ization effects, which are, absent in Group I I b ions, but of importance in the case of nickel(I1) and copper(I1). In the periodic Group IIb, the mercury(I1) ion is apart from zinc(I1) and cadmium(I1) in the stability of both the bis(ethy1enediamine) and tetraamine complexes. There is a marked increase in - A H ” between the latter two members of the series which is much larger than can be ascribed to the increase in ionic radius. The relative changes in AS0 are not as great, indicating that the mercury(I1)-nitrogen bond is unusually strong and accounts for the large free energy of formation of these mercury(I1) complexes. The similarity of the constants in Table I11 for the formation of bis(ethy1enediamine) mercury(11) and bis (propylenediamine)mercury(II) suggests that a methyl group in the place of hydrogen has only a slight effect on the coordinating ability of a n attached amine group. The same conclusion v-ould also be reached from consideration of the similarity of the basicity constants of these two alkylamines. Other investigations ( I ) have shown that
(7) McIntyre, G. R., Jr., Block, B. P. Fernelius, W. C., Ibid., 81,529 (1959).
Table IV.
Thermodynamic Data a t 25’ C. for Reaction
+ 2 en
M(NHa)i+
-AH Kcal./ Mole 4.19 5.4 -1.6 0.8 1.3
-AF
M Si Cu Zn Cd Hg
Kcal./ Mole 8.17 10.08 2.32 4.34 5.0
M(en);* AS
(8) . , Nvman. C. J.. Roe. D. K..’ Masson. D. B.. Ib;dd..’77.4191 (1955). (9) Nyman, C. j . , Salazar,’.T., ANAL. CHEM.33,1467 (1961). (10) Poulsen, I., Bjerrum, J., Acta Chem.
+ 4 NHI
E.U.
Reference
13.3 15.7 13.3 11.8 12
(10)
Scand. 9,1407’(1955). ’ (11) Prue, J. E., Schwarzenbach, G., Helv. Chim. Acta 33, 985 (1950). (12) Rossotti, F. J. C., Thermodynamics of Metal Ion Complex Formation in
(10) (16)
Solution, in Lewis, J., Wilkins, R. G., eds. “Modern Coordinatim Chemistry,” p. 58, Interscience, New York, N. Y., 1960. (13) Schwarzenbach, G., Helv. Chim. Acta 33,947 (1950). (14)Schwarzenbach, G., Anderegg, G.,
(15)
Thiswork
N-alkyl substitutions alter only slightly the stability of complex ions having a nitrogen-metal ion bond.
ma., 37,1289 (1954). (15) Spike, C. G., Parry, R. W., J . A m . Chem. Sac. 75,2726, 3770 (1953). (16) Watters. J. I.. Mason. J. G.. J . A m . ’ h e m . SOC.’~~, 285 (1956). (17) Yatsimirskii, K. B., Milyukow, P. M., Zhur. Neorg Khina. 2 , 1046 (1957).
LITERATURE CITED
(1) Basolo, F., Murmann, R. K., J. A m . Chem. SOC.74. 5243 (1952). (2) Bjerrum, J:, Chem. Revs. 4 6 , 381
.----,-
(19,iOl.
RECEIVEDfor review June 16, 1961. Accepted July 31, 1961. Division of Analytical Chemistry, 139th Meeting, ACS, St. Louis, Mo., March 1961. Work Bupported in part by the Office of Ordnance Research, U. S. Army, Project No. DA04200-ORD-65 and Projeot KO.DA-04-
(3) Ciampolini, M., Paoletti, P., Sacconi, L., J . Chem. SOC.1960,4555. (4) Cotton, F. A., Harris, F. E., J . Phvs. Chem. 59, 1203 (1955). (5) Davies, T., Singer, S. S., Staveley, L. A. K., Ibid., 1954,2304. (6) DeFord, D. D., Hume, D. N., J . A m . Chem. SOC.73, 5321 (1951).
200-ORD-567.
