3288
JAMES N. BUTLER
Conclusions When eq 5 was derived, the radial term of eq 1 was neglected and the Poiseuille velocity distribution was replaced by the average streaming velocity. These two assumptions seem to be related, in that for low Peclet numbers and a l l 1 day. It is the author's intention to show this by a more exact solution of eq 1 in which the radial component is retained. I n systems of the type considered here, a steady state is reached in which the net transport of solute is composed of the simple sum of that by diffusion and by convection along the longitudinal axis, Le., diffusion occurs relative to a moving frame of reference. This simplifies the mathematical analysis. For very high Peclet numbers, the system may be treated by neglecting b2C/bX2 as has been done by
Taylor2 and by A r k 6 No attempt has been made in the present work to determine the range of applicability of eq 5 . At present the work is being extended to porous systems in an effort to obtain a better description of convective diffusion in membrane systems. This should provide a better understanding of the flow processes through soils as well as through artificial and biological membranes.
Acknowledgment. The work upon which this publication is based was supported in part by funds provided by the United States Department of Interior as authorized under the Water Resources Act of 1964, Public Law 88-379. (5) R. Aris, Proc. Roy. Soc., A235, 67 (1956).
Solubility and Complex Formation Equilibria of Silver Chloride in Anhydrous Dimethylformamide
by James N. Butler Tyco Laboratories, Inc., Waltham, Massachusetts 02154 (Received April 25s 1968)
The equilibria of silver chloride in dimethylformamide solutions containing excess chloride have been studied potentiometrically in a constant ionic medium (0.1 M tetraethylammonium perchlorate) at 25'. Equilibrium constants were fitted by a nonlinear least-squares pit-mapping technique. Only mononuclear complexes AgCl and AgC12- were found. The over-all formation constants for these complexes are: log = 12.11 0.085 and log 02 = 16.295 0.015. The complex AgCW is negligible under the conditions of these experiments, and log p3 is less than 17.7. The solubility product of silver chloride is log KBo= 14.49 f 0.01 (errors are standard deviations). Estimates of the constants at zero ionic strength are made, and the results are discussed in terms of ionic solvation.
*
Introduction Dimethylformamide (DMF) is a solvent of considerable interest for studies of electrochemical reactions and coordination chemistry. The silver-silver chloride reference electrode is in common use, 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 1aboratory'J have reported detailed studies of the equilibria of silver chloride in propylene carbonate. This paper presents the results of a brief potentiometric study in dimethylformamide. While this work was in progress, results The Journal of Physical Chemistry
on the same system were published by Alexander, KO, Mac, and Parker,3 but their experiments were preliminary in character, not all the equilibrium constants were evaluated, and no statistical limits of error were established for the constants they reported. By analogy with water and propylene carbonate,'J the following equilibria are expected AgCl(s)
Ag+
+ (31-
(KO)
(1) J. N. Butler, Anal. Chem., 39, 1799 (1967). (2) J. N. Butler, D. R. Cogley, and W. Zurosky, J. Electrochem. SOC.,115, 446 (1968). (3) R. Alexander, E. C. F,KO, Y. C. Mac, and A. J. Parker, J. Amer. Chem. SOC.,89, 3703 (1967).
SILVERCHLORIDE IN ANHYDROUS DIMETHYLFORMAMIDE
+ C1Ag+ + 2C1Ag+ + 3C1-
Ag+
AgCl(so1n)
(PI)
AgC1,-
(p2)
AgCla2-
(03)
(The IUPAC notation for equilibrium constants4 is used.) These equilibria have been verified by our experiments, arid the complex AgC132- has been shown to be negligible.
