4 are shown in Figure 15. For the calculation it is assumed that a substance of molecular area 50 X cm.? undergoes a 2-electron reduction. A diffusion coefficient of 5 x cm.2 sec.-l and an electrode area of 3 x lo-' cmS2are taken. It is further assunied that a monolayer adsorption equilibrium, obeying a Langmuir isotherm, with half coverage a t a soiution concentration of 1.9 x l0-dXj is valid. Applied current densities are such as to bring the total transition times into a convenient range below 1 second. I t is evident that, in principle, this method is capable of determining the surface excess in amounts corresponding to fractional monolayers. Experiments are now under way to test the validity of this approach. It is hoped that this method may serve not only as a method of determining adsorption isotherms, aid of proving the existence of multilayers, but also as a method of calibration for the double layer capacity rwthod.
LITERATURE CITED
(1) Bockris, J. O'M., Huq, A . K. M. S., Proc. Roy. SOC.(London) A237, 277 (1956). (2) Bockris, J. O'hI., Oldfield, L. F., Trans. Faraday SOC.55,249 (1955). (3) Brodd, It. J., Hackerman, N., J . Electrochem. SOC.104, 704 (1957). (4) Chno, ?If. S., Ph.D. thesis, University of Illinois. 1961. (5) DelahaG, P., Trachtenberg, I., J. Am. Chem. SOC.79, 2355 (1957); 80, 2094 (1958). (6) Eda, K., J . Chem. SOC.Japan, Pure Chem. Sect. 80, 343, 461, 708 (1959); 81,689,875 (1960). (7) Enke, C. G., Ph.D. thesis, University of Illinois, 1959. (8) Frumkin, A. N., Nova Acta Leopoldina 19,a (1957). (9) Frumkin, -4.K.,Gorodetskaya, A . Chugunov, P., Acta Physicochim. U.R.S.S. 1. 12 11934'1. (10) Graham;, D'. C., 'J. d i n . Chem. SOC. 68,301 (1946). (11) Hansen, R. S., Minturn, R. A., Hickson, D. A., J . Phys. Chern. 60, 1185 1956). (12) Laitinen, H. A,, Enke, C. G., J . Electrochem. SOC.107, 773 (1960). (13) Laitinen, H. A., Morinaga, K., ARL Technical Kote 60-129, U. S. Air
Force, Wright-Patterson .4ir Forre Base, Ohio. (14) Laitinen, H. A., Mosier, B., J A m Chem. SOC.80, 2363 (1958). (15) Laitinen, H. A,, Roe, D. K., Coll. Czechosloa. Chem. Cornmuns. 25. 3065 (1960). (16) Laitinen, H. -4., Scarr, R. F., WADD Technical Note 60-104, U. S. Air Force, Kright-Patterson Ai1 Force Base, Ohio, July 1960. 171 Lorenz, W.,2. Elektrochem. 59, 730 (1955). 18) Lorenz, W.,blockel,, F.., Ibid.,, 60,. ' 507,939 (i95sj. (19) Los, J. M.,Tompkins, C. K., Can. J . Chem. 37, 315 (1959). (20) Loveland, J. W.,Elving, P. J., J . Phys. Chem. 56, 935, 941, 945 (1952). (21) Melik-Gaikazyan, V. I., J . Phys. Chem. (U.S. S . R.) 26,1184 (1952). (22) Parsons, R., Trans. Faraday SOC. 55,999 (1959'1. (23) Reinmuth, W.H., ANAL. CHEM.33. 324! (1961). (24) Scarr, R. F., Ph.D. thesis, University of 1[Ilinois, 1960. \ - - - - ,
RECEIVED for review May 1, 1961 Accepted June 23, 1961. Division of Analytical Chemistry, Fisher Bward Symposium Honoring H A. Laitinen, 139th Meeting, .ICs, St Louis, No., March 1961
Thermodynamic Constants of Complex Ion Formation between Mercury(l1) and Three Alkylamines D. K. ROE,' D. B. MASSON,2and C. J. NYMAN Deparfment of Chemisfry, Washington State University, Pullman, Wash. Formation constants of the ions Hg(en)22+, Hg(pn)Z2+, and Hg(dien)22+ have been measured polarographically as a function of temperature. The enthalpy and entropy of formation of these ions are calculated from the temperature coefficient of the free energy data, and comparisons are made with the Zn(ll) and Cd(ll) analogs.