Complex Ion Formation of Mercury(l1) and Thiosulfate Ion C. J. NYMAN and TERESA SALAZAR Deparfmenf o f Chemisfry, Washington Sfafe Universify, Pullman, Wash.
b The potential vs. concentration data for the anodic polarographic oxidation of mercury in solutions of sodium thiosulfate a t unit ionic strength may b e interpreted on the basis of the formation of complex ions of the i type [Hg(S~03),12‘’-”, where has values of either 2 or 3. The logarithms of the formation constants a t zero ionic strength were calculated i o b e 29.27 for i = 2 and 30.8 for j = 3. Previous workers have determined the potential of the Hg/Hg f 2 half-cell as a function of sodium thiosulfate concentration a t varying ionic A recalculation of !heir strength. results yielded values of log K2 = 29.18 and log K; = 30.3 in excellent agreement with the polarographically determined values. The activity coefficients in both cases were obtained from Davies’ modification of the DebyeHiickel equation.
s
OME YEARS AGO,
KoIthoff and Miller
( 4 ) showed that the complex ion
[Hg(&O&] -* was formed when mercury was oxldized polarographically in the presence of sodium thiosulfate, but these
authors did not estimate the formation equilibrium constant of the complex ion. More recently, Toropova (12) studied the system potentiometrically and found additional complex species. The values log K i = 29.86, log K i = 32.26, and log K i = 33.61 were determined for the equilibrium constants corrected to zero ionic strength, but the assumptions concerning the activity coefficients were somewhat unusual in that the activity coefficients of all species, regardless of charge, were assumed to be the same. By a solubility method, Toropova also obtained the value log K i = 29.4 (13). As part of an investigation of a series of complexes of mercury(I1) with various sulfur-containing ligands, and because of the questionable treatment of activity coefficients by Toropova, the mercury-thiosulfate complex system was investigated polarographically to determine the formation constants of the complex ions formed. EXPERIMENTAL
The procedure employed in determining polarograms and half-wave potentials was identical with that employed in another study (8) using a
polarographic cell described elsewhere (11).
Stock solutions were prepared from redistilled water with chemicals of reagent grade. The sodium thiosulfate stock solutions were prepared from Merck reagent grade crystals and were standardized volumetrically with potassium iodate solution using the procedure of Kolthoff and Sandell (6). The solutions for polarographic study were made by pipetting exact volumes of the stock solutions into 100-ml. volumetric flasks, adding sufficient 2.OM sodium perchlorate solution to give an ionic strength ai 1.0 on dilution to volume. The p H of the solutions was determined using a Beckman Model G p H meter. In all cases, th0 pH was close to 7.0 without the use of buffer solutions, and no polarograms were made a t p H less than 6.5 to avoid any difficulties due to decomposition of sodium thiosulfate in solutions of low pH. It was found experimentally that potentials were independent of p H from below p H 0.2 up to a t least pH 9.6. RESULTS
The finding of Kolthoff and Miller
(4) that the polarographic anodic wave in the presence of dilute solutions of VOL. 33, NO. 1 1 , OCTOBER 1961
1467
the sodium thiosulfate was due to the formation of [Hg(S203)2]"2J has been confirmed in the following two ways: 1. A series of polarograms was run in which the total concentration of thiosulfate ion was varied from 2 X IOw4 to 5 X mole per liter. with sufficient added sodium perchlorate to adjust the ionic strength to 1.0-11. The data obtained are recorded in Table I. and the observed potentials are believed to be precise to *3 mv. If only one complex exists in solution, i t has been shown (4, 8, 9) that a plot of log ( i / i d - i ) ' us. Ed e for a given polarogram should produce a straight line of reciprocal slope 2.303 R T / n F for some value of j in the formula M X , . At these low concentrations, it was found that the best straight line was obtained with a value of j = 2. The value of the reciprocal slope increased with concentration of sodium thiosulfate, and this could indicate that either the oxidation process becomes more irreversible or that the value of [the average number of
5
S203-2 ions per mercury(I1) ion] increases with concentration. iit higher concentrations, the complete wave is not used and the potential at 1 pa., rather than the half-wave potential is used as the indicator criterion of complex formation. Since the process in these solutions proved to be reversible, it is presumed that j is changing in the solutions in Table I as the concentration of thiosulfate increases. 2. It has also been shown that a plot of (EipJc US. log (S203-') should have a slope of -2.303 (j-1) R T / n F if only one complex species exists over a wide concentration range. From the data in Table I it was found that a plot of this type had a limiting slope of 0.029 a t the lowest concentration range, indicating an average value of j = 2, in agreement with the observation of Kolthoff and Miller. Evaluation of the Constant Ki. Table I contains the d a t a for the oxidation half-wave potential of mercury in the presence of varying concentrations of thiosulfate ion. T h e
Table I. Variation of Half-Wave Potentials of Sodium Thiosulfate Solutions and Values h ( X ) as Function of Thiosulfate Concentration at Electrode Surface
(25" C.,
p =
1.0, kt
= 5 X lo3pa./mole/l.,
k, = 5.65 X 103 pa./mole/l.)