Experimental Section The method was the same as described previously.’ The potential of a concentration cell consisting of two silver electrodes separated by a salt bridge was measured with a high-impedance differential voltmeter. The reference compartment contained 0.1 M Et4NC1 saturated with AgC1, the salt bridge contained 0.1 M Et4NC104, and the titration compartment contained 0.1 M Et4NC104, to which additions of 0.1 M Et4NC1 and 0.1 M AgC104were made from micrometer burets. DMF (Fisher Certified) was dried with a 5A molecular sieve and Contained less than 0.005% water and less than 0.003% volatile organic impurities, as analyzed by gas chromatography. The solutions of Et4NC1 and Et4NC104(Eastman, dried over CaSO4) also contained less than 0.005% water, but the AgC104 solution (Chemical Procurement) contained 0.016% water. Solutions of AgC1o4in DMF were colorless and clear when first prepared, but within 7 days they became crimson and turbid, even though they were not exposed to light for more than about 1 hr during that period. The AgCl precipitate also was white when first formed but turned brownish over the course of 1 day. I n freshly prepared solutions, the silver-silver ion electrode in 0.1 M Et4NC104obeyed the Nernst equation to within ~ 0 . 2mV in the unsaturated region and to within f1 mV in the saturated region and in the region where excess silver ion was present. To minimize possible decomposition of the reference electrode solution, we used a silver chloride-saturated chloride solution for the reference electrode. The potential of this electrode is approximately 0.4 V more negative than the fixed concentration of AgC104 which we used in our previous work. Solution preparation, storage, and all experiments were carried out in a dry-nitrogen atmosphere in a glove box. The cell was jacketed, and (except for one preliminary experirnent) the temperature was maintained a t 25.0 f 0.05” by means of a Haake circulating thermostat. Results Typical titration curves are shown in Figure 1. Table I lists the detailed numerical data for the portion of the titration curve before the end point in four titrations which we considered to be accurate and on which the calculations were performed. Although the concentrations are given to four decimal places, this is merely a
3289
computational convenience to avoid round-off errors and does not reflect the true accuracy of the concentration values, which is approximately kO.01 mM. As can be seen from Figure 1, 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.
Table I: Titration Data” CAB
(T
=
CCl
c.4,
E
Set No. lb 25.0°, EO = 0.6585 V)
7 -
0.0574 0,1721 0.2866 0.5718 1.1382 1.6993 2.2551 r
2.5310 2.8057 3.3513 3.8918 4,1601 4.2672 4.3206 4.4273 4.5338
Unsatd4.8273 4.8227 4.8181 4.8067 4.7840 4.7615 4.7392
-0.1819 -0.1750 - 0.1685 -0.1600 -0.1406 -0.1204 -0.0269
-Satd4.7282 4.7171 4.6953 4.6736 4.6629 4.6586 4.6564 4.6522 4.6479
0.0639 0.0701 0.0800 0.0942 0.1050 0.1119 0.1162 0.1277 0.1469
Set No. 2” (T = 25.0”, EO = 0.585 V)
Set No. 3d (T = 25.0”, EO = 0.6265 V) P U n s a t d 0.0517 1.2944 - 0.2543 C.2581 1.2922 -0.1781 0.5152 1.2894 -0.1202
0.0598 0.1196 0.1793 0.2389
Satd1.2872 1.2861 1.2850 1.2840 1.2829 1.2818
0.0642 0.0660 0.0743 0.0843 0.0963 0.1306
-0.1616 -0.1530 -0.1325 -0,0900
-Satd0.6904 0.6901 0.6898 0.6894 0.6891 0.6887 0.6884 0.6882
r
0.2985 0.3580 0.4175 0.4769 0.5362 0.5955 0.6548 0.6844
1
0.0330 0.0400 0.0450 0.0533 0.0617 0.0716 0.0965 0.1502
Set No. 4e
(T = 25.0°, Eo = 0.637 V) Unsatd0.0001 1.5369 -0.1616 0.0586 1.5362 -0,1614 0.2924 1.5332 -0.1437 0.5833 1.5294 -0.1040 --Satd0.8729 1,5257 1 0171 1.5238 1.1610 1,5220 1.2184 1.5212 1.2758 1.5205 1.3332 1.5197 1.3905 1.5190 1.4477 1.5182 1.5049 1.5175 I
0.7200 0.8222 0.9242 1.0260 1.1276 1.2291
Unsatd 0.6918 0.6915 0.6911 0.6908
c-
-
E
CCl
0.0829 0.0924 0 1024 0.1079 0.1150 0.1217 0.1319 0.1506 0.2010 I
‘ The approximate precision of CA. and Ccl is 0.01 mM. E is in volts and concentrations are millimolar. The residual The AgCl is 1.2 mM. The residual AgCl is 0.37 mM. residual AgCl is 0.075 mM. The residual AgCl is 0.5 mM. From the data for unsaturated solutions in Table I, we selected a single set of data to obtain the equilibrium constants for complex formation. The preliminary (4) L. G. Sillen and A. E. Martell, “Stability Constants,” Bpecial Publication No. 17, The Chemical Society, London, 1964. Volume 78, Number 9 September 1968
