12) LERIS, G. S . :J. Am. Chem. SOC.28, 158 (1906). F. H . : J. Am. Chem. SOC.62, 1390 (1930). (13) MACDOGCALL, MACDOGGALL, F. H., ANU I ~ E H S E RJOHK, . JR.: J. Am. Chem. SOC.68, 368 (1934). F. H.. .ASU BARTSCH, C. E . : J. Phys. Chem. 40, 649 (1936). MACDOUGALL, F. H., ASD LARSOS,W. D.: J. Phys. Chem. 41, 417 (1937). ~IACDOUGALL, (14) MACDOTGALL, F. H.. ASD ALLES,~ I A R T I K J.: Phys. Chem. 46, i30 (1942); 46, 7 3 i (1942); 49, 245 (1945). 1151 MACISSES,D . A. : T h e P r i m p l e s of Electrochemistry, p . 244. Ileinhold Publishing Corparation. S e n . l-ork (1539). (16) ROSIN, J . : Chenizcal Reagents and Slandards. D . Van Sostrand Conipnny, S e w York (153i). : l i ) TREADWELL, F. P.?ASU HALL,W.T . : Analytical Chemistry.
1’02. 11. Quantitatice, 8th edition, p. 703. John U’iley and Sons, Inc., Ken. York (1935). I 1s) Reference l i , pp. 58, 59, 55. (101 WYJIAS,J., J R . : Phys. Rev. 36, 623 (1930).
T H E SH.4PE OF HEAT-C.\PhCITY AXD EQUILIBRIUbI COOLIKG CURVES I S T H E REGIOY OF MELTING OF SOLID SOLGTIONS K4ROL J. MYSELS‘ Department G$ Chemistrg, S e w I‘orb I‘niuersity, I‘nizlersity Heights, .\-ew
I-ork, .Yezo l’oi,‘
Receired J u n e 4 , 1947 Cooling curves are n.idely used in phase studies to determine the position and shape of solidus and liquidus, the equilibrium lines between solid and liquid phases. It is generally accepted that changes in the slope of cooling curves correspond to beginnings or ends of phase changes, and at the same time it is recognized that lack of equilibrium in phase changes and in thermal conductivity renders interpretation difficult. In Yiew of these difficulties there has been little point heretofore in analyzing more thoroughly the shape of cooling curves, and such analysis seems not to have k e n made. The development of adiabatic calorimeters has nowadays removed, in principle at) least, the difficulties due t o lack of equilibrium and allows the construction of “equilibrium cooling curves” (heat removed us. temperature: -Q us. 2’) and heat-capacity curves (d(S/dT us. 2‘) from the measured values of heat introduced, Q,and temperature reached, 5”. These measurements may be made very precisely and reproducibly, but it remains generally difficult t o ascertain how closely equilibrium has been approached because of the unidirectional character of the experiments. Therefore it may be worthwhile to correlate the shapes of these curves with that of the phase diagram and with other properties of the system in order to provide a check on their internal consistency and a help in interpolations. Present address: Drpartment of Chemistry, Vniversity of Southern California, Los AngJes 7, California.