C
REACTIONS involving the first transition metal series have been the center of many studies, con"ATE
current with interest in the corresponding entropy changes of such reactions and in testing the predictions of the crystal field theory. Values of the thermodynamic constants, AF, AH, and AS, of the formation of alkylamine complexes of cadmium(I1) and zinc(I1) are available (3-6, 7, 16), but only equilibrium constants (2, 8, 11, IS, 16) have been found in the literature for the corresponding reactions involvPresent address, Shell Development Co., Emeryville, Calif. Present address, Department of Metallurgy, Washington State University, Pullman, Wash. 1
1464
ANALYTICAL CHEMISTRY
ing the third member oi periodic Group IIb, mercury. Data are reported here which, when combined with previous polarographic results a t 25" C. ( 8 ) , permit the calculation of the enthalpy and entropy changes accompanying the formation of the bis(alky1amine) complexes of mercury(I1) and ethylenediamine, 1,2propanediamine, and diethylenetriamine; the notations en, pn, and dien, respectively, mill be used for these alkylamines. The present measurements were made with solutions at 10" and 40" C., again using the polarographic method. EXPERIMENTAL
Anodic polarograms of the dissolution of mercury in the presence of aqueous alkylamine solutions were measured point by point. -4Sargent Nodel XXI Polarograph recorded the current a t a set applied voltage, and the potential of the dropping mercury electrode was measured relative to a saturated calomel reference electrode. Corrections were subsequently made for the cell iR drop. The polarographic cell contained a supporting electrolyte of 0.1V KS03 and was thermostated to within =l=0.05" C. Purified nitrogen ~ m s bubbled
through the cell to remove dissolved oxygen. Individual solutions of the respective alkylamines were prepared from standardized stock solutions, which were made up from distilled chemicals. TREATMENT OF EXPERIMENTAL DATA
In the presence of increasing concentrations of alkylamines, the anodic current-voltage curve of mercury is shifted in the negative direction. The relation between the current and the voltage is obtained from the Xernst equation, assuming that the electrode reaction is ideal, or nearly so, at low current densities, In the present case, successive coordination ions are formed, so that the potential a t any given current is a rather complex function of the chelate concentration (6). The general form of the equation is
where FJX)
=
1
+ K? [ Y ]+ K ; [Y12+ K," [ Y ] 3+ . . . .