JAMES N. BUTLER
3290 I
I
I
I
I
I
I
I
I
I
fined quadratic valleys, from which standard deviations can be calculated. The best values of the constants, with their standard deviations, are log /I1 = 12.11 log 0 2
=:
f
0.085
16.295 f 0.015
To obtain 90% confidence limits, multiply these deviations by 2. The cross section in p3-space1 using the optimum values for the other two constants, shows no minimum at all, but there is a clear upper bound for /I3. If we allow for a one-sided statistical error in a manner similar to that used to obtain the standard deviation, we may say (with 90% confidence) that log pa < 17.7 ?3 1
0
0.2
I
0.4
1
0.6
I
I
0.E
1.0
1.2
1.4
1.6
1 1.6
CAdCCl
Figure 1. Potentiometric titration curves: 0, 30°J 0.006 M ; 25O, 0.005 M (set 1); m, 250J 0.0005 M (set 2); A, 25O, 0.0013 M (set 3); X, 250J 0.0015 M (set 4). The concentration given is CCI. All titrations were carried out in 0.1 M EtaNCl01 supporting electrolyte.
+,
measurements (at 29.8") were discarded because the solutions appeared somewhat unstable. Set 1 showed small systematic deviations from the theoretical form of the titration curve which appeared to be due to excess AgCl (approximately 1.2 mM) being present in the titration cell before the titration was begun. Thus from set 1 we used only the unsaturated point of highest CAg/CC1 ratio (point 7), and this was corrected for the estimated amount of AgCl present. We included points 2-4 from set 2 and points 1-3 of set 3. To each of these sets was also applied a small correction for residual AgCl: 0.37 mlM for set 2 and 0.075 mM for set 3. These residual corrections were estimated from the potential a t the beginning of the titration curve; if there were no residual AgC1, the potential a t this point should be infinitely negative, and its value gives a sensitive measure of the traces of Agf present in the solution. Set 4 was not included in this group of most reliable data because the solutions appeared slightly discolored. The combined set of selected unsaturated data was used in our least-squares valley-search program1 to obtain the optimum values of the equilibrium constants PI, Pz, and ,& for the formation of complexes with one, two, and three chloride ions, respectively, on silver. Figure 2 shows the map of the valley in Pz-P3-space, with log ,& fixed a t 12.00. There is no pit as such; the value of /32 is quite well defined in the region near 16.30, but the minimum value of U (defined by eq 8 in ref l ) is obtained with & = 0. Cross sections in ,&-space and ,&space show well-deThe Journal of Physical Chemistry
With somewhat less confidence, we may infer that /Ia is even smaller and that the complex AgCls2- is of negligible importance in DMF solutions. Here is the supporting evidence for this statement. The shape of the valley in Figure 2 is such that if an erroneous value is used for /I2 it is possible to obtain a cross section in /Is-space, which indicates a minimum a t values of log Pa = 18 or higher. This is a mathematical deception, however, because when the full map of the valley is available, it is seen that the minimum value of U lies a t fia = 0. One might argue that this comes about be cause we used data with a relatively high CA,/CCI ratio, but Table I shows that we have included points = 0.58-0.086 without any eviranging from CA~/COL dence of a minimum in &space. This is a marked contrast to our experience with propylene carbonate,
I
I
I
I
5 109
Be
Figure 2. Map of the deviation function U (defined in ref 1) &s a function of equilibrium constants PZ and 68: - - standard-deviation contour (calculated with log pi = 12.00). Note that the minimum occurs at pa = 0. -J
SILVERCHLORIDE IN ANHYDROUS DIMETHYLFORMAMIDE
I *
Do &’
3291
I 14.3
-
25.0%
F
Figure 3. Deviation of experimental points from theoretical curve for unsaturated solutions: A, set 1; set 2; m, set 3; X , set 4. Calculated with log p1 = 12.11, log p2 = 16.295, and log ps = 17.5. The functions 2 and 2’are defined in ref 1. The observation that there is no trend among the various data sets indicates that the complexes are mononuclear.
