JOHN C. SYNNOTT AND JAMES N. BUTLER
1470
Solubility and Complex Formation Equilibria of Silver Chloride in Dimethyl Sulfoxide-Water Mixtures by John C. Synnott and James N. Butler Tyco Laboratories, Inc., Waltham, Massachusetts
OR154
(Received October 1 1 1968) ~
The equilibria of silver chloride in dimethyl sulfoxide-water solutions containing excess chloride have been studied potentiometrically in a constant ionic medium (0.1 M lithium perchlorate or tetraethylammonium perchlorate) at 25’. Equilibrium constants were fitted by a nonlinear least-squares pit-mapping technique. Mononuclear complexes AgCl, AgClZ-, and AgCV- were found. The over-all formation constants for these complexes in anhydrous dimethyl sulfoxide are log PI = 6.8 f 0.7, log p2 = 11.73 f 0.02, and log /I3 = 13.1 f 0.4. The solubility product of silver chloride is log K,o = -10.279 f 0 003 (errors are statistical 95% confidence limits). With increasing water content, S , decreases and K.0 increases. Discrepancies between previous results in the literature appear to be due to differences in ion pairing with the supporting electrolyte. Ion pairing is probably negligible in LiC104 and Et4NC104 medium. Estimates of the equilibrium constants at zero ionic strength are made, and the results are discussed in term of ionic solvation.
Introduction
Experimental Section
Dimethyl sulfoxide (DMSO) is a solvent of considerable importance in coordination chemistry and electrochemistry.’ The silver-silver chloride reference electrode is common, and the solubility and complex formation equilibria of silver chloride are important both for an understanding of this reference electrode and for their relevance to solvation phenomena in this solvent. Previous publications from this laboratory have reported detailed studies of the equilibria of silver chloride in propylene carbonate,2propylene carbonatewater mixture^,^ and dirnethylf~rmamide.~This paper presents the results of our investigations in dimethyl sulfoxide-water mixtures, a system of particular interest because of the strong coordinating tendency of DMSO and the strong hydrogen-bonding tendency of water. Other measurements on this system have been published,6v6 but there is disagreement among the various results, no statistical limits of error for the constants have been established, and no study of the effect of water on the equilibrium constants has been made. By analogy with water, propylene carbonate,2J and DMF,4 the following equilibria are expected.
Dimethyl sulfoxide (Matheson Coleman and Bell, Spectroquality) was dried over molecular sieves (Linde, Type 5-A) in an argon atmosphere glove box and then passed through a size D glass frit. Chromatographic analysis (Barber-Coleman Model 5000, Porapak Q column, thermal conductivity detection) indicated that the dried solvent contained less than 35 ppm of water and organic impurities. LiC1, LiC104 (Anderson Physics Laboratories, ultrahigh purity) and Et4NC104 (Eastman) were stored under argon in a glove box in which all weighings were made. Experiments with anhydrous DMSO were carried out under argon in a glove box. Experiments with added water were carried out in the laboratory using as-received DMSO (-0.03% water) to prepare solutions. Organic impurities were less than 1 0 ppm. Mixtures of DMSO and triply distilled water were prepared by weight (except where noted) and molar concentrations calculated using the density data of Kentamaa and Lindbergag The method was the same as described previously.2
AgCl(s) e Ag+
+ C1-
+ C1- +AgCl (soln) Ag+ + 2C1AgC12Ag+ + 3Cl- eAgCla2-
Ag+
K O P1
PZ PS
(The IUPAC notation for equilibrium constants7 is used.) These equilibria have been verified by our experiments. Previous workers evaluated only K,o and 02, but we have also evaluated and /3~ for a number of experiments including some already published.8 The Journal of Physical Chemiatry
(1) J. N.Butler, J . Eleclroanal. Chem., 14, 89 (1967). (2) J. N. Butler, Anal. Chem., 39, 1799 (1967). (3) J. N. Butler, D. R . Cogley, and mi. Zurosky, J. Electrochem. Soc., 1 1 5 , 445 (1968). (4) J. N.Butler, J . Phys. Chem., 7 2 , 3288 (1968). (5) D. C. Luehrs, R . T. Iwamoto, and 3. Kleinberg, Inorg. Chem., 5 , 201 (1966); D. C. Luehrs, Thesis, University of Kansas, 1965; University Microfllms No. 66-6033. (6) R.Alexander, E.C. B. KO,Y. 0.Mac, and A. J. Parker, J . Amer. Chem. Soc., 89, 3703 (1967). (7) L. G. Sillen and A. E. Martell. “Stability Constants,” Special Publication No. 17,The Chemical Society, London, 1964. (8) N . A. Rumbaut and H. L. Peeters, Bull. Soc. Chim. Belges, 7 6 33 (1967). (9) J. Kentamaa and J. Lindberg, Suomen Kemistilehti, B , 3 3 , 32 (1960).