(-EI/Z)e
(&03-')
Reciprocal Slopes
Mole/L. 1.98 X 2.98 X 3.97 X 4.96 X 6.94 X 9.92 X 1.50
2.00 2.50 3.50 5.00
lo-' lo-'
lo-' lo-' lo-'
x 10-3
X X
X X
Table II.
0.0334 0.0353 0.0390 0.0406
(Sz03-2)o
Mole/L. (at E1d 0.95 x 1.42 X 1.87 X 2.25 X 2.96 X 4.13 X 6.60 X 7.87 X 9.03 X 1.073 X 1.40 X
FdX)
x 10-29 7.5 8.5 8.5 10.2 8.7 9.6
lo-'
lo-' lo-' lo-'
8.8
13.5 12.9 27.6 40.7
lo-' 10-3
Variation of the Potential at 1 pa., (E,')and F 3 ( X ) as Function of Thiosulfate Ion Concentration at Electrode Surface
(25" C.,
6.95 9.93 1.986 2.99 3.98 5.02 7.03
0.0300 0.0354 0.0316 0.0310 0.0309 0.0334
j' Volt us. (at Eiiz) S.C.E. 0.500 2.06 0.127 0.745 2.09 0.134 0.996 2.11 0.137 1.265 2.14 0.141 1.83 2.17 0.141 2.59 2.23 0.147 3.96 2.32 0.153 5.14 2.36 0.159 6.68 2.39 0.159 9.99 2.43 0.167 14.41 2.50 0.175 id
pa.
x 10-3 x 10-3 x lo-*
X lo-' X X X lo-% 1.004 X 10-l
x 10-1 3.00 x 10-1 4.02 X 10-l 5.02 x 10-l 2.01
7.03 X 10-l 1 005
p =
1.0," kt
=
5 X 10Spa./mole/l.,k,
0,242 0.247 0.272 0.292 0.309 0.319 0.320 0.335 0.366 0.385 0.402 0.413 0.421 0.432
2.81 2.86 2.92 2.95 2.98 3.00 3.00 3.00 3.00 3.00 3 .oo 3.00
3.00 3
.oo
=
5.65 X lO3prt./mole/l.)
6.39 x 9.36 x 1.928 X 2.92 X 3.92 X 4.96 X 6.97 x 9.98 x 2.00 x 3.00 x 4.01 X 5.02 x 7.02 x 1.004
10-3
10-3 10-2
10-2 10-1
10-1 10-1 10-1 10-l
2.8 1.2 1.0 1.6 2.5 2.7 1.1
1.2 1.6 2.1 2.7 2.0 4.5 5.1
a Last four concentrations have ionic strength greater than unity, determined by NazSzOs concentration.
1468
0
ANALYTICAL CHEMISTRY
values of and t h e concentration of thiosulfate a t t h e electrode surface were estimated by a n approximation procedure outlined previously (8). The values of F 2 ( X ) were obtained from the graphical procedure of Leden (7) and DeFord and Hume (3) employing the latter authors' definition of F , ( X ) including activity coefficients. Thp value E" for the standard oxidation potential of the mercury-mercury(J1) couple was taken to be 0.612 volt us. S.C.E. (e), and the values of F , ( X ) for the data in Table I were calculated from Equation 4 of ( 8 ) . The activity coefficients for the mercuric ion, the thiosulfate ion, and the mercury(I1) thiosulfate complexes were estimated from Davies' modification of the entended Debye-Huckel equation (1, 2) where
- logf,
=
0.509 Zf
[-(1 +
pl/z
p1'2)
-0.24
where j t is the activity coefficient of ion of charge 2, and p is the ionic strength. It mas found from the data in Table I that the 1 : l (S203-2)t o Hg(I1) complex was not present in detectable amounts by thp method of DeFord and Hunie as indicated by the fact that the value of F 1 ( X )defined as [ F , ( X ) - I/ fs]/(S203-2) extrapolates to 0 when plotted us. (S203-2)0fZ.Continuing with DeFord and Hume's method, F z ( X ) is calculated and plotted us. (SZO3-*) ofr. The intercept K&'fm,,, was found to be 7.6 X 1029, and with fmz, = 0.245, K i is calculated to be 1.86 X loz9,or log K i = 29.27. The plot of F 2 ( X )has a somewhat positive slope, indicating an additional species present, probably [Hg(S203)3]- 4 . An approximate value of the formation constant of this species can be estimated from the slope of this plot, and a value of the order of was obtained. However, a better value can be derived from the data in Table 11. Evaluation of Ki. I n more concentrated solutions where the development of t h e complete wave is impractical, the potential