+,
before the start of the titration. Although as much as in which the complex AgC132- is significant at C A g / C C l 0.10 mM AgCl may have been present, the deviations ratios as high as 0.4 or 0.5 and the minimum in P3probably resulted from a failure to equilibrate the referspace is well defined.’ ence electrode adequately in this early experiment Figure 3 shows the deviation Z‘/Z (defined by eq or from decomposition of the solutions because of the 8-10 of ref 1) of the points from the theoretical curve. higher temperature. The solubility product values I n addition to the points used to obtain the constants, also show strong systematic deviations, and two sepawe have also plotted the other points (in parentheses) rate sets gave log Kso = -14.55 f 0.05 and -14.7 f from sets 1-4. Although they scatter more widely 0.1. Thus it does not seem to be profitable t o estimate than the “best data,” there is no systematic deviation enthalpies and entropies of solvation in this system by which would indicate that we prejudiced our choice of measuring temperature coefficients of equilibrium conbest data. All the points are normally distributed stants at temperatures above room temperature, since about Z‘/Z = 1, which lends further confidence to our decomposition appears to be a problem. It may be least-squares procedure and t o the constants derived by possible, however, to obtain accurate data below room it. The fact that the assumed equilibria fit the experimental data with no obvious trend, even though C A ~ temperature, since the freezing point of DMF is around -60”, if sufficient time is allowed for equilibrium to be varies by a factor of 40, indicates that only monoestablished. nuclear complexies are present. I n Figure 4 we have plotted the solubility-product Discussion values obtained by the previously described method’ Alexander, KO,Mac, and Parker3 obtained values for from all the saturated points of sets 1-4. The data of Keo and p2 from potentiometric titrations of 0.01 M set 4 appear t o be significantly lower than those of the Et4NC1 with 0.01 M Agl\TOa in DMF without supportother three sets, as well as exhibiting stronger systeming electrolyte. Thus the ionic strength varied over atic deviations. This is consistent with the fact that the course of the titration. Their cell was open to the the solutions useld in obtaining set 4 were discolored and atmosphere, but they reported no substantial differmay have partially decomposed. No systematic ences when experiments were performed under dry error in KSowould result from the presence of AgCl in nitrogen or in the dark. They did not report analyses the solution at the beginning of the titration, since the of their solvent but dried it with 4A molecular sieves equation from which Ksois calculated1 involves only the and fractionated it twice at reduced pressure under dry ~ C a and not the concentrations themdifference C A so that it probably contained less than 0.02% nitrogen, selves. Similarl,y, p1 does not enter the expression for water. Their constants were log p 2 = 16.3 and log KsO Kso so errors in this constant are irrelevant for this = 14.5, which agree remarkably well with our results, purpose so long as they do not affect the value of Pz. From this excellent agreement, we may infer several The best value for the solubility product of AgCl in conclusions: (1) water has little effect on the equilibDMF is found to be rium constants for AgC1, (2) there is little ion pairing lo^ K,o = -14.49 f 0.01 in the supporting electrolyte, (3) neither nitrate nor perchlorate form appreciable complexes with Ag+, and where the error is the standard deviation of the best (4) Et4N+ does not form appreciable complexes with estimate. The data obtained at 29.8” are consistent with the either C1- or AgC12-. Thus we may conclude that our constants are reasonably accurate approximations to above constants but show systematic deviations which the values which would be obtained in absolutely ancannot be explained on the basis of AgCl being present
-
Volume 78, Number 9 September 1968
JAMES N. BUTLER
