R. L. BENOIT, A. L. BEAUCHAMP, AND M. DENEUX
3268 of free ion yields is seen to be a promising method for liquids of neutral or acidic character. For liquids such
as alcohols possessing any basic character, the use of negative charge scavengers6 would appear preferable.
Equilibria between Silver, Chloride, and Bromide Ions in Sulfolane' by R. L. Benoit, A. L. Beauchamp, and M. Deneux Departement de Chimie, Universite de Montrdal, Montreal, Canada (Received February $0,1969)
The equilibria between silver, chloride, and bromide ions in sulfolane have been studied potentiometrically in several ionic media at 30°, Equilibrium constants were obtained with the help of a new program. The solubility products of AgX are pK,, = 18.5 (Cl-), 18.9 (Br-) and the stability constants for AgX2- are log p 2 = 20.3 (Cl-), 20.2 (Br-) at zero ionic strength. The complexesAgX and A g X p are not detected and reexamination of data in propylene carbonate leads to similar conclusions. The results are used, together with those known for other polar aprotic solvents, to evaluate some ionic transfer energies on the basis of Strehlow's extrathermodynamic assumption.
Introduction The results of a preliminary electrochemical study in sulfolane (TMS) have recently been reportedS2 The silver-silver ion electrode, which was shown to obey the Nernst equation, is now used to study the equilibria between silver, chloride, and bromide ions in this polar aprotic solvent. This work was undertaken to provide, with the help of Strehlow's extrathermodynamic assumption,* data for the evaluation of ionic transfer energies between polar aprotic solvent^.^ A new program was written and used to interpret the potentiometric data in terms of equilibrium constants for the reactions AgX(s) J_ Ag+ Ag+
+ X-(K,,)
+ 2X- J_ Ag&-(/%)
This program is compared with that described by Butlerj for a similar instance. Parker, et aLje published recently a paper in which they quoted an approximate figure for K,, (AgCl). During the preparation of reported values of the manuscript, Della Monica, et K,, and /32 for the system Ag+-Br- in 0.1 M Et4NC104.
Experimental Section Sulfolane, kindly supplied by Shell Canada Ltd., was oxidized by air, a t 160", during one night. The solvent was then treated with activated charcoal; this was followed by filtration and distillation under reduced pressure a t a temperature below 90". The fraction representing the middle 80% of the distillate was collected and stored in a refrigerator. Before it was used, liquid sulfolane was vigorously stirred under vacuum. Karl Fischer titration showed the water content to be about The Journal of Physical Chemistry
10 ppm. Analysis for volatile organic impurities was made by vapor-phase chromatography a t 170", on a column of UC-W98, using a flame detector and nitrogen as a carrier gas. Impurities were less than 0.1%. Anhydrous silver perchlorate (Alfa Inorganics) and lithium perchlorate (Smith) were dried a t 60" in vucuo before use. Titration with aqueous standard KSCN solution showed the purity of AgC104 to be higher than 99.5%. Tetraethylammonium chloride and bromide (Eastman) were twice recrystallized from an ethanolethyl acetate mixture and dried a t 40" under vacuum. Tetraethylammonium perchlorate (Eastman) was twice recrystallized from an ethanol-water mixture and dried a t 40" under vacuum. All solutions were prepared by weight immediately before use. Solutions of AgC104 were colorless and clear when kept away from light. They became yellow when exposed to air and light after one day. The AgCl precipitate turned brownish a t the end of the titration, though light was excluded as much as possible. The cell consisted of two electrode compartments, connected by a salt bridge (0.1 M EtdNC104), and was (1) Presented on Nov 8,1968,at the 36th Meeting of A.C.F.A.S. in Ottawa, Canada. (2) J. Desbarres, P. Pichet, and Et. L. Benoit, Electrochim. Acta, 13, 1899 (1968). (3) J. J. Lagowski, "The Chemistry of Non-Aqueous Solvents," Academic Press, New York, N. Y., 1966. (4) R.L.Benoit, Inorg. Nucl. Chem. Lett., 4,723 (1968). (5) J. N. Butler, Anal. Chem., 39,1799 (1967). (6) A. J. Parker and Et. Alexander, J. Amer. Chem. Soc., 90, 3313 (1968). (7) M. Della Monica, U. Lamanna, and L. Senatore, Inorg. Chim Acta, 2,363 (1968).
SILVER,CHLORIDE, AND BROMIDE IONEQUILIBRIA I N SULFOLANE jacketed and maintained a t 30.0 f 0.1” by means of a Haake circulating thermostat. All titrations were performed with silver-plated platinum electrodes freshly prepared.8 The reference compartment contained Agor M concentrations. Clod a t approximately M The second compartment contained or halide solutions and various amounts of AgC104 added from a 2-ml microburet. Potentials were measured with a Tacussel high-impedance millivoltmeter (type S9R2) and the equilibrium was usually reached within 15 min in homogeneous medium and 30 min in solutions saturated with AgX.