of 1 pa. is taken as the indicator potential, and in Table I1 are recorded values of these potentials as a function of both total thiosulfate and thiosulfate concentrations a t the electrode surface. That the oxidation process is reversible is shown by the fact that a plot of log i us. Ede has a slope of 2.303 R T / n F . This is required (9) if the concentration of thiosulfate is so large that its concentration at the electrode surface is essentially equal to that in the bulk of the solution. At currents below 2 Ma. and at the concentrations listed in Table 11, these conditions are satisfied. Values of F , ( X ) are calculated from Equation 2 of ( 8 ) employing the data in Table 11, and in turn, the values of F 3 ( X ) are calculated. X o general
trend is observed u p t o the concentration of thiosulfate equal to 0.30M, beyond which p can no longer be held constant. The average value of Fs(X) through 0.30M is 1.77 X and is equal to Ki/jmz2. From Davies’ equation the activity coefficient of and hence [Hg(S203)3]-4is 3.6 X k‘; = 1.77 X 3.6 X lo+“ = 6.4 X I O t 3 0 , ur log K i = 30.8. Analysis of Toropova’s Data. Toropova (fd) determined the potential of a Hg/”g(II) half cell as a function of sodium thiosulfate vs. the saturated calomel electrode a t 25” C. This author presented two sets of data which are included in Tables I11 and IV. Using Leden’s (7) procedure and estimating activity coefficients from Davies’ equations, the data were treated by calculating successive values of F , ( X ) . As pointed out previously (IO),careful definition of F , ( X ) allows the proper functions to be plotted so that the graphical method yields as intercept the equilibrium constants a t zero ionic strength. For the data in Table 111, the values of F”,X) showed little trend nith increasing sodium thiosulfate concentration except the two values at the higher concentrations. This indicates that over the range of thiosulfate concentration 2 x 10-8 to 8 X 10-3;Cf, the species [Hg(S20&-2 predominates. The average value of F i ( X ) in this region is taken as K ; and equals 1.5, X lon9 or log K i = 29.18. This compares favorably with the value 29.4 which Toropova obtained from solubility measurements (IS). For the last two values of F ; ( X ) , the increase in F i ( X ) above the average of the first five values can be attributed entirely to formation of the species [Hg(Sfi3)3]-4, as indicated by the fact that F i ( X ) values calculated here are compatible with those in Table IV, where the data indicate only one species, [ H ~ ( S Z O , ) ~from ]-~ 1 X to 6 X 10-llcI. The average of all values of F i ( X ) was 1.9 x 1030, yielding log K i = 30.3.
Table 111.
Variation of Potential of Hg/Hg+2 Electrode as Function of Thiosulfate Concentration and Values of F i I X ) and Fi(X)
Total Na2S203 Mole/L. 3- . 94 -- x , . 10-3 -. 5.91 x 10-3 6.69 X
7.88 x 10-3 9.85 x 10-3 1.97 X 3.94 x 10-2
Table IV.
0.187 0.193 ( 7 ) 0.201 0.209 0.237 0.263
1.94 x 3.91 X 4.69 x 5.88 x 7.85 x 1.77 x 3.74 x
10-3 10-3
10-3 10-3 10-3 10-2 10-2
10-3M
x
io+z
Fi(X)
Fi(X)
1.6 1.1 1.3
...
1.7 3.7 7.7
2.1 2.6
x 10-29 x io-”
1 08
1.68 1.91 2.27 2.86 5.31 11.73
...
...
1.5
Total mercury concentration of 2 X 10-3M Corrected ( S Z O ~ -Mole/L. ~) - E Volt Assuming = 3 I.c 0 254
3.91 X 7.82 X
x lo-’
1.56 X 1.95 X 3.13 X 3.91 X 6.26 X
0 175
= 1X
...