3292 hydrous DMF with an ideally noncomplexing supporting electrolyte. If there is no ion pairing in these solutions, we may use the Debye-Huckel theory t o calculate equilibrium constants a t zero ionic strength. Using a dielectric constant of 36.716 and an ion-size parameter of 3 A for all monovalent ions, we obtain at zero ionic strength log Pio = 12.80 h 0.09 log Pzo
16.99 h 0.03
log Koso =: -15.18 h 0.03
If ion pairing were important, we would obtain more positive values of log Pl0 and /3z0 and a more negative value of log Koso. It is of particular interest to examine two other equilibrium constants which may be obtained by combination of the above constants. The equilibrium constant K,1, for the formation of AgCl complexes in solution from solid AgCI, is independent of electrostatic effects and reflects primarily the coordination of the solvent to the silver ion AgCl(s)
AgCl(so1n)
For this reaction K,1 = KaoP1= 10-2*as*o+oO
For w ~ t e r ,this ~ , ~constant is 10--6-6*o.1, and for propylene carbonate,' it is 10-4.7k0*2.Thus the coordination of DMF to the silver atom in the AgCl complex is considerably stronger than that of water or propylene carbonate. The equilibrium constant K,,z for the formation of AgC12- from solid AgCl C1-
+ AgCl(s)
AgClz-
is also simple to interpret. For this reaction
KBz = KSo&= 10+1*so*O.oz This constant reflects the difference in free energy between two monovalent ions. On the basis of size alone, one expects that K,z should be slightly greater than unity, but hydrogen bonding of the solvent to C1may cause it t o become smaller, and coordination of the solvent to silver ion may cause it to become larger. Here again, we may compare with ~ a t e r(log ~ , K,z ~ = -4.7 f 0.1) where hydrogen bonding is strong and with propylene carbonate (log K,z = 1.00 f 0.05) where both hydrogen bonding with C1- and coordination to AgCl2- are weak.
The Journal of Physical Chemistry
Within this framework, we mag also examine the equilibrium constant K,z for AgCl in other amides. The hydrogen bonding of the solvent t o chloride decreases and the coordination of solvent to silver increases in the following order: formamide,s log K S z = -2.1; N-methylforrnamide,* log K,z = -1.5; dimethylformamide, log Ksz = 1.80 f 0.02; dimethylacetamide,%log K,z = 2.9 ; hexamethylphosphorotriamide,3 log KR2 = 4.6. No information is available on K,z in any of the other amide solvents. These two equilibrium constants K,1 and K S z are particularly useful for theoretical interpretation, because they are almost unaffected by either ionic strength or ion pairing with the supporting electrolyte. Thus even though substantial systematic error due t o these sources may exist in Kso, PI, or pz, these errors are almost entirely canceled in the combinations Kel and Ka2.
One final point may be made concerning the very small value of p3 that we have obtained, which reflects the low concentration of the complex Ag(X2-. I n both water and propylene carbonate, this complex is of considerable importance, and its absence in DMF implies that the coordination sphere of silver is saturated when only two chloride ligands are bound. The other ligands must be solvent. This again reflects the stronger coordination of DMF to the silver ion as compared with other solvents. Nuclear magnetic resonance studies9 have shown that dimethylformamide complexes with silver salts have a structure similar to those with Lewis acids or protonating acids, implying that coordination takes place through the carbonyl oxygen rather than through the nitrogen.1°
Acknowledgments. The author thanks Mr. Walter Zurosky, Jr., for his assistance with the experimental work and Mr. David Cogley for assistance with the computer calculations. This research was supported by the Air Force Cambridge Research Laboratories, Office of Aerospace Research, under Contract No. 19(628)-6131 but does not necessarily constitute the opinion of that agency. (6) G . R. Leader and J. F. Gormley, J. Amer. Chem. Soc., 73, 5731 (1951). (6) I. Leden, Soensk. Kern. Tidskr., 64, 249 (1952). (7) E. Berne and I. Leden, ibid., 65, 88 (1953). (8) Yu. M. Povarov, V. E. Kazarinov, Yu. M. Kessler, and A. I. Gorbanev, Zh. Neorg. Khim., 9, 1008 (1964). (9) 5. J. Kuhn and J. S . McIntyre, Can. J . Chem., 43, 995 (1966). (10) G . Fraenkel and C. Neimann, Proc. Nat. Acad. Sci. U.S.,44, 688 (1958).