(2)
The roncentration of the complexing
agent is denoted by [Y].The current density is sufficiently low so that it can be assumed that [ Y ] at the electrode surface is nearly equal to the bulk value. (E&+), is the potential at a specific current, here chosen as 1 pa., when the complexing agent is present in solution. The corresponding potential in the presence of the simplr supporting electrolyte is (E&gi+)8,and must be experimentally or theoretically determined. The K's in Equation 2 are the formation constants of the complex ions Hg( Y)*+, Hg( Y):', etc. The constant ( E k g z - ) s cannot be measured directly because mercurous ions are primarily produced in the presence of simple electrolytes, such as KNOa. However, the equilibrium constant for the reaction Hg:'+ Hg2+ Hg(l) has been measured from 0" to 40" C. by Schwarzenbach and Anderegg ( 1 4 ) . From these data and the measured temperature coefficient of the anodic polarogram of mercury/mercury(1) in 0.1M KNOs, the previously reported (8) value of ( E H ~ ~ 0.488 +)~, volt a t 25" C. was corrected to 10" and 40" C. The potential of the ouidation of mercury to mercury(I1) ions a t a current of 1 pa. was taken to be 0.493 volt a t 10' C. and 0.483 volt at 40" C. An accuracy of +1 mv. can be expected in these quantities; the uncertainty is due to the difference in the diffusion coefficients of the mercuric and mercurous ions. The difference between the calculated ( E h g , ~ + and ) a the measured (E&Z+)? are listed with the free alkylamine concentrations in Table I. The analytical alkylamine concentrations were corrected by using the following hydrolysis constants, listed here as pKh, in the order en, pn, dien: a t 10' C., 4.14, 4.09,--; at 40" C., 4.00, 3.94, 4.15. These constants were taken from literature values of acid dissociation constants or proton association constants, interpolating or extrapolating to 10' and 40" C. when necessary. Correction of the analytical alkylamine concentrations for only the first hydrolysis reaction is significant. The quantity F J X ) was calculated according to Equation 1. If the assumptions are valid that the activity coefficients of the simple and complex ions are equal and that the activity coefficient of the uncharged free ligand is unity, than the formation constants calculated from F,(X) are thumodynamic constants (9). The extraction of the formation constants from the calculated F , ( X ) ekpression can be accomplished by the graphical method described by DeFord and Hume ( 6 ) , or by direct solution using least squares. Because of the tedium involved in least squares analysis of polynominals having a n order of
+
Table 1. Experimental Values of Difference and Formation Function F,(X) as Function of Concentration of Ethylenediamine, 1,2Propanediamine, and Diethylenetriamine in 0.1M KN03
-
-
i2s-c)
t24 03' C2 i
(IO'CI
Free Aminea
(Mole/liter)
-
(EH,z+ (volt)
Fo( X )
L T x 10'
Figure 1 . Variation of log Ki with the reciprocal of the absolute temperature for Hg(en)%'and Hg(pn):+
three or greater, It is preferable to program the data for a digital computer. This was done with the data in Table I as well as for the data at 25' C. reported previously. Second-, third-, fourth-, and fifth-order solutions were tried, and in every case the best fit of the ruperimental points up to a concentration of about 0.831 in the alkylamine was shown by a thirdorder polynominal. The predominate species in the investigated concentration range are the bis and tris ions; the formation constant, Ky, of Hg(en)2+ is many powers of ten smaller than K ; and K i and, therefore, cannot be calculated with any reasonable precision from measurements taken at these concentrations of alkylamines. The results of the computer solutions are given in Table 11, with the root mean square deviations. The significant advantage in using a digital computer is the avoidance of ambiguity in the graphical extrapolation of successive functions, F , , ( X ) , to zero ligand concentrations. Undue emphasis is placcd on the point in the low concentration range in the extrapolation procedure, while a11 the points are weighed equally when fitted by the least squsrrs method. If a particular point is seen to be greatly in error, it can b t eliminated in a subsequent solution. From a graph, the precision of the result is difficult to assess, but the rms error can be easily calculated by a computer. Using the classical method of plotting log K" os. the reciprocal of the
Ethylenediamine Temperature, 10" c. 4.79 X lozo 0,0192 0.581 6.03 X lo2' 0.0590 0.612 1.62 X lo2' 0.0991 0.624 0.647 1.06 X loz3 0.200 4.68 X IOz3 0,402 0.665 0.680 1.59 X loz4 0,705 Temperature, 40" c.
n niw
0
0.576 o 609 0.621 0 667 0.689
0587
0 0988 0 502 1 01
3.31 3 so 9 34 2 82 1 41
X
10'*
x 1019
X IOi9 X lozL X loz2
1,2-Propanediamine Temperature, loo 0 0 0 0 0 0
c.