SOLUBILITY AND COMPLEX FORMATION EQUILIBRIA OF SILVERCHLORIDE All measurements were made using a water-jacketed cell of three compartments, connected by salt bridges. Temperature was maintained a t 25.0 f 0.1” by means of a Haake circulating thermostat. Etched silver wires were used as electrodes in both titration and reference compartments and a uniform ionic strength of 0,100 M was maintained in all compartments with LiC104 or Et4NC104. The common reference electrode compartment contained 0.004M AgNOs in the same solvent mixture and supporting electrolyte. To the titration compartment were added 20 ml of supporting electrolyte and known volumes of 0.100 M LiCl solution and 0.100 M AgN03 solution, using 2-ml RGI micrometer burets. The stock solutions were analyzed by potentiometric titration for chloride with aqueous AgN03 solutions of known concentration and for silver with LiC1-DMSO solutions of known concentration. Potentials were measured using a high-impedance differential voltmeter (Fluke) and were usually steady within 0.1 mV.
Results Table I lists the detailed numerical data for the portion of the titration curve before the end point in 11 titrations which we considered to be accurate and on which the calculations were performed. Although the concentrations are given to three decimal places, this is merely a computational convenience to avoid round-off errors and does not reflect the true accuracy of the concentration values, which is ca. f0.01 mM. The saturation limit is clearly defined by a discontinuity in slope and the points in Table I are labeled “saturated” or “unsaturated” according to whether they fell above or below the saturation limit. The potentiometrically determined saturation limit was verified by visual observation of precipitate formation in the titration cell. In the region following the end point, where excess silver ion was present, the Nernst equation in the form
E
=
EO
+ (RT/F) In [Ag+]
where [Ag+] is the excess free silver ion concentration, was obeyed within =t0.2mV. The values of Eo obtained from this region are listed in Table I for each titration. Free silver ion concentrations in the other regions of the titration curve were calculated from the same equation using this value of EO, together with the measured value of E. Constancy of the solubility product in the saturated region (see below) showed that here the Nernst equation was also obeyed to within =tO.ZrnV. Thus, in the 0.1 M EtdNC104 medium used, the activity coefficient of silver ion was constant and is included in EO. From each set of data for unsaturated solutions we determined equilibrium constants for complex formation by the nonlinear least-squares pit-mapping technique described p r e v i o u ~ l y . ~For , ~ sets 1, 2, and 3 a sufficient number of data points of high accuracy was
N \
N
I--
0
1.00 .98 1.02
-
1471
.96 .94
4
--
’ ’
SET 2
-92-
-
*s8r
1.00
SET 3
.96
I
I
I
I
I
I
-n
Figure 1, Deviation of experimental points from theoretical curve for unsaturat,ed region, expressed as the function Z’/Z, defined in ref 2. The constants used to calculate the theoretical curve are given in Table 11. The arrow indicates the direction in which the titration proceeded.
available so that we were able to determine the constants P I , p2, and p3 within reasonable confidence limits. For the other data sets only p2 could be determined. Insufficient data were available to determine confidence limits on p2 for sets 6 , 7, and 8. The constants determined are listed in Table 11. Systematic deviations from the theoretical form of the equations were observed for points where only a very small amount of silver or chloride had been added to the supporting electrolyte, and these deviations could be removed by assuming that a small amount of residual AgCl remained in the cell. This residual concentration was determined by curve fitting a t the lowest concentration regions, and values are listed in Table 11. These corrections were essentially negligible except for set 1. The data in Table I do not contain the correction for residual AgC1. The mononuclear nature of the complexes has been already established by the measurements of Luehrs, et aZ.,6 and of Rumbaut and PeetersV8 This can be further verified by comparing the results of sets 9 and 10 which differ in silver ion concentration by a factor of 5. The same value is obtained for p2 in both titrations within experimental error. Complexes of the type Ag2X+ are found in solutions containing excess silverlo but are negligible in excess chloride. Typical deviations of experimental values from the theoretical curves, expressed as the function2 Z’/Z, are (10) D. C . Luehrs and K. (1968).