Results and Calculations
=
E”
+
RT In (Agf) F
(1)
The value of E” was obtained from portion (c) of each titration curve, assuming that excess AgC104 is present as free silver ion. Approximate values of Pz, Ksoand K (LiC1 or EtdNC1 ion-pair association constant) were estimated by rough calculations or by comparison with values given in literature for similar solvents. Further interpretation was carried out using a computer program POTAG2.’ This program deals with silver electrode potential measurements for both saturated and nonsaturated media and refines a set of estimated equilibrium constants by the Gauss nonlinear least-squares method.1° The function U minimized during the least-squares calculations is the squared residual sum of potential
U =
C ( E , - Egca1)2= i
CAg
+ ajPj(Ag)a3(X)Zj(M)Wj (X) + C2,Pj(Ag)u3(X)’3(M)m3 (31)+ mjPj(Ag)‘3(X)’j(M)m>
= (Ad
3
CX =
a
(2)
For each measurement, a computed value Etca1 is obtained as follows. Given a three-reactant system (Ag, X, M), where M stands for the supporting electrolyte metal ion, the formation constants of soluble complexes are defined by (3) and the following material balance equations are valid for nonsaturated media
(4)
3
C~+I=
3
In the presence of insoluble AgX, (Ag) and (X) are related through
Kso = (Ag)(X)
(5)
and replacement of (Ag) by KsO/(X)in set (4) yields the following equations for saturated media
+
C A= ~ Kso/(X)
The titration curve of Et4NC1 with AgC104 shows three well defined portions labeled : (a) nonsaturated medium where AgC12- is the predominant species formed; (b) saturated medium in which the solution is in equilibrium with solid AgCl; (c) a high potential tail corresponding to excess AgC104. Curves of this type are observed for experiments performed a t low ionic strength (no supporting electrolyte) and in presence of Et4NC104as supporting electrolyte. I n the presence of 0.1 M LiC104, portion (a) is much shorter. When Et4NC1 is replaced by HCl, portion a (a) disappears. The experimental value of the potential E is related to the concentration of free silver ion by the Kernst equation
E
3269
CX = (X) CbI =
(&I)
+
+
ajPjKso(X)(’3 - aJ)(M)mj (E) 3
+
~jP&so(X)(’3 - uj)(M)mj (S) 3
+
(6)
m3PjKSo(X)(”3 - “3’(M)m3 3
The extra term (S) accounts for the “concentration” of solid AgX which is treated as a pseudosolute. The equations are handled by the computer under the general form above. When only AgClZ-, LiC1, and solid AgCl are assumed to be present, eq 4 and 6 yield CAg
=
(Ad
Ccl = (C1)
C L ~= (Li)
+ flZ(Ag)(C1)2
+ ~ P z ( A ~ ) (+C K(Li)(Cl) ~)~
+ K(Li)(Cl)
(7)
for the homogeneous medium and CAg
+ pZKso(C1) + (8) (C1) + 2PzKso(C1) + (S)
= Kso/(cl)
CCl =
C L ~= (Li)
(8)
+ K(Li)(Cl)
for the saturated solution, with
pz
= (AgClz-)/(Ag)(C1)2
K,,
K
= (LiCI)/(Li)(Cl)
= (AgI(C1)
The appropriate set of simultaneous equations is solved for (X), (AI) and (Ag) (or (S)) by the Raphsonn’ewton iterative method, the convergence criterion being that all three computed total concentrations C, agree with the experimental values within lO-5%. Edca1 is then generated by substitution of (Ag) in eq 1. Concentrations of all species and ionic strength are obtained as a by-product of this calculation. The collection of all Edca‘actually defines ideal titration curves, which would be obtained for the hypothetical system where no error would occur and the assumed reaction scheme and equilibrium constants would hold. (8) J. G . Ives, and G. J. Janz, “Reference Electrodes, Theory and Practice,” Academic Press, New York, N. Y.,1961. (9) The PO TAG^ version used here is still being improved and several features are being added and tested. Further details may be obtained from A. L. B. (10) W. E. Wentworth, J. Chem. Educ., 42,96 (1966). v o h r n e 75,Number 10
OCtObeT
1969
R. L. BENOIT, A. L. BEAUCHAMP, AND n!t. DENEUX
3270
Table I : Equilibrium Constants for the Ag+-X- Systems in Sulfolane at 30" X
Expt
C1-
1 2 3 4
Bra
log 82
I
5.7 x 0.1 M 0.1 M ~ 5 . 1.5
10-4-10-2a EtrNClOa LiClO4 x3 10-3-
x
20.19 19.82 19.83 20.01
log K
PKBO
R ,mV
-
18.38 k 0.003 18.08 4 0.02 18.09 i 0.02 18.67 k 0.02
3.1 1.2 0.7 1.5
f 0.03
It 0.03 zk 0.03 f 0.03
-.
3.5 f 0.2
No supporting electrolyte.