0 0 0 0
0201 0619 104 210 422 741
641 657 o 678 0 693
Temperatwe, 40" C. 0 0198 0 0 0 0
600 629
0615 104 427 740
0 0 0 0 0
588 618 631 670 687
2 24 X 2 40 X G 46 X 2 40 X 1 35 x 4 57 X
lo2' loz2 10'' loz3 1024
loz4
8 12 X 10lh
7 1 9 1
41 95 22 23
X X lo2" X 10" X 10''
Diethylenetriamine Temperature, 40" C .
0 0 0 0 0
0578 0962 196 493 990
0 0 0 0
o
662 675 695 723 744
1 95 X los1 5 01 X lo2' 2 24 X lo2* 1 78 X 8 31 x 1 0 2 3
a Corrected for hydrolysis using constants listed in text; pH range 11 to 12, determined only by total amine present.
Table 11. Formation Constants of Chelate Ions of Mercury(l1) and Ethylenediamine, 1,2-Propanediamine, and Diethylenetriamine a t 10", 25", and 40" C.
Wen);' Hg(en; Hg(pn); + Hg(pn),"+ Hg(dien); Hg( dien); + +
+
I O 0 C.
25' C.
40" c.
2 . 3 i 0 . 2 x 1024 1.3 5 0.3 x 1024 5 . 6 i 0 . 2 X loz4 3 . 7 zk 0 . 5 x 1024 ... ...
1 . 5 0 i 0.04 x 1023 1.24 f 0.05 x 1023 3 . 2 zk 0 . 1 X loz3 2.0 0.1 x 1093 1.05 f 0.04 X 10s 2 . 9 i 0 8 X lop4
8 . 7 i 0 . 2 x 1021 5 . 5 f 0 . 2 x 1021 1 . 7 f 0 . 1 X loz2 7 zk 1 x 1021 5.8 5 0 . 2 X loa3 2 . 7 i 0 . 2 x 1023
*
VOL 33,
NO. 1 1 , OCTOBER 1961
7465
3-
I r , -
Et5)rrnec
0
0.2
0.4 Alkylamine, m i l
-
0
- Computer solutions absolute temperature, the enthalpies of the formation of the ions Hg(en)i+, Hg(pn)i+, and Hg(dien)i+ were calculated from the slope of the best straight line (Figure l), again using least squares, but weighing the points according to their precision. Although A H o can be obtained with fair accuracy by this method, the subsequent calculation of the entropy of chelation is subject to relatively large uncertainties because AF" and AH" are of nearly equal values. Only the formation constants measured for the bis(alky1amine) complexes were considered to be precise enough to warrant a calculation of AHo and AS". The results are given in Table 111. The limits of error in AHo and AS" were calculated from the rms deviation in AF". The slight curvature of the plots of log K ; us. 1/T introduces additional uncertainty in the precision so that the actual limits of error may be greater than those listed. The values of AH" and hso given for Hg(dien)i+ are based on measurements a t two temperatures and are considered t o be very approximate. DISCUSSION
The computer solutions give a good fit of the data, as is shown in Figures 2 and 3. The lines represent the calculated variation of F l ( X ) with con-
Table 111.