Abate, J . Inorg. Nucl.
Chem., 30, 649
Volume 79,Number 6 May 1969
JOHN C. SYNNOTT AND JAMESN. BUTLIT&
1472 Table I: Experimental Data" CAgr m M
E,V
Cci, mM
CAg,
mM
Set 1: EO = 0.1435 V Unsaturated 0.532 0.795 1.084 1.439 2.083 2.253
4.635 4.622 4.608 4.590 4.558 4.550
-0.4530 -0.4347 -0.4157 -0.3906 -0.3122 -0.2504
Saturated 2.304 2.617 3.476 3.847 4.255 4.311
4.457 4.532 4.439 4.470 4.450 4.447
-0.2212 -0.2179 -0.2012 -0.1880 -0.1585 -0.1500
Set 2: EO = 0.1442 V Unsaturated 0.189 0.377 0.471 0.937 1.399 1.856 2.083 2.309
5.100 5.090 5.085 5.061 5.038 5.014 5.002 4.991
-0.4939 -0.4710 -0.4628 -0.4318 -0.4038 -0.3695 -0.3446 -0.3046
2.534 2.758 3.070 3.203 3.644
Saturated 4.979 4.968 4.952 4.945 4.922
-0.2230 -0.2206 -0.2166 -0.2150 -0.2075
Set 3: EO = 0.1448 V Unsaturated 4.990 4.981 4.976 4.930 4.907 4.895 4.884
0.190 0.380 0.475 1.411 1.872 2.101 2.329
-0.4873 -0.4648 -0.4563 -0.3949 -0.3567 -0.3266 -0.2651
Saturated 4.877 4.872 4.861 4.839 4.817 4 * 795
2.465 2.556 2.782 3.231 3.675 4.116
-0.2223 -0.2213 -0.2187 -0.2121 -0.2032 -0.1895
Set 4: Eo = 0,1410 V
Unssturated 0.463 0.922 1.376 1.826 2.050 2,272 The Journal o j Phyeical Chemistry
5.009 4.986 4.962 4.939 4.928 4.916
-0.4475 -0.4165 -0.3888 -0.3546 -0.3297 -0.2897
CCI, mM
E, V
Saturated 2.714 3 * 152 3.585 4.015 4.228
4.894 -0.2287 4.871 -0.2233 4.849 -0.2160 4.826 -0.2052 4.815 -0.1971 Set 5 : EO = 0.1440V Unsaturated 0.476 5.019 -0.3460 1.415 4.972 -0.2858 Saturated 1.879 4.949 -0.2621 2.108 4.937 -0.2608 2.337 4.926 -0.2587 2.792 4.903 -0.2534 3,242 4.880 -0.2470 3.688 4.858 -0.2384 4.130 4.336 -0.2253 4.350 4.825 -0.2153 Set 6: Eo = 0.1443 V Unsaturated 0.093 5.062 -0.3040 Saturated 0.278 5.052 -0.2831 0.463 5.943 -0.2823 2.270 4.949 -0.2674 3.148 4.903 -0.2567 3.582 4.881 -0.2490 4.011 4.858 -0.2380 4.224 4.847 -0.2301 4.436 4.836 -0.2191 4.648 4.826 -0.1991 Set 7: EO = 0.1433V Unsaturated 0.048 5.059 -0.2859 Saturated 0.095 5.057 -0.2833 0.191 5.052 -0.2829 5.043 -0.2820 0.381 0.475 5.038 -0.2815 4.967 -0.2719 1.875 4.921 -0.2627 2.786 3.681 4.876 -0.2481 4.122 4.854 -0.2359 -0.2253 4.341 4.843 -0.2105 4.559 4.832 Set 8: EO = 0.1436 V Unsaturated 0.047 4.993 -0.2879 Saturated 4.990 -0,2841 0.094 4.983 -0,2833 0.236 4.972 -0.2827 0.471 4.925 -0.2753 1.399 4.879 -0.2667 2.309 4.834 -0.2547 3.203 4.790 -0.2322 4.081 4.779 -0.2210 4.298
1473
SOLUBILITY AND COMPLEX FORMATION EQUILIBRIA OF SILVERCHLORIDE
Table I (Continued) CA,, mM
0.435 0.455 0.477 0.488 0.494
Cci, m M
CAR, mM
E, V
Set 9: Eo = 0.1515 V Unsaturated
Unsaturated
12.999 9.037 4.699 2.373 1.166
0.048 0.095 0.190 0.285 0.380 0.475 0.711 0.945 1.179 1.411 1.873 2.102 2.330 2.398
-0.5062 -0.4855 -0.4537 -0.4106 -0.3491
Saturated 0.497
0.646
-0.2260
Set 10: F = 0.1515 V Unsaturated 1.383 1.615 1.846 1.948 2.030 2.085 2.131 2.191
4.720 4.709 4.698 4.693 4.689 4.686 4.684 4.681