Variation of Potential of Hg/Hg+2 Electrode as Function of Thiosulfate Concentration of Values of F i ( X )
Total Na2SzOa Mole/L.
1 . 1- 7 -
Total mercury concentration Corrected ( SnOa -2) Mole/L. - E Volt AFuming j = 2 os. S.C.E.
lo-’ lo-’ lo-’
lo-’
lo-’
0.282 0.298 0.311 0.311 0.333 0.342 0 358
3.31 X 7.22 X 10-2 1.11 x 10-1 1.50 X 10-1 1.89 X 10-l 3.07 x 10-l 3.85 x 10-1 6.20 X 10-l
ing activity coefficients from Davies’ equation yielded a value of log K i = 30.3 in much better agreement with the polarographically determined value. On the basis of the results obtained here and on the re-evaluation of Toropova’s data, i t appears that the species [Hg(Sz03),]--2 predominates below about 10-3.14 free thiosulfate concentrations for solutions containing 10-31M total Hg(I1). I n solutions containing up t o 2 x 10-3Af Hg(TI), the species [Hg(S203)3]-4grows in rapidly above about lO-3Af free thiosulfate and predominates u p to about 0.6N. No evidence was found for [Hg(S203)4]” reported by Toropova. His data indicating the DISCUSSION species containing four thiosulfates/mercury are not subject to In addition to the species recalculation, because, while he re[Hg(S203)2]-*,the species [Hg(S~03)31-~ ported “activities” of sodium thiosulwas found necessary for a complete fate, he did not report either activity interpretation of the polarographic coefficients or concentrations. Furdata. The value of log K” was esthermore, i t appears his case was based timated to be 30.8 from data a t conon only three points, because he restant unit ionic strength at 25” C. ported data for only three. Thus there Toropova reported on the basis of is little evidence to support the case of electromotive force measurements the an ion with a charge of -6. value log K i = 32.8, corresponding to a discrepancy of a factor of 100. I n ACKNOWLEDGMENT Toropova’s assignment of activity coThe authors are indebted to the Washefficients, he assumed that [Hg(S203)3]-4 ington State University Committee had the Same activity coefficient as a on Research for financial support of this doubly charged ion. Recalculation of project. his data at varying ionic strength, us-
F30(X)
x 10-a0
0.124 0.240 0.357 0.473 0.586 0 945 1.18 1.88
2.8 2.1 1.8
1.8 1.o
1.4 1.5 1 9
LITERATURE CITED
(1) Bale, W. D., Davies, C. W., Monk, C. B., Trans. Faraday Soc. 52, 816 (1956). (2) Davies, E. W., J . Chem. SOC.1938, 2093. (3) DeFord, D. D., Hume, D. N., J . Am. Chem. SOC.73, 5321 (1951). (4) Kolthoff, I. M., Miller, C. S., Ibid., 63, 1405 (1941). (5) Kolthoff, I. &I.,Sandell, E. B., “Textbook of Quantitative Inorganic Analysis,” 3rd ed., p. 593, MaciLlillan, New York, 1952. (6) Latimer, W. M., “Oxidation Potentials,” 2nd ed., pp. 177-9, PrenticeHall, Yew York, 1952. (7) Leden, I., 2. physik Chem. 188A, 160 ( 1 941). \ - - - - / -
(8) Nyman, C. J., Aiberts, G. S., ANAL.
CHEM.32, 207 (1960). (9) . , Nvman. C.. J.. Parry, _ ,E. P., Ibid.,. 30, . 1255 (1958,. ‘ (10) Nyman, C. J., Roe, D. K., Plane, R. A., J . Am. Chem. SOC.83,323 (1961). (11) Roe, D. K., Xyman, C. J., C h a i s t Analyst 49, 27 (1960). (12) Toropova, V. F., J . Gen. Chem., U.S.S.R. (English transl.), 24, 429 (1954). (13) Toropova, 1’.F., Z h w . Neorg. Khim. 2 , 515 (1957).
RECEIVEDfor review May 12, 1961. Accepted July 17, 1961. Division of Analytical Chemistry, 139th Meeting, ACS, St. Louis, Mo., March 1961. Based on the M. S. thesis of Teresa Salaear (Manrique),Washington State University, 1958. VOL. 33, NO. 1 1 , OCTOBER 1961
1469