Hg( dien); Hg(pn):
f
Wen);+
Cd(en):+ Zn( en):
f
Hg(NHs):+ Cd("3): + Zn(NH3):+
1466
points
centration of the indicated alkylamine, Since K i is very small compared to K i and K i , the intercept is essentially zero. It is conceivable that in addition to, or instead of, the ion Hg(en)i+, species such as Hg[(en)a(OH)]+ or Hg[(en) (en-H)]+ are formed, where (en-H) represents an ethylenediamine molecule which has lost a proton, and, thus, the constants for the tris(alky1amine) complexes should be used with caution. With the present information, the relative concentrations of these or other ions cannot be estimated; further data as a function of pH would permit a more detailed interpretation to be made. Large positive entropy changes accompanying the formation of highly stable chelate complexes are conspicuously absent in the results presented for Hg(en)i+ and Hg(pn)i+. The indications are that the entropy changes are small and apparently negative. The high stability of these compleses is reflected in the large negative change in AH", according to these results. Generally, this observation is interpreted to mean that the high stability of these two bis(alky1amine) complexes is a result of a high bond strength, I n considering the chelate effect, it is instructive to compare the present results with the thermodynamic con-
Thermodynamic Data at 25" C. on Formation of Complex Ions of Hg(ll), Cd(ll), and Zn(ll)
-AFo Kcal./Mole 34.15 j = 0 . 0 3 31.91 h 0 . 0 2 31.52 =t 0 . 0 1 14.50 15.67 26.52 10.16 13.35
ANALYTICAL CHEMISTRY
-AHo Kcal./Mole 36 f 1 3 3 . 8 zk 0 . 8 3 2 . 9 =t 0 . 6 13.5 12.5 31.6 12.7 14.1
A S " E.U. - 7 h 4 -6 h 2 -5 + 2 3.4 10.7 -17.0 - 8.5 - 2.7
-I
Figure 3. Formation function, FI(X), as a function of ethylenediamine concentration
0.6
Figure 2. Formation function, Fl(X), as a function of 1,2-propanediamine and diethylenetriamine concentrations 0 Experimental
j.ni ii
Reference This work This -work This work (15) (15) (17) (15) (15)
Computer solutions Experimental points
stants of the formation of the ammonia complexes of mercury(I1). These data for mercury(II), as well as for zinc(I1) and cadmium(I1) are listed in Table 111. Also included is the same type of information on the bis(ethy1enediamine) complexes of zinc(I1) and cadmium(I1). The enthalpy values selected from the literature are from calorimetric measurements [Hg(NH3):+] and log K z us. 1/T plots [Zn and Cd]. General agreement exists between these data and those obtained by other workers; variations can be found however, especially in cases where different ionic strengths were employed. I n Table 111, it is apparent that the enthalpy changes upon the formation of the tetraamine and bis(ethy1enediamine) complexes of each metal ion are nearly the same. That is, the increased stability of the bis(ethy1enediamine) complex relative to the tetraamine complex of Zn, Cd, and Hg is an entropy effect. This can best be seen by the data given in Table IT' for the reaction M ( S H 3 ) i + 2 en $ M(en)i+ 4 S H I . The information in Table IV, except for mercury(II), is that given by Rossotti (f2). rllthough most of the enthalpy data are not from calorimetric measurements, which are available (4, 5 ) , the same general trends are evident in the results of both temperature variations of log K:! and calorimetric measurements. The behavior of the mercury(I1) ion, according to the values listed in Table IV, is very similar, as might be expected, to that of the other two members of periodic Group IIb. The equilibrium between tetraamine complexes and ethylenediamine is shifted to the right, as written, because of a favorable entropy change or chelate effect. The enthalpy changes are small, and perhaps negligible. I n contrast, the equivalent reactions involving nickel(I1) and copper(I1) show relatively large enthalpy changes as well as entropy changes of equal magnitude to the other three ions. The enthalpy changes can be resolved with ligand field stabil-
+
+
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
-AF
M Si Cu Zn Cd Hg
M(en);*
+ 4 NHI
Kcal./ Kcal./ Mole Mole
E.U.
Reference
8.17 4.19 10.08 5.4 2.32 -1.6 4.34 0.8 1.3 5.0
13.3 15.7 13.3 11.8 12
(10)
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.
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.
(15)
Thiswork
Acta 33,947 (1950).
N-alkyl substitutions alter only slightly the stability of complex ions having a nitrogen-metal ion bond.
(14)Schwarzenbach, G., Anderegg, G.,
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 pH of the solutions was determined using a Beckman Model G pH meter. In all cases, th0 pH was close to 7.0 without the use of buffer solutions, and no polarograms were made a t pH 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 pH from below pH 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