-0.3773 -0.3580 -0.3318 -0.3141 -0.2948 -0.2732 -0.2516 -0.2180
4.681 4.668 4.654 4.633 4.622 4.603 4.586 4.586 4.578 4.578
5.036 5.033 5.029 5.024 5.019 5.014 5.002 4.991 4.979 4.967 4.944 4.932 4.921 4.917
-0.5240 -0.5070 -0.4860 -0.4730 -0.4630 -0.3550 -0.4380 -0.4230 -0.4080 -0.3940 -0.3570 -0.3270 -0.2790 -0.1510
Saturated 2.467 2.512 2.702 2.783 3.677 4.118 4.555
Saturated 2.196 2.469 2.760 3.211 3.434 3.834 4.187 4.196 4.354 4.494
E, V
Cci, mM
Set 11: Eo = 0.1439V
-0.2156 -0.2124 -0.2088 -0.2013 -0.1965 -0.1848 -0.1676 -0.1670 -0.1529 -0.1319
4.914 4.912 4.902 4.898 4.853 4.831 4.809
-0.2230 -0.2220 -0.2210 -0.2195 -0.2037 -0.1906 -0.1657
Sets 1-8, LiC104 supporting electrolyte; sets 9-11, EtrNClO4 supporting electrolyte.
given in Figure 1. The systematic dip at high values of n (average number of chlorides bound to a silver ion) occurs near the start of the titration curve and is probably related to inaccuracies in the micrometer buret. Correction for the presence of residual AgCl in the system (see above) compensates for most of this deviation but does not completely remove it. Solubility products were obtained from the saturated region of the titration curves, using the constants pn obtained above, by the method previously described.2 A separate value of the solubility product was obtained for each point, and the average value for each set together with its confidence limits is listed in Table 11. There were no obvious systematic deviations from the theoretical form of the titration curve, except set 10, for which -log K,O exhibited a dip (similar in form to those in Figure 1) of approximately 0.02 logarithmic unit near the equivalence point. The only simple systematic error which could produce such a deviation is a slow drift with time of the reference electrode. For set 9 only one saturated point was obtained, and no
limits are given on K,o in Table I1 for this set. Because of the high dilution, impurities in the Et4NC104 make this titration much less accurate than the others.
Discussion The results of other workers are summarized in Table 111. The results of Luehrs6and Rumbaut and Peeters* were recalculated using our method and good agreement was obtained with the published values of p2 and Ks0. From the data of Rumbaut and Peeters we also obtained p1 and &. The constants obtained by recalculation, together with their limits of error, are given in Table 111. In addition, we report values obtained by Rumbaut" in anhydrous DMSO without supporting electrolyte, which have been corrected to an ionic strength of 0.1 M . These various results are compared with our results in Figures 2, 3, and 4. By analogy with propylene carbonate-water mixturesa we chose the square root of (11) N. A. Rumbaut,
private communication. Volume 7% Number 6 May 1OBg
JOHNC. SYNNOTT AND JAMESN. BUTLER
1474 Table I1 CHS,
Seta
mol/l.
1 2 3 4 5 6 7 8 9 10 11