Table I1 : Titration Data for Experiment 1
CA*= 1.755 X 10-2 M , Cci = 1.045 X lo-' M V = 21.17 ml, E" = 100 i 2 mV V , ml
- E , mV
(0.198) (0.414) 0.712 1.015 1.318 1.722 2.327 2.841 3.543 4.130 4.650 5.497 5.948 6.451 6.938 8.142 9.253 10.490 11.607 12.228 12.763 13.795 14.495 15.313 16.140 17.349 18.458
(1087.0) (1072.2) 1056.7 1046.9 1038 9 1028.3 1013.5 1001.5 984.4 968.0 950.4 907.3 857.2 753.8 752 3 744.6 734.4 721.4 700.0 667.8 145.5 92.5 80.6 71.7 64.6 57.6 52.6 I
-ECal0, mV
1063.3 1050.8 1040.5 1028.7 1012.7 999.7 981.3 964 2 946.3 903.5 858.1 751 .O 748.4 741.0 732.6 719.5 699.0 673.0 145.6 93.9 82.3 73.5 67.2 60.3 55.6 I
IT/,
C A= ~ 1.945 X M, CCI= 8.145 X lo-* M V = 23.02 ml, E" = 94 f 2 mV mV
6.6 3.9 1.6 0.4
0.8 1.8 3.1 3.8 4.1 3.8 0.9 2.8 3.9 3.6 1.8 1.9 1.0 5.2 0.1 1.4 1.7 1.8 2.6 2.7 3.0
Five least-squares cycles in which U (eq 2) was minimized generally resulted in convergence and the refined values of p2 and K 2 are given in Table I, together with the R factors
R
=
[ C r t 2 / ( N- M ) ] " 2 i
where N is the total number of measurements and M is the number of constants refined. Experimental points and corresponding computed values for the titration of C1- a t low ionic st,rengthare given in Table 11." In a first step, ,&constants were refined from points in nonsaturated media. K,, was then refined from data corresponding to saturated media, using the value of /?z previously obtained. On the other hand, simultaneous refinement of PZ and K,, over combined data for both The Journal of Physical Chemistry
V , ml
(0.208) (0.289) 0.660 1.174 1.556 2.210 2.987 3 749 5.650 6.934 8.105 9.279 9.646 11.207 12.017 12.896 14.034 15.121 16.285 I
- E , mV
(1008.7) (1004.6) 989.2 972.2 960.4 940.6 914.2 878.0 685.8 677.0 661.2 619.0 298.0 152.1 141.2 133.2 125.6 120.8 116.0
-EC**O,~V
996.4 974.0 960.4 938.9 911.7 877.0 687.3 676.0 660.2 621.4 292.4 149.7 139.5 131.9 124.9 119.9 115.6
lrl, mV
7.2 1.8 0.0 1.7 2.5 1.0 1.5 1.0 1.0 2.4 5.6 2.4 1.7 1.3 0.7 0.9 0.4
media yielded nearly identical results. Variations of ionic strength in each experiment would result in a change of 0.01 and 0.03 for log pz and pK,, a t I cv- lod3 and respectively. These extreme variations are smaller than the accepted errors. Furthermore, discrepancies found in these constants in experiments perand are also small, so that exformed a t I 'v periments without supporting electrolyte were collected and treated as a whole. Errors on the refined parameters are set equal to three times the standard deviation estimated from the diagonal elements of the inverse matrix corresponding to the last least-squares cycle. (11) Extensive data tables for the other experiments are deposited with the National Auxiliary Publications Service (NAPS) of the American Society for Information Science (ASIS).
SILVER,CHLORIDE, AND BROMIDE IONEQUILIBRIA
IN
SULFOLANE
Unit weights were applied throughout this work and this might deserve some justification. I n least-squares curve fitting, only random errors are assumed to occur. Consequently, systematic errors arising from initial conditions (initial volume, initial total concentrations of reactants, reference potential) or slow equilibrium attainment or electrode response should not be carried by statistical weights, but should be treated as parameters to be adjusted just like the equilibrium constants.12 For our systems, experimental points are described by a pair of coordinates (Et, Vi)(where V iis added volume) and they generate the titration curve E = f(V), where E and V are random variables with null correlation. Therefore, weights wtequal to l / u t 2 , where (9) should be applied. Values of u t zwere calculated for one system, assuming uE, = 0.5 mV and rv, = 0.004 ml. The second term on the right side of eq 9 turned out to , ~ for measurements be much smaller than u ~ except lying very close to the equivalent point, which were discarded in the refinement. This means that ut2 c1 u ~ ,ie., ~ , most of the random error arises from fluctuations in potential measurements. Furthermore, the low R factors and nearly uniform distribution of Irtl within a given set of data did not justify extra computer time for applying a weighting scheme. Attempts were made to provide for less important species like AgC132- and soluble AgCl ion pairs. The values for these constants either steadily decreased from one cycle to the other or oscillated endlessly in a range of h-2 log units about a low value, while pz and K,, did not shift appreciably. Similar behavior was observed by other workers13 when attempts were made to refine constants for unimportant species. Concentration tables actually showed these species to be formed in negligible amounts (